ABDELAZIZ عبد العزيز Amroune عمرون

SAADI Djazia

Picture fuzzy orderings and related structures

DIAFI Mokhtar

On fuzzy rings and their ideals

KAKA Soad

On fuzzy groups and their ideals

Belkaaloul Riha , Tayabi Siham

On Boolean Lattices (Sur les Treillis Booléens)

KOUIDER Khaoula

Construction des notions d'ordre et de treillis

ARAB Cheyma

On Picture Fuzzy Sets

ZIANE Brahim

Ordre flou intuitionniste et structures reliées

BOUDAOUD Sara

Sur Les ensemlbles pseudo ordonnés flous

DOUADI Imane

Filtres et idéaux dans un treillis classiques

Daoula Chaima

Filters and Ideals in a Fuzzy Lattice

YETTOU Mourad

(F,G)-derivations on lattices

Hasbaia, Kaddour

Fuzzy sets: Concepts Results and Uses

MAKHLOUF Djamila , TOUINA Wahiba

Intuitionistic Fuzzy Sets: Theory and Applications

Aissa Bouad

Fuzzy ordered sets and aggregations

Zahra Amroune

Some aspects of triangular norms

Djazia Saadi

Filters and ideals in a fuzzy lattice

BOUAD Aissa

Fuzzy ordered sets and Aggregation

LADJAL Khadidja

Etude de certaines hyperstructures (Study of certain hyperstructure)

ABDELKARIM, Samia

Etude des treillis résiduels

Ali Oumhani

Ordres flous et ordres flous intuitionnistes

Bouguerra, Nassima

Etudes et représentations des certaines algèbres trivalentes

KHARCHI, Somia , Korichi Safia

Etude des relations binaires

Azzdine Kheniche

Compatibility of fuzzy relations

MIHOUBI Cherif

CLASSIFICATION DES CODES LINEAIRES TERTIAIRES OPTIMAUX [n, n/2]

Bouad aissa

Relation de Couverture Floue et Ordre

Ziane Brahim

Relation d'ordre flou et ensemble partiellement Fuzzy ordonné

Oumhani Ali

Fuzzifucation (Fuzzifying) d'un système de fermeture et treillis flou

Saadaoui Khier

Dualité de Priestley pour les D-treillis flous

Kheniche Azzedine

Sur les relations floues

Lemnaouar ZEDAM

Sur les Algèbres de MOISL-LUKASIEWICZ

Since the invention of the concept of fuzzy sets and fuzzy relations [4, 5], this notion has continued to evolve. In this work, we highlight some inconsistencies or inadequacies in the presentation of certain operations that have emerged in this developing notion of picture fuzzy set [1]. Additionally, we o¤er our perspective on how this operations should be properly formulated. Also, in this work, we explore some fundamental properties of the set of truth values called D for picture fuzzy sets. We introduce operations on picture fuzzy sets by applying a suitable point-by-point order to D* [2, 3]. Additionally, we use this order to de…ne and examine various characteristic sets of picture fuzzy sets, including support, kernel, -cut, strong -cut, and the picture fuzzy line of degree \alpha, where \alpha in D*.

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Abdelaziz عبد العزيز AMROUNE عمرون , ,(2024-09-17), On picture fuzzy sets,The 4th International Conference On Applied Algebra-BARIKA 17-18 _2024,Barika, Algeria

In this paper, some basic properties of the set of a picture fuzzy set truth values D∗ are studied. Also, using an adequate order of D∗, some picture fuzzy set operations are introduced by meaning a punctual order (point by point). As well as the order of D∗ is used to show some characteristic sets of a picture fuzzy set, such as support, kernel, α-cut, strong α-cut and picture fuzzy line of degree α of a picture fuzzy set, where α 2 D∗ have been defined, some properties of them have been established, and some decomposition theorems of picture fuzzy sets have been proved. Finally, some of Atanassov’s modal operators are extended to the picture fuzzy case.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2024-07-03), MORE ON PICTURE FUZZY SETS AND THEIR PROPERTIES, Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, Vol:14, Issue:3, pages:1136-1151, Isik University

A new concept of picture fuzzy sets was introduced in 2013, which are direct extensions of Zadeh’s fuzzy sets and Antanssov’s intuitionistic fuzzy sets. In this paper, some basic properties of a picture fuzzy set and the set of picture fuzzy set truth values D* are investigated. Also, some of Atanassov’s modal operators are extended to the picture fuzzy case.

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Djazia Saadi , Abdelaziz عبد العزيز AMROUNE عمرون , ,(2023-09-26), EXTENSION OF SOME OF ATANASSOV’S MODULAR OPERATORS ON PICTURE FUZZY SETS,Second International Conference on Mathematics and Applications,Blida, Algeria

In this paper, we introduce the notion of integration with respect to a given derivation on a lattice. More precisely, we give the defnitions 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 fxed 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 suffcient conditions under which a linear differential equation on this Boolean lattice has a solution.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2023-07-18), Integrations on lattices., Miskolc Mathematical Notes, Vol:24, Issue:1, pages:505-513, UNIV MISKOLC INST MATH

In this work, we present the concept of picture fuzzy relations, which are direct extensions of fuzzy relations and intuitionistic fuzzy relations. Then several fundamental concepts related to picture fuzzy relations are studied, and some characterizations of picture fuzzy ordering are obtained. Furthermore, various picture fuzzy analogs of the results of crisp relations theory are established.

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Djazia Saadi , Abdelaziz عبد العزيز AMROUNE عمرون , ,(2023-06-01), ON PICTURE FUZZY RELATIONS AND THEIR PROPERTIES,The 4th Mathematics National Seminar,Constantine

Picture fuzzy sets are direct extensions of the notions of fuzzy sets and of intuitionistic fuzzy sets. In this work, some basic properties of the set of a picture fuzzy set truth values D* are studied. Also, some picture fuzzy set operations have been introduced. The order of D* is used to show some characteristic sets of a picture fuzzy set, such as support, kernel, a-cut, strong a-cut and picture fuzzy line of degree of a picture fuzzy set, where a in D*, have been defined, some properties of them have been established and some decomposition theorems of picture fuzzy sets have been proved.

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Djazia Saadi , Abdelaziz عبد العزيز AMROUNE عمرون , ,(2022-10-26), ON PICTURE FUZZY SETS,Célébration du 25 ème anniversaire de la Rencontre d.Analyse Mathématiqueet ses Applications (RAMA),M.sila

In this paper, the concept of homoderivation on a lattice as a combination of two concepts of meet-homomorphisms and derivations is introduced. Some characterizations and properties of homoderivations are provided. The relationship between derivations and homoderivations on a lattice is established. Also, an interesting class of homoderivations namely isotone homoderivations is studied. A characterization of the isotone homoderivations in terms of the meet-homomorphisms is given. Furthermore, a sufficient condition for a homoderivation to become isotonic is established.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2022-02-25), HOMODERIVATIONS ON A LATTICE,, Jordan Journal of Mathematics and Statistics (), 15(2), 2022, pp, Vol:15, Issue:2, pages:325 – 338, Yarmouk University

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

In this paper, we consider the problem of representation and construction of intuitionistic fuzzy preorders and weak orders, where many fundamental representation results extending those of Ulrich Bodenhofer et al. are presented.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2021-06-30), Representation and Construction of Intuitionistic Fuzzy T- Preorders and Fuzzy Weak T –Orders,, Discussiones Mathematicae-General Algebra and Applications, Vol:41, Issue:, pages:81-101, Sciendo

In this paper, we study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals with respect to an intuitionistic fuzzy t-norm on an adequate lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to intuitionistic fuzzy t-norm are established.

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Abdelaziz عبد العزيز AMROUNE عمرون , ZIANE Brahim, , (2019-11-24), More on intuitionistic fuzzy lattices and their filters, Facta Universitatis, Series: Mathematics and Informatics, Vol:34, Issue:5, pages:871-888, University of Niš

The main goal of this presentation is to investigate the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are explored

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Abdelaziz عبد العزيز AMROUNE عمرون , ,(2019-09-04), On the aggregation of some fuzzy relations and their related structures,3rd International Conference of Mathematical Sciencees (ICMS 2019),Istanbul, Turkey)

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, 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 study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals with respect to an intuitionistic fuzzy t-norm on an adequate lattice. Some characterizations and properties of these intuitionistic fuzzy sublattices and ideals with respect to intuitionistic fuzzy t-norm are established.

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Abdelaziz عبد العزيز AMROUNE عمرون , Brahim Ziane, , (2019), More on intuitionistic fuzzy lattices and their filters, Facta Universitatis, Series: Mathematics and Informatics, Vol:34, Issue:5, pages:871-888, University of Niš, Serbia

The main goal of this presentation is to investigate the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are explored.

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Abdelaziz عبد العزيز AMROUNE عمرون , ,(2019), On the Aggregating of Some Fuzzy Relations and their Related Structures,International Conference of Mathematical Sciences (ICMS 2019),Maltepe University, Istanbul, Turkey

A representation theorem for bounded distributive hyperlattices is given. The equivalence between the category of Priestley spaces and the dual of the category of bounded distributive hyperlattices is established.

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Abdelaziz عبد العزيز AMROUNE عمرون , Ali Oumhani, , (2018), A representation theorem for bounded distributive hyperlattices, Quasigroups and Related Systems, Vol:26, Issue:1, pages:1-12, Institute of Mathematics of the Moldovian Academy of Sciences until 1992 ...

The main goal of this paper is to investigate the aggregation of diverse families of binary fuzzy relations, fuzzy filters, and fuzzy lattices. Some links between these families and their images via an aggregation are explored.

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Abdelaziz عبد العزيز AMROUNE عمرون , Aissa Bouad, , (2018), Aggregating Fuzzy Binary Relations and Fuzzy Filters, DiscussionesMathematicae-General Algebra and Applications, Vol:38, Issue:2, pages:273-296, FACULTY OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMETRICS UNIVERSITY OF ZIELONA GORA

In this paper, some characterizations of fuzzy filters and their prime filters are given. Also, we characterize fuzzy filters and fuzzy prime filters using their α−cuts. Finally, we give necessary and sufficient conditions under which a fuzzy set is a prime filter and we introduce the notion of fuzzy lattices isomorphism.

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Abdelaziz عبد العزيز AMROUNE عمرون , Ali Oumhani, , (2018), More on fuzzy lattice and their filters, journal Ann. Univ. Oradea, fasc. Math, Vol:25, Issue:2, pages:143-155, Department of Mathematics and Computer Science, Faculty of Sciences, University of Oradea, Romania

The starting point of this work comes from the results obtained by Inheung Chon in his paper “Fuzzy partial order relations and fuzzy lattices”. In this way, some characterizations of filters and prime filters are given. Also, we characterize fuzzy t-filters and fuzzy prime t-filters using their α-cuts. Finally, we give necessary and sufficient conditions under which a fuzzy set is a prime t-filter, presenting the notion of fuzzy lattices isomorphism.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2017), Kinds of t-fuzzy Filters of Fuzzy Lattices, Fuzzy Information and Engineering, Vol:9, Issue:3, pages:325-343, Taylor & Francis

In this paper, we show that the category of infinite fuzzy Priestley spaces is equivalent to the dual of the category of infinite fuzzy distributive lattices. A representation theorem for the infinite fuzzy distributive lattices is also given.

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Abdelaziz عبد العزيز AMROUNE عمرون , Ali Oumhani, , (2017), A representation theorem for infinite fuzzy distributive lattices, Journal of Intelligent & Fuzzy Systems, Vol:32, Issue:1, pages:35-42, IOS Press

The starting point of this work is the results obtained by Inheung Chon in his paper "Fuzzy partial order relations and fuzzy lattices". In this way, some characterizations of fuzzy filters and their prime filters are given. Also, we will characterize fuzzy filters and fuzzy prime filters using their α-cuts. Finally, we give necessary and sufficient conditions under which a fuzzy set is a prime filter, and we give the notion of fuzzy lattices isomorphism.

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Abdelaziz عبد العزيز AMROUNE عمرون , ,(2017), On fuzzy lattices and their filters,INTERNATIONAL CONFERENCE ON APPLIED ANALYSIS AND MATHEMATICAL MODELING,Istanbul

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, we extend some results obtained by A. Amroune and B. Davvaz in [1]. More precisely, we will develop a representation theory of intuitionistic fuzzy perfect distributive lattices in the finite case. To that end, we introduce the notion of intuitionistic fuzzy perfect distributive lattices and the one of fuzzy perfect Priestley spaces. In this way, the results of A. Amroune and B. Davvaz are extended to the intuitionistic fuzzy perfect case and the equivalence between the category of finite intuitionistic fuzzy perfect Priestley spaces the dual of the category of finite intuitionistic fuzzy perfect distributive lattices is proved.

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Abdelaziz عبد العزيز AMROUNE عمرون , Oumhani Ali, , (2016), Representation theorem for finite intuitionistic fuzzy perfect distributive lattices, Journal of Fuzzy Set Valued Analysis, Vol:2016, Issue:3, pages:326-344, ISPACS

, AbdelazizAmroune and Titre:. Référence: , 9(5) (2015) . URL:JIFACTOR: 1.1147 In this paper, we prove that any partial intuitionistic fuzzy ordering defined on an arbitrary non-empty set X can be linearized or can be extended to a linear (total) intuitionistic fuzzy ordering. This is an intuitionistic fuzzy generalization of the Szpilrajn theorem. This result has allowed us to characterize every partial intuitionistic fuzzy ordering by the intuitionistic fuzzy intersection of their linear extensions.

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Abdelaziz عبد العزيز AMROUNE عمرون , ZEDAM Lemnaouar, BijanDavvaz, , (2015), Szpilrajn theorem for intuitionistic fuzzy orderings, Annals of Fuzzy Mathematics and Informatics, Vol:9, Issue:5, pages:703-718, Kyung Moon Sa

Atanassov introduced another fuzzy object, called intuitionistic fuzzy set as a generalization of the concept of fuzzy subset. The aim of this paper is the elaboration of a representation theory of involutive interval-valued ÃLukasiewicz-Moisil algebras by using the notion of intuitionistic fuzzy sets.

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Abdelaziz عبد العزيز AMROUNE عمرون , Bijan Davvaz, , (2015), Many valued logic and intuitionistic fuzzy sets: A stone representation theorem generalisation, Honam Mathematical J, Vol:37, Issue:3, pages:269-279, Honam Mathematical Society

https://www.worldcat.org/title/journal-of-fuzzy-mathematics/oclc/27088829

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2010), Representation of T-fuzzy finite distributive lattices by means of T-fuzzy Priestley spaces, The journal of fuzzy mathematics, Vol:18, Issue:4, pages:13-824, Los Angeles, USA : International Fuzzy Mathematics Institute, ©1993

http://www.pphmj.com/journals/fjms.htm

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Abdelaziz عبد العزيز AMROUNE عمرون , Lemnaouar Zedam, , (2005), PRIESTLEY DUALITY FOR MV-ALGEBRAS, Far East Journal of Mathematical Sciences (FJMS), Vol:16, Issue:1, pages:89 - 96, Pushpa Publishing House

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

Le but de cet article est de donner une représentation des algèbres de Lukasiewicz θ-valentes involutives par des algèbres de structure floues involutives.

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Abdelaziz عبد العزيز AMROUNE عمرون , , (2004), Representation of involutive many valued Moisil- Łukasiewicz algebras by means of Priestley spaces, Far East Journal of Mathematical Sciences (FJMS), Vol:12, Issue:3, pages:299-313, Pushpa Publishing House

The purpose of this study is to give a topological representation for the Heyting algebras by means of Priestley spaces.

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Abdelaziz عبد العزيز AMROUNE عمرون , Messoud Gheboli, Lemnaouar Zedam, , (2003), Priestley Duality and Representation of Heyting Algebra, Far East Journal of Mathematical Sciences (FJMS), Vol:11, Issue:3, pages:65 - 74, Pushpa Publishing House