LEMNAOUAR Zedam

Hamza Boughambouz

Properties and classes of ternary fuzzy relations

Mehenni Abdelkrim

Classes of associative binary operations on ordered structures

Boudaoud Sarra

Fuzzy pseudo-ordered sets

Bakri Nourelhouda

Closures and openings of ternary relations

Abdelhamid Benoui

Particular neutrosophic subsets on a lattice

Yettou Mourad

Sur les (F,G)-derivations

Omar Barkat

Compatibilités des relations ternaires

Soheyb Milles

Sur les ensembles ordonnés flous intuitionnistes

Hassane Bouremel

Clonal sets of a binary relation: Theory and Applications

poster

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Djamel SARRI , Djamel KHOUDOUR , Lemnaouar ZEDAM , BENSEFIA Sofiane, BELOUDH Khiera Nada, LAHRECHE Abir, ,(2025-12-02), Utilisation du SIG et création d’une base de données pour l’inventaire des plantes Médicinales en zone steppique ca de a wilaya de M’sila – Algérie),1er séminaire national sur la valorisation des ressources naturelles dans le milieu agro-steppique : potentialité – stratégie d’amélioration et sauvegarde,Djelfa

Based on the concept of Atanassov’s intuitionistic fuzzy set on a universe X, we introduce the concepts of intuitionistic fuzzy ideals and intuitionistic fuzzy filters on an intuitionistic fuzzy lattice. More specifically, we provide characterizations of these concepts in terms of the intuitionistic fuzzy lattice meet and join operations, in terms of some associated fuzzy sets, as well as, in terms of their crisp level sets. Furthermore, we introduce the concepts of prime intuitionistic fuzzy ideals (resp. filters) as interesting kinds, and investigate their various properties and characterizations.

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Lemnaouar ZEDAM , Abdelhamid Bennoui, Soheyb Milles, , (2025-01-20), Ideals and filters on intuitionistic fuzzy lattices, International Journal of Neutrosophic Science, Vol:25, Issue:4, pages:80-100, Americaspg

Due to the lack of transitivity of the pseudo-order relation of a proper trellis, its meet and join operations are not increasing. In this paper, we identify weaker forms of increasingness of binary operations that are satisfied by the meet and/or join operation of a trellis or lattice. Some of these forms coincide with the classical notion of increasingness when the trellis is a lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.

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Lemnaouar ZEDAM , , (2024-12-30), Weaker forms of increasingness of binary operations and their role in the characterization of meet and join operations, Fuzzy Sets and Systems, Vol:497, Issue:, pages:1-18, Elsevier

In this conference, we present a systematic approach to the study of the composition of ternary relations from the point of view of the degrees of freedom available when linking a $3$-tuple to two given $3$-tuples. We propose a way of enumerating all possible $4$-point compositions (one degree of freedom) and $5$-point compositions (two degrees of freedom) of ternary relations, and establish a correspondence between them. Furthermore, we identify the associative compositions and explore interesting mixed-associativity cases. Finally, we use the tools of projection and cylindrical extension to relate the $4$-point and $5$-point compositions of ternary relations to the $3$-point compositions of binary relations

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Lemnaouar ZEDAM , ,(2024-09-17), Compositions of fuzzy ternary relations,The 4th International Conference On Applied Algebra, ICAA'2024,Barika University Center, Algeria

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters.

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Lemnaouar ZEDAM , Ravi P. Agarwal, Soheyb Milles, Brahim Ziane, Abdelaziz Mennouni, , (2024-04-25), Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations, Axioms, Vol:13, Issue:5, pages:1-20, MDPI

Recently, we have introduced and studied all possible four-point compositions (one degree of freedom) and five-point compositions (two degrees of freedom) of ternary relations in analogy with the usual composition of binary relations. In this paper, we introduce and study new types of compositions of ternary relations inspired by the compositions of binary relations introduced by Bandler and Kohout (BK-compositions, for short). Moreover, we pay particular attention to the link between BK-compositions and the traces of binary relations and use it as source of inspiration to introduce traces of ternary relations. Moreover, we show that these new notions of BK-compositions and traces are useful tools to solve some relational equations in an unknown ternary relation. Keywords: ternary relation; Bandler–Kohout compositions; traces MSC: 03E20; 08A02; 03E72

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Lemnaouar ZEDAM , , (2024-03-23), Traces of Ternary Relations Based on Bandler–Kohout Compositions, Mathematics, Vol:12, Issue:7, pages:1-17, MDPI

In this paper, we present a systematic approach to the study of the composition of ternary relations from the point of view of the degrees of freedom available when linking a 3-tuple to two given 3-tuples. We propose a way of enumerating all possible 4-point compositions (one degree of freedom) and 5-point compositions (two degrees of freedom) of ternary relations, and establish a correspondence between them. Furthermore, we identify the associative compositions and explore interesting mixed-associativity cases. Finally, we use the tools of projection and cylindrical extension to relate the 4-point and 5-point compositions of ternary relations to the 3-point compositions of binary relations.

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Lemnaouar ZEDAM , , (2024-02-20), A holistic approach to the composition of ternary relations, Computational and Applied Mathematics, Vol:43, Issue:2, pages:1-18, Springer

In this paper, we expound weaker forms of increasingness of binary operations on a lattice by reducing the number of variables involved in the classical formulation of the increasingness property as seen from the viewpoint of dominance between binary operations. We investigate the relationships among these weaker forms. Furthermore, we demonstrate the role of these weaker forms in characterizing the meet and join operations of a lattice and a chain in particular. Finally, we provide ample generic examples.

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Lemnaouar ZEDAM , Yuntian Wang, Bao Qing Hu, Bernard De Baets, , (2024-01-12), A dissection of the monotonicity property of binary operations from a dominance point of view, International Journal of Approximate Reasoning, Vol:175, Issue:12, pages:109304, Elsevier

Social and economic factors, such as education, employment, social support, income, and community safety, can directly affect how well and long we live. Under the presence of the above factors, we easily look at health decisions, afford medical care and housing, manage stress, and so on. In this analysis, we derive the Choquet-integral aggregation operators based on Hamacher t-norm and t-conorm for complex Atanassov intuitionistic fuzzy (CAIF) such as CAIF Choquet-integral Hamacher averaging (CAIFCIHA), CAIF Choquet-integral Hamacher ordered averaging (CAIFCIHOA), CAIF Choquet-integral Hamacher geometric (CAIFCIHG), CAIF Choquet-integral Hamacher ordered geometric (CAIFCIHOG) operators and exposed their properties. Additionally, we discover the Technique for Order Preference by Similarity to the Ideal Solution “TOPSIS” technique under the consideration of the above-derived theory. Moreover, it is very famous and interesting to note that various unpredicted factors such as road, diesel prices, weather, and traffic conditions affect the cost of transportation. Therefore, decision-makers deal with vague and unreliable information to estimate the cost of transportation. To evaluate the above problem, we select a transportation problem with CAIF parameters, and for its evaluation, a simple and well-known computational technique is derived and illustrated. Finally, we compared our derived results with some prevailing results to show the worth and reliability of the exposed approaches.

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Lemnaouar ZEDAM , Abdulgawad A. Q. Al-Qubati, Hadba Flah Al-Qahtani, Kifayat Ullah, , (2024-01-01), Choquet-Integral Aggregation Operators Based on Hamacher t-norm and t-conorm for Complex Intuitionistic Fuzzy TOPSIS Technique to Deal with Socio-Economic Problems, IEEE Access, Vol:12, Issue:1, pages:3098 - 3113, IEEE

In this paper, we introduce the notion of integration with respect to a given derivation on a lattice. More precisely, we give the definitions of integrable elements of a lattice and their integral sets. We investigate several characterizations and properties of integrations on a lattice. Also, we give a lattice structure to the family of integral sets with respect to a given integration. Further, we provide a representation theorem for the lattice of fixed points of an isotone derivation based on the family of integral sets. As an application of this notion of integration, we use the integrable elements of a Boolean lattice to determine the necessary and sufficient conditions under which a linear differential equation on this Boolean lattice has a solution.

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Lemnaouar ZEDAM , , (2023-12-01), Integrations on lattices, Miskolc Mathematical Notes, Vol:24, Issue:1, pages:515-528, Miskolc University Press

The key property of the partial order relation of a poset or lattice is its transitivity. Lack of transitivity can manifest itself in two flavors: the presence of cycles (A better than B, B better than C, and C better than A) or simply incomparability (A better than B, B better than C, but A and C being incomparable). Corresponding mathematical structures are pseudo-ordered sets (psosets, for short) and, in particular, trellises~\cite{Fried1970,Skala1971}. Psosets generalize posets by eliminating the transitivity property, while (proper) trellises do the same compared to lattices, while preserving the existence of meets and joins of 2-element subsets. The impact of abandoning transitivity causes the meet and join operations of the related proper trellises no longer to be associative (hence, the alternative name `weakly associative lattices' for trellises~\cite{Chajda1977,Fried1975}), and of interest to this contribution, no longer to be increasing. In this note, we aim to investigate weaker forms of monotonicity of binary operations on a trellis and/or a lattice. We restrict our attention to those satisfied by the meet and join operations of a trellis or lattice. Furthermore, we demonstrate the role of these weaker forms in the characterization of the meet and join operations of a trellis, lattice or chain as specific idempotent operations.

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Lemnaouar ZEDAM , ,(2023-09-04), Monotonicity of binary operations: an unexplored territory,13th Conference of the European Society for Fuzzy Logic and Technology EUSFLAT 2023,Palma (Spain) from 4th to 8th September 2023.

Recently~\cite{ZedamBaets2022}, we have introduced and given some basic examples of t-norms on a more general mathematical structure known under various names, such as trellises~\cite{Skala1971}, tournament lattices~\cite{Fried1970} or weakly associative lattices~\cite{Chajda1977,Fried1975}. A trellis is more general than a lattice since the partial order relation is replaced by a more general reflexive and antisymmetric relation, while preserving the existence of meets and joins of 2-element subsets. We have provided a generic construction method that allows to extend a t-norm on an interior range of a given meet-semi-trellis to the entire meet-semi-trellis. In this contribution, we discuss more alternative construction methods to obtain t-norms on bounded trellises. We first discuss a construction method based on retractions. Inspired by the fact that ordinal sums are the most important constructions studied in the theory of t-norms on the unit interval~\cite{Klement2000} and on bounded lattices~\cite{Cayli2019,DvorakHolcapek2020,Ouyang2021,Ouyang2022}, we pay special attention to this construction method in the setting of trellises.

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Lemnaouar ZEDAM , ,(2023-09-04), Construction methods for triangular norms on bounded trellises,13th Conference of the European Society for Fuzzy Logic and Technology EUSFLAT 2023,Palma (Spain) from 4th to 8th September 2023.

In this paper, we introduce three types of monotonicity of an L-fuzzy multifunction on a given L-fuzzy complete lattice and investigate their various properties. Furthermore, we show that any L-fuzzy multifunction with respect to these types of monotonicity has the fixed point property. Specific attention is paid to show for one type of these monotonicities that the set of fixed points of an L-fuzzy monotone multifunction is an L-fuzzy complete lattice.

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Lemnaouar ZEDAM , abdelghani.derardja@univ-msila.dz, Sohyeb Milles, , (2023-07-27), Fixed Point Theorems for L-Fuzzy Monotone Multifunctions, Thai Journal of Mathematics, Vol:21, Issue:2, pages:265–276, The Mathematical Association of Thailand

In this paper, we introduce the notion of a t-norm on bounded pseudo-ordered sets and in particular on bounded trellises (also known as weakly associative lattices), and provide some basic examples. The impact of abandoning transitivity is considerable: on a proper bounded trellis, the meet operation is not a t-norm, and there might actually exist no or even multiple maximal t-norms. We provide a first generic construction method that allows to extend a t-norm on an interior range of a given ∧-semi-trellis to the entire ∧-semi-trellis. Also, we discuss at length an instantiation of this method based on a particular interior range, namely a finite sub-trellis of the set of right-transitive elements of a given trellis. We pay specific attention to bounded pseudo-chains and modular trellises.

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Lemnaouar ZEDAM , Bernard De Baets, , (2023-06-30), Triangular norms on bounded trellises, Fuzzy Sets and Systems, Vol:462, Issue:, pages:108468, Elsevier

Brain carcinoma is one of the massive dangerous diseases in the human body, and certain intellectuals have been affected by them. Additionally, by using the complex q-rung orthopair fuzzy set, which is the massive important, and dominant technique to manage indeterminate and ambiguous information in genuine life troubles. This study aims to employ the principle of variation coefficient similarity measures and generalized variation coefficient similarity measures under the complex q-rung orthopair fuzzy sets and illustrated their properties. Certain special cases of the elaborated measures are investigated to expand the superiority of the investigated works. Moreover, by using the presented generalized variation coefficient similarity measures under the complex q-rung orthopair fuzzy information, a medical diagnosis is illustrated to determine the most dangerous sorts of brain carcinoma in the human body to determine the supremacy and dominance of the elaborated measures. Lastly, certain examples are illustrated based on proposed measures under a complex q-rung orthopair fuzzy set to find the advantages and sensitive analysis of the initiated measures to illustrate the rationality and dominance of the developed measures.

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Lemnaouar ZEDAM , Zeeshan ALi, Tahir Mahmood, Hanen Karamti, Kifayat Ullah, , (2023-06-27), Investigation of the brain carcinoma based on generalized variation coefficient similarity measures using complex q-rung orthopair fuzzy information, Soft Computing, Vol:27, Issue:19, pages:14187-14187, Springer

Relationships between the elements of a same set or between the elements of different sets can be represented at a very basic level through the use of the mathematical construct called relation. Relations come in many flavours, such as binary or ternary, crisp or fuzzy, et cetera.

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Lemnaouar ZEDAM , ,(2023-06-22), Operations on ternary relations,1st National Conference on Applied Algebra (NCAA’23),Centre universitaire Barika

The concepts of relations and information measures have importance whenever we deal with medical diagnosis problems. The aim of this paper is to investigate the global pandemic COVID-19 scenario using relations and information measures in an interval-valued T-spherical fuzzy (IVTSF) environment. An IVTSF set (IVTSFS) allows describing four aspects of human opinions i.e., membership, abstinence, non-membership, and refusal grade that process information in a significant way and reduce information loss. We propose similarity measures and relations in the IVTSF environment and investigate their properties. Both information measures and relations are applied in a medical diagnosis problem keeping in view the global pandemic COVID-19. How to determine the diagnosis based on symptoms of a patient using similarity measures and relations is discussed. Finally, the advantages of dealing with such problems using the IVTSF framework are demonstrated with examples.

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Lemnaouar ZEDAM , , (2023-05-30), Methods for Detecting Covid-19 Patients Using Interval-Valued T-Spherical Fuzzy Relations and Information Measures, International Journal of Information Technology & Decision Making, Vol:22, Issue:3, pages:1033-1060, World Scientific

In contemporary information fusion theory, the Maclaurin symmetric mean (MSM) operator is a traditional mean type aggregation operator (AO) that is an appropriate-able technique for aggregating numerical quantities. The MSM operator’s ability to record the relationships between the several input arguments is one of its standout features. The spherical fuzzy set (SFS) is also a remarkable technique that covers the maximum information from real-life scenarios with the help of four grades. This manuscript consists of the development of the MSM and weighted MSM for the information obtained by SFS. Consequently, the spherical fuzzy MSM (SFMSM) and spherical fuzzy weighted MSM (SFWMSM) operators are developed, and their basic properties are studied. Finally, the developed SFMSM and SFWMSM operators have been applied to the real-life problem of the multi-attribute decision-making problem. All the results are compared and then clearly tabulated and graphed.

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Lemnaouar ZEDAM , Kifayat Ullah, Hafiz Muhammad Sajjad, Amir Hussain, Azra Parveen, , (2023-02-02), Maclaurin Symmetric Mean Aggregation Operators Based on Spherical Fuzzy Information and Application to Decision-Making, Journal of Computational and Cognitive Engineering, Vol:2, Issue:4, pages:266-277, ON VIEW PUBLISHING PTE. LTD

In this paper, we introduce and study the notions of prime, maximal and principal single-valued neutrosophic ideals (resp. filters) on a lattice. Several properties and characterizations of these types of ideals and filters are given, and relationships between them are discussed.

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Lemnaouar ZEDAM , Abdelhamid Bennoui, Soheyb Milles,, , (2023), Several types of single-valued neutrosophic idealsand filters on a lattice, TWMS J. App. and Eng. Math., Vol:13, Issue:1, pages:175-188, Isık University

In this paper, we introduce and study the notion of aggregation operator with respect to a given function f (f -aggregation operator, for short) on a bounded lattice. This new notion is a natural generalization of the aggregation operators on bounded lattices. More precisely, we show some new properties of binary operations based on a given function on a lattice, and study their composition with respect to a given aggregation operator. Also, we investigate the transformation of f -aggregation operators based on a lattice-automorphism and a strong negation. Moreover, under some conditions on a given function f , we give the smallest (resp. the greatest) f -aggregation operator on a bounded lattice.

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Abdelkrim Mehenni , Lemnaouar ZEDAM , , (2022-01-01), f-aggregation Operators on a Bounded Lattice, Azerbaijan Journal of Mathematics, Vol:12, Issue:1, pages:109-128, Institute of Mathematics and Mechanics NAS of Azerbaijan

Cleaner production (CP) is defined as a preventive approach to managing the environmental effect of business processes and products. CP is also related to the use of less but more efficient energy and materials and the substitution of products harmful to the environment/health with less dangerous ones. The Hamacher Aggregation (HA) operator is an easy technique that permits several comparison declarations to be prepared while yet securing an overall confidence coefficient is sustained. The major benefit of HA operator based on Hamacher t‐norm and Hamacher t‐conorm is that they provide a lot of specific aggregation operators due to their parameters included in the mathematical form of HA operator. Another hand, the conception of complex T-spherical fuzzy (CTSF) strategy is a novel and original technique that exists with a well-known theme and advantages in the circumstance of fuzzy set theory. The key influence of this hypothesis is to evaluate the conception of Hamacher operational laws and their influential results. Moreover, the theory of CTSF Hamacher weighted averaging (CTSFHWA) and CTSF Hamacher weighted geometric (CTSFHWG) operators and described their influential properties with several strong results. Moreover, a strategic decision-making technique is evaluated in the existence of the deliberated operators for CTSF settings. Finally, to check the stability and accurateness of the invented operators, we assessed the comparative analysis and geometrical shape of the presented works with the help of many numerical illustrations.

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Lemnaouar ZEDAM , Nimet Yapici Pehlivan, Zeeshan Ali, Tahir Mahmood, , (2022), Novel Hamacher Aggregation Operators Based on Complex T-Spherical Fuzzy Numbers for Cleaner Production Evaluation in Gold Mines, International Journal of Fuzzy Systems, Vol:24, Issue:1, pages:2333–2353, Spronger

In the present paper, we introduce the notion of (F, G)-derivation on a lattice as a generalization of the notion of (∧, ∨)-derivation. This newly notion is based on two arbitrary binary operations F and G instead of the meet (∧) and the join (∨) operations. Also, we investigate properties of (F, G)-derivation on a lattice in details. Furthermore, we define and study the notion of principal (F, G)- derivations as a particular class of (F, G)-derivations. As applications, we provide two representations of a given lattice in terms of its principal (F, G)-derivations.

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Lemnaouar ZEDAM , Abdelaziz عبد العزيز AMROUNE عمرون , Mourad Yettou, , (2022), (F,G)-Derivations on a Lattice, Kragujevac Journal of Mathematics, Vol:46, Issue:5, pages:773–787, University of Kragujevac, Kragujevac, Serbia

This manuscript is aimed at developing some novel operational laws named scalar neutrality operation and neutrality addition on picture fuzzy numbers (PFNs). The main focus of this work is to involve the neutral behaviour of the experts towards the priorities of entities where it presents equal degrees to independent membership functions. Moreover, based on these operations, some novel aggregation operators are established to aggregate the different priorities of experts. Some useful relations and characteristics are examined thoroughly. Lastly, the multiattribute group decision-making algorithm in accordance with the suggested operation is illustrated and examined a case study in order to choose a suitable mining company for a mining project along with several numerical examples. The advantages, as well as the superiority of the suggested approach, are exhibited by comparing the results with a few existing methods.

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Lemnaouar ZEDAM , Mubashar Javed, Shumaila Javeed, Jihad Ahmad, Kifayat Ullah, , (2022), Approach to Multiattribute Decision-Making Problems Based on Neutrality Aggregation Operators of Picture Fuzzy Information, Journal of Function Spaces (2022),, Vol:2022, Issue:1, pages:Article ID 2762067, Hindawi

In this study, the authors explore the complex q-rung orthopair fuzzy sets, which are preferred to be enhanced of the complex intuitionistic fuzzy sets and the complex Pythagorean fuzzy sets, individually. The intention is regarding the buildup of certain innovative operational laws and their related weighted aggregation operators based on the complex q-rung orthopair fuzzy (CQROF) information. In this regard, they characterize certain original neutral or fair operational laws that involve the model of proportional distribution to accomplish a neutral or fair usage to the truth and falsity functions of CQROFSs. Consequently, with these operations, they acquire CQROF weighted fairly aggregation (CQROFWFA) and CQROF ordered weighted fairly aggregation (CQROFOWFA) operators which can neutrally or fairly provide the truth and falsity degrees. They implement an MADM (multi-attribute decision-making) methodology with multiple decision makers and partial weight knowledge in the structure of CQROFSs.

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Lemnaouar ZEDAM , Zeeshan Ali, Tahir Mahmood,, , (2022), A multi-attribute decision-making procedure based on complex q-rung orthopair fuzzy weighted fairly aggregation information, International Journal of Fuzzy System Applications, Vol:11, Issue:1, pages:1-30, IGI Global

The concept of fuzzy graph (FG) and its generalized forms have been developed to cope with several real-life problems having some sort of imprecision like networking problems, decision making, shortest path problems etc. This paper is based on some developments in generalization of FG theory to deal with situations where imprecision is characterized by four types of membership grades. A novel concept of the domination of T-spherical fuzzy graph (TSFG) is proposed as a common generalization of the domination of FG, intuitionistic fuzzy graph (IFG) and picture fuzzy graph (PFG) based on a recently introduced concept of T-spherical fuzzy set (TSFS). This paper aims to bring into focus the proposal of the graph of T-Spherical fuzzy sets. Moreover, this research analyzes the concepts of domination and double domination theory in T-spherical fuzzy environment. More precisely, the framework of T-spherical fuzzy graphs is introduced, and their related theory is provided with the help of illustrative examples. Further, the domination theory that attached to T-spherical fuzzy graphs is developed. Some cardinality, order, strength and completeness on domination, neighbors in a TSFG bipartite TSFG and double domination set and some results are also studied in the environment of T-spherical fuzzy graphs. As an application, a political campaign is modeled using the proposed work, and explored that how the double domination could deal with political campaign. Finally, a comparison amongst the proposed and the existing studies is developed and advantages of the work in the environment of T-spherical fuzzy graph are discussed.

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Lemnaouar ZEDAM , NaeemJan, Tahir Mahmood, Lazim Abdullah, Kifayat Ullah, , (2021-08-04), Analysis of double domination by using the concept of spherical fuzzy information with application, Journal of Ambient Intelligence and Humanized Computing, Vol:14, Issue:1, pages:1147–1162, Springer

In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.

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bakri norelhouda , Lemnaouar ZEDAM , Bernard De Baets, , (2021-07-07), Compositions of ternary relations, Journal of Kybernetika, Vol:57, Issue:3, pages:404–425, Journal of Kybernetika

Recently, we have introduced six types of composition of ternary fuzzy relations. These compositions are close in spirit to the composition of binary fuzzy relations. Based on these types of composition, we have introduced several types of transitivity of a ternary fuzzy relation and investigated their basic properties. In this paper, we prove additional properties and characterizations of these types of transitivity of a ternary fuzzy relation. Also, we provide a representation theorem for ternary fuzzy relations satisfying these types of transitivity. Finally, we focus on the problem of closing a ternary fuzzy relation with respect to the proposed types of transitivity.

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Lemnaouar ZEDAM , , (2021), Transitive closures of ternary fuzzy relations, International Journal of of Computational Intelligence Systems, Vol:14, Issue:1, pages:1784-1795, Atlantis Press

In this paper, we introduce six basic types of composition of ternary relations, four of which are associative. These compositions are based on two types of composition of a ternary relation with a binary relation recently introduced by Zedam et al. We study the properties of these compositions, in particular the link with the usual composition of binary relations through the use of the operations of projection and cylindrical extension.

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Lemnaouar ZEDAM , Norelhouda Bakri, Bernard De Baets, , (2021), Compositions of ternary relations,, Kybernetika, Vol:57, Issue:3, pages:404–425, Institute of Information Theory and Automation of The Czech Academy of Sciences

The theory of complex dual type-2 hesitant fuzzy sets (CDT-2HFSs) is a blend of two different modifications of fuzzy sets (FSs), called complex fuzzy sets (CFSs) and dual type-2 hesitant fuzzy sets (DT-2HFSs). CDT-2HFS is a proficient technique to cope with unpredictable and awkward information in realistic decision problems. CDT-2HFS is composed of the grade of truth and the grade of falsity, and the grade of truth (also for grade of falsity) contains the grade of primary and secondary parts in the form of polar coordinates with the condition that the sum of the maximum of the real part (also for the imaginary part) of the primary grade (also for the secondary grade) cannot exceed the unit interval [0, 1]. The aims of this manuscript are to discover the novel approach of CDT-2HFS and its operational laws. These operational laws are also justified with the help of an example. Additionally, based on a novel CDT-2HFS, we explored the correlation coefficient (CC) and entropy measures (EMs), and their special cases are also discussed. TOPSIS method based on CDT-2HFS is also explored. Then, we applied our explored measures based on CDT-2HFSs in the environment of the TOPSIS method, medical diagnosis, pattern recognition, and clustering algorithm to cope with the awkward and complicated information in realistic decision issues. Finally, some numerical examples are given to examine the proficiency and validity of the explored measures. Comparative analysis, advantages, and graphical interpretation of the explored measures with some other existing measures are also discussed.

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Lemnaouar ZEDAM , Tahir Mahmood, Zeeshan Ali, Harish Garg, Ronnason Chinram, , (2021), Correlation Coefficient and Entropy Measures Based on Complex Dual Type-2 Hesitant Fuzzy Sets and Their Applications,, Journal of Mathematics, Vol:2021, Issue:1, pages:Article ID 2568391., Hindawi

In this paper, we study the problem of closing or opening a ternary relation with respect to various relational properties, with a focus on the many transitivity properties that have been proposed for ternary relations over the past years. In particular, we consider the transitivity properties corresponding to the six relational compositions of ternary relations recently introduced by Bakri et al., making a careful distinction between the four associative ones and the two non-associative ones.

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Lemnaouar ZEDAM , Norelhouda Bakri, Bernard De Baets,, , (2020), Closures and opening of ternary relations, International Journal of General Systems, Vol:49, Issue:7, pages:760–784, Taylor and Francis

In this paper, we study and characterize some properties of a given binary operation on a lattice. More specifically, we show necessary and sufficient conditions under which a binary operation on a lattice coincides with its meet (resp. its join) operation. Importantly, we construct two new posets based on a given binary operation on a lattice and investigate some cases that these two posets have a lattice structure. Moreover, we provide some representations of a given lattice based on these new constructed lattices. Keywords: lattice, binary operation, neutral element, lattice representation Classification: 06B05, 06B15

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Abdelaziz عبد العزيز AMROUNE عمرون , Lemnaouar ZEDAM , Mourad Yettou, , (2019), A binary operation-based representation of a lattice, KYBERNETIKA, Vol:55, Issue:2, pages:252-272, Nakladatelstvi Academia

In a recent paper, De Baets et al. have studied the compatibility of a(n) (strict) order relation with a fuzzy relation, and have characterized the fuzzy tolerance (and, in particular, fuzzy equivalence) relations that a given strict order relation is compatible with. We extend this study by considering the left- and right-compatibility of a(n) (strict) order relation with a fuzzy tolerance relation and vice versa. We characterize the fuzzy tolerance relations that are compatible with a given (strict) order relation. Conversely, we provide a representation of the fuzzy tolerance relations that a given strict order relation is left- or right-compatible with. Specific attention is paid to the case of fuzzy equivalence relations. We conclude by pointing out that the representation theorems in the above-mentioned paper need some minor rectification. Keywords:Left-compatibility; Right-compatibility; Clone relation; Order relation; Fuzzy equivalence relation; Fuzzy tolerance relation

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Lemnaouar ZEDAM , Hassane Bouremel, Bernard De Baets, , (2019), Left and right compatibility of order relations and fuzzy tolerance relations, Fuzzy Sets and Systems, Vol:360, Issue:, pages:65-81, Elsevier

Recently, De Baets et al. have characterized the fuzzy tolerance relations that a given strict order relation is compatible with. In general, the compatibility of a strict order relation with a binary fuzzy relation guarantees also the compatibility of its associated betweenness relation with that binary fuzzy relation. In this paper, we study the compatibility of an arbitrary ternary relation with a binary fuzzy relation. We prove that this compatibility can be expressed in terms of inclusions of the binary fuzzy relation in the traces of the given ternary relation. Keywords: Ternary relation; binary fuzzy relation; traces of a ternary relation; compatibility

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Lemnaouar ZEDAM , Omar Barkat, Bernard De Baets, , (2019), On the compatibility of a ternary relation with a binary fuzzy relation, Int. J. of Uncertainty, Fuzziness & Knowledge-Based Systems, Vol:27, Issue:4, pages:595-612, World Scientific Publishing Company

The ideas of q-rung ortho pair fuzzy set (qROPFS) and interval-valued q-rung ortho pair fuzzy set (IVq-ROPFS) are two major recent developments in the field of fuzzy set theory. A q-ROPFS and IVq-ROPFS improved the limited structures of Pythagorean fuzzy set, intuitionistic fuzzy set as well as fuzzy set by improving the conditions that makes these concepts restricted. The goal of this research is to introduce a new notion of interval-valued q-rung ortho pair fuzzy graph (IVQROPFG) and to study the related graphical terms such as subgraph, complement, degree of vertices and path etc. Each of the graphical concept is demonstrated with an example. Another valuable contribution of this manuscript is the modeling of some traffic networks, telephone networks and social networks using the concepts of IVQROPFGs. First, the famous problem of finding a shortest path in a traffic network is studied using two different approaches. A study of social network describing the strength of co-authorship between different researchers from several countries is also established using the concept of IVq-ROPFGs. Finally, a telephone networking problem is demonstrated showing the calling ratios of incoming and outgoing calls among a group of people. Two engineering decision-making problems are also studied using some aggregation operators and the concepts of IVq-ROPFGs. Through comparative study, the advantages of working in the environment of IVq-ROPFG are specified. Keywords: q-rung ortho pair fuzzy graph, Interval-valued, q-rung ortho pair fuzzy graph, Social network, Communication network, Shortest path problem.

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Lemnaouar ZEDAM , Naeem Jan, Tahir Mahmood, K. Ullah, J. C. Rodriguez Alcantud, Bijan Davvaz, , (2019), Analysis of Social Networks, Communication Networks and Shortest Path Problems in the Environment of Interval-Valued q-Rung Ortho Pair Fuzzy Graphs, International Journal of Fuzzy Systems, Vol:21, Issue:6, pages:1687-1708, Springer

Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated. Show less Keywords: Cubic fuzzy graphs, bipolar fuzzy graphs, cubic bipolar fuzzy graph, strong cubic bipolar fuzzy graphs

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Lemnaouar ZEDAM , Naeem Jan, Kifayat Ullah, Tahir Mahmood, , (2019), Cubic bipolar fuzzy graphs with applications, Journal of Intelligent & Fuzzy Systems, Vol:37, Issue:2, pages:2289-2307, IOS Press

Recently, we have introduced six types of composition of crisp ternary relations. These compositions are close in spirit to the definition of the composition of binary relations. In this note, we extend these notions to the fuzzy setting. Based on these types of composition, we introduce several types of transitivity of a ternary fuzzy relation and investigate their properties. Keywords: Fuzzy ternary relation, relational compositions, Transitivity.

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Lemnaouar ZEDAM , Bernard De Baets, ,(2019), Transitivity properties of ternary fuzzy relations,The 11th Conference of the European Society for Fuzzy Logic and Technology, organized jointly with the IQSA Workshop on Quantum Structures (EUSFLAT2019), September 9-13, 2019,Prague, Czech Republic.

In this paper, the concept of linguistic cubic number (LCN) is introduced which further extends the concept of linguistic intuitionistic fuzzy number (LIFN). More specifically, the notions of internal (external) developed and (P-)R-order for LCN are studied. For a given LCN, some basic operational laws, score and accuracy function are proposed. Also, some generalized aggregation operators based on the operational rules are developed and their related properties are investigated. As application, a multi-attribute decision-making (MADM) method is established based in the environment of LCNs and with the help of defined aggregation operators. Finally, an illustrative example is provided to show the effectiveness of the proposed MADM method. Keywords: Cubic set, linguistic cubic number, (P-) R-order, multi-attribute decision making

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Lemnaouar ZEDAM , Naeem Jan, Tahir Mahmood, Kifayat Ullah, Zeeshan Ali, , (2019), Multiple attribute decision making method under linguistic cubic information, Journal of Intelligent & Fuzzy Systems, Vol:36, Issue:1, pages:253–269, IOS Press

In this paper, we introduced a new concept of single valued neutrosophic graph (SVNG) known as constant single valued neutrosophic graph (CSVNG). Basically, SVNG is a generalization of intuitionistic fuzzy graph (IFG). More specifically, we described and explored somegraph theoretic ideas related to the introduced concepts of CSVNG. An application of CSVNG in a Wi-Fi network system is discussed and a comparison of CSVNG with constant IFG is established showing the worth of the proposed work. Further, several terms like constant function and totally constant function are investigated in the frame-work of CSVNG and their characteristics are studied. Keyword(s): Single valued neutrosophic graph. Constant single valued neutrosophic graph; constant function; totally constant function; Wi-Fi network

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Lemnaouar ZEDAM , Naeem Jan, Tahir Mahmood, Kifayat Ullah, Said Bourmi, Florentin Smarandache, , (2019), Constant single valued neutrosophic graphs with Applications, Neutrosophic Sets and Systems, Vol:24, Issue:1, pages:77-89, University New Mexico

In a recent paper, C¸ even and Ozt¨urk have generalized the notion of derivation on a lattice to f-derivation, where f is a given function of that lattice into itself. Under some conditions, they have characterized the distributive and modular lattices in terms of their isotone f-derivations. In this paper, we investigate the most important properties of isotone f-derivations on a lattice, paying particular attention to the lattice (resp. ideal) structures of isotone f-derivations and the sets of their f-fixed points. As applications, we provide characterizations of distributive lattices and principal ideals of a lattice in terms of principal f-derivations. Keywords: lattice, isotone f-derivation, principal f-derivation, f-fixed points set.

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Lemnaouar ZEDAM , Abdelaziz عبد العزيز AMROUNE عمرون , Yettou Mourad, , (2019), f-Fixed points of isotone f-derivations on a lattice, Discussiones Mathematicae-General Algebra and Applications, Vol:39, Issue:1, pages:69-89, University of Zielona Góra, Poland

In this paper, we generalize the notion of traces of a binary relation to the setting of ternary relations. With a given ternary relation, we associate three binary relations: its left, middle and right trace. As in the binary case, these traces facilitate the study and characterization of properties of a ternary relation. Interestingly, the traces themselves turn out to be the greatest solutions of relational inequalities associated with newly introduced compositions of a ternary relation with a binary relation (and vice versa). KEYWORDS: Binary relation; ternary relation; traces; relational compositions

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Lemnaouar ZEDAM , Omar Barkat, Bernard De Baets, , (2018), Traces of ternary relations, International Journal of General Systems, Vol:47, Issue:4, pages:350-373, Taylor and Francis

In a recent paper, we have introduced the notion of clone relation of a given binary relation. Intuitively, two elements are said to be “clones” if they are related in the same way w.r.t. every other element. In this paper, we generalize this notion from pairs of elements to sets of elements of any cardinality, resulting in the introduction of clonal sets. We investigate the most important properties of clonal sets, paying particular attention to the introduction of the clonal closure operator, to the analysis of the (lattice) structure of the set of clonal sets and to a distance metric expressing how close two elements are to being clones. KEYWORDS: Clone relation; clonal set; clonal closure; clonal lattice; clonal distance metric

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Lemnaouar ZEDAM , Raúl Pérez-Fernández, Hassane Bouremel, Bernard De Baets, , (2018), Clonal sets of a binary relation, International Journal of General Systems, Vol:47, Issue:4, pages:329-349, Taylor and Francis

In this study, we consider the functional equation of modularity in a special class of aggregation operators with an absorbing element. First, we focus on the modularity between commutative binary operators and their duals, and then we examine the modularity for operators from the class of 2-uninorms, which generalize nullnorms by extending their certain conditions. In particular, for these operators, depending on the positions of their neutral elements and possessing the same absorbing element, we obtain positive and negative results, which are analogous to the results in the general case for operators with different absorbing elements. Keywords: 2-UninormAggregation operationDual aggregation operationModularity equationNullnormUninorm

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Lemnaouar ZEDAM , W. Fechner, Ewa Rak, , (2018), The modularity law in some classes of aggregation operators, Fuzzy sets and Systems, Vol:332, Issue:, pages:56–73, Elsevier

In a recent paper, De Baets et al. introduced the clone relation of a strict order relation. Two elements of a poset are said to be a pair of clones (or to be clones) if every other element that is greater (resp. smaller) than one of them is also greater (resp. smaller) than the other one. This clone relation played a key role in the characterization of the L-fuzzy tolerance relations and the L-fuzzy equivalence relations that a strict order relation is compatible with. In this paper, we extend the notion of clone relation to any binary relation. Although the definition of such extension is trivial, the corresponding properties significantly differ from those of the clone relation of a strict order relation. We analyse the most important ones among these properties, paying particular attention to a partition of the clone relation in terms of three different types of pairs of clones. Keywords: Binary relation, Clone relation, Tolerance relation, Equivalence relation, Disjoint union

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Lemnaouar ZEDAM , Hassane Bouremel, Raul Perez Fernandez, Bernard De Baets, , (2017), The clone relation of a binary relation, Information Sciences, Vol:383, Issue:, pages:308-325, Elsevier

In this paper, based on the concept of intuitionistic fuzzy lattice previously introduced by Tripathy and his colleagues, a class of intuitionistic fuzzy complete lattices is proposed with some interesting characterizations given. In particular, we show the fixed point property for this proposed class. Conversely, we show that any intuitionistic fuzzy lattice is complete having its fixed point property. These results establish a criterion for completeness of intuitionistic fuzzy lattices in terms of the fixed points of their intuitionistic fuzzy monotone mappings. Keywords: Atanassov's intuitionistic fuzzy set, Intuitionistic fuzzy relation, Intuitionistic fuzzy lattice, Fixed point property

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Lemnaouar ZEDAM , Soheyb MILLES , Ewa Rak, , (2017), The fixed point property for intuitionistic fuzzy lattices, Fuzzy Information and Engineering, Vol:9, Issue:3, pages:359-380, Taylor and Francis

We show that although there exists no non-trivial (fuzzy) tolerance relation a partial order relation is compatible with (in the sense of Bělohlávek), the situation is quite different when considering its strict part. More specifically, we provide a representation of all fuzzy tolerance (and, in particular, all fuzzy equivalence) relations a strict order relation is compatible with. To that end, we introduce the notion of clone relation associated with a partially ordered set and discuss its basic properties. The mentioned representation is intimately connected with this clone relation. Keywords: Clone relation, Compatibility, Equivalence relation, Fuzzy relation, Order relation, Tolerance relation

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Lemnaouar ZEDAM , Bernard De Baets, Kheniche Azzedine, , (2016), A clone-based representation of the fuzzy tolerance or equivalence relations a strict order relation is compatible with, Fuzzy Sets and Systems, Vol:296, Issue:, pages:35-50, Elsevier

The notion of extensionality, introduced by Höhle and Blanchard, and the notion of compatibility, as coined by Bělohlávek, of a fuzzy relation with respect to a fuzzy equality are trivially equivalent. Here, this compatibility property is dissected into left and right compatibility, mimicking the original twofold definition of extensionality, and studied in detail in the context of arbitrary fuzzy relations. Relying on the notions of left and right traces of a fuzzy relation, it is shown that compatibility can be characterized in terms of inclusions, shedding another light on the matter.

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Lemnaouar ZEDAM , Kheniche Azzedine, Bernard De Baets, , (2016), Compatibility of fuzzy relations, International Journal of Intelligent Systems, Vol:31, Issue:3, pages:240-256, Wiley

In a recent paper, De Baets et al. have characterized the fuzzy tolerance and fuzzy equivalence relations that a given strict order relation is compatible with. In this paper, we generalize this characterization by considering an arbitrary (crisp) relation instead of a strict order relation, while paying attention to the particular cases of a reflexive or irreflexive relation. The reasoning largely draws upon the notion of the clone relation of a (crisp) relation, introduced recently by Bouremel et al., and the partition of this clone relation in terms of three different types of pairs of clones. More specifically, reflexive related clones and irreflexive unrelated clones turn out to play a key role in the characterization of the fuzzy tolerance and fuzzy equivalence relations that a given (crisp) relation is compatible with. Keywords: Crisp relation, Fuzzy relation, Clone relation, Compatibility, Tolerance relation, Equivalence relation

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Lemnaouar ZEDAM , Bernard De Baets, Hassane Bouremel, , (2016), On the compatibility of a crisp relation with a fuzzy equivalence relation, Iranian Journal of Fuzzy Systems, Vol:13, Issue:7, pages:15-31, University of Sistan and Baluchestan

The aim of this article is to develop a representation theory of interval-valued Łukasiewicz–Moisil algebras; the concept of interval fuzzy sets involves the role that the notion of field of sets plays for the representation of Boolean algebras. This theory provides both a semantic interpretation of a Łukasiewicz interval-valued logic and a logical basis for the interval fuzzy sets theory. Keywords: Fuzzy set; lattice; interval-valued Łukasiewicz–Moisil algebra; fuzzy algebra

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Abdelaziz عبد العزيز AMROUNE عمرون , Lemnaouar ZEDAM , Bijan davvaz, , (2016), Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras,, Journal of Intelligent Systems, Vol:25, Issue:2, pages:96-106, De Gruyter

In this paper some interesting relationships known between continuous, sequentially continuous, strongly continuous maps, bounded and weakly bounded linear operators on the crisp normed spaces are generalized to the case of fuzzy normed spaces. Keywords: Fuzzy metric space, fuzzy normed space, continuous map, bounded linear operator

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Lemnaouar ZEDAM , A. Al-Qubati, , (2015), Properties of continuous maps and bounded linear operators in fuzzy normed spaces, Journal of Intelligent and Fuzzy Systems, Vol:29, Issue:1, pages:127-133, IOS Press

In this paper, we show that in an involutive -valuedLukasiewicz-Moisilalgebra monomorphic with an involutive fuzzy algebra the condition of continuity (for each is necessary

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Abdelaziz عبد العزيز AMROUNE عمرون , Lemnaouar ZEDAM , , (2005), 20. Which role plays the condition of continuity in the representation of L-M algebra, Fart, Vol:18, Issue:3, pages:313-320, Ed , PushpaPublishing House