ABDELKRIM Mehenni
عبد الكريم مهني
abdelkrim.mehenni@univ-msila.dz
0675067281/ 0792677014
- Mathematics Department
- Faculty of Mathematics and Informatics
- Grade MCB
About Me
Doctorat en mathématiques. in L'université des sciences et de la technologie Houari-Boumédiène (USTHB)
Research Domains
LATTICE THEORY WEACLY ASSOCIATIVE LATTICE ALGEBRAIC OPERATIONS Mathematics
LocationMsila, Msila
Msila, ALGERIA
Code RFIDE- 17-11-2022
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Doctorat en mathématiques
Algebraic operations in ordered structures. - 15-06-2016
- 18-06-2014
- 1992-07-27 00:00:00
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ABDELKRIM Mehenni birthday
- 2024-10-04
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2024-10-04
The first training season on Python language
The first training season on Python language in univ m'sila
Citation
Abdelkrim Mehenni , ,(2024-10-04), The first training season on Python language,Training season on Python language,univ m'sila
- 2023-12-06
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2023-12-06
OPERATIONS ON NON-ASSOCIATIVE ALGEBRAIC STRUCTURES
In the present work, we study operations on non-associative algebraic structures like trellises as a generalization of lattices by considering sets with a reflexive and antisymmetric, but not necessarily transitive, relation and by postulating the existence of least upper bounds and greatest lower bounds similarly as for partially ordered sets; and, alternatively, by considering sets with two operations that are commutative, absorptive, and, what will be called, part-preserving. Using this approach we are able to prove theorems analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity.
Citation
Abdelkrim Mehenni , ,(2023-12-06), OPERATIONS ON NON-ASSOCIATIVE ALGEBRAIC STRUCTURES,The Second International Workshop on Applied Mathematics 2nd-IWAM'2023,Constantine, ALGERIA.
- 2023-11-08
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2023-11-08
Triangular norms on algebraic structures
The ideas of transitivity and partial order are, without question, fundamental in a wide variety of mathematical theories. However, has been simmering for some time with notions of non-transitive relation, some arising from common, every-day observations and some from purely mathematical considerations such as games, the relation of closeness, graphs, and logic of non-transitive implications. Maybe, the most common and illustrative example of a non transitive relation in our real life is the acquaintance relation. The preference loop or cycle is also a non-transitive relation. For instance, the non-transitive relations also appear in the football tournament.
Citation
Abdelkrim Mehenni , ,(2023-11-08), Triangular norms on algebraic structures,National Conference on Mathematics and its Applications (NCMA'2023) 7-8 November 2023,Setif
- 2023-10-12
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2023-10-12
Weakly associative Lattices
In the present paper, we study the weakly associative lattices (trellises, for short)) that introduced by E. Fried and H. L. Skala, by considering sets with a reflexive and antisymmetric, but not necessarily transitive relation. Of course, by postulating the existence of least upper bounds and greatest lower bounds of each pair of elements similarly to the case of lattices. Also, we present some properties analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity
Citation
Abdelkrim Mehenni , ,(2023-10-12), Weakly associative Lattices,2nd International Conference on the ’Evolution of Contemporary Mathematics and their Impact in Sciences and Technology’. October 11th and 12th, 2023 at the Brothers Mentouri University of Constantine. Algeria,Constantine. Algeria
- 2023-05-25
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2023-05-25
Pseudo triangular norms on bounded trellises
In this paper, we introduce the notion of pseudo-triangular norm (pseudo-t-norm, for short) as a classes of weakly associative operations on trellises and as a generalization of triangular norm (t-norm, for short) on bounded trellises and we investigate their various properties and present some constructions of pseudo-t-norms on bounded trellises. Also, we study the T-distributivity on bounded trellises. Moreover, we show the relationship among pseudo-t-norms and isomorphisms on bounded trellises, which are more complicated in absence of the property of (transitivity) associativity of the trellis meet and join operations.
Citation
Abdelkrim Mehenni , , (2023-05-25), Pseudo triangular norms on bounded trellises, arXiv, Vol:0, Issue:0, pages:23, arXiv éditeur
Default case...
- 2022-11-30
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2022-11-30
Class of NonAssociative Algebraic Structures
In the present work, we study a non-associative algebraic structures like trellises as a generalization of lattices by considering sets with a reflexive and antisymmetric, but not necessarily transitive, relation and by postulating the existence of least upper bounds and greatest lower bounds similarly as for partially ordered sets; and, alternatively, by considering sets with two operations that are commutative, absorptive, and, what will be called, part-preserving. Using this approach we are able to prove theorems analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity.
Citation
Abdelkrim Mehenni , ,(2022-11-30), Class of NonAssociative Algebraic Structures,National Conference on Mathematics and Applications NCMA 2022 Mila,Abdelhafid Boussouf, University Center of Mila
- 2022-11-17
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2022-11-17
Algebraic operations on ordered structures
In this thesis, we study algebraic operations on ordered structures. More precisely, we study a class of associative and weakly associative operations on bounded lattices and bounded trellises. First, we generalize the notion of aggregation operator to 𝒇-aggregation operator with respect to an arbitrary function 𝒇 on a bounded lattice and we discuss its fundamental properties. Second, we study a specific class of associative (resp. weakly associative) operations on trellises with additional properties, like; commutative and increasing properties.
Citation
AbdelkrimMehenni , ,(2022-11-17); Algebraic operations on ordered structures,University of Science and Technology Houari Boumediene (USTHB),
- 2022-05-24
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2022-05-24
Trellis theory and some new results
In the present paper we study a generalization of lattices by considering sets with a reflexive and antisymmetric, but not necessarily transitive, relation and by postulating the existence of least upper bounds and greatest lower bounds similarly as for partially ordered sets; and, alternatively, by considering sets with two operations that are commutative, absorptive, and, what will be called, part-preserving. Using this approach we are able to prove theorems analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity. Moreover, in the presence of certain additional assumptions, such as distributivity, relative complementation and modularity, or others, associativity follows as a consequence.
Citation
Abdelkrim Mehenni , ,(2022-05-24), Trellis theory and some new results,2nd International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences,Turkey
- 2022-05-05
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2022-05-05
Weakly associative lattices
In the present paper, we study the weakly associative lattices (trellises, for short)) that introduced by E. Fried and H. L. Skala, by considering sets with a reflexive and antisymmetric, but not necessarily transitive relation. Of course, by postulating the existence of least upper bounds and greatest lower bounds of each pair of elements similarly to the case of lattices. Also, we present some properties analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity.
Citation
Abdelkrim Mehenni , ,(2022-05-05), Weakly associative lattices,INTERNATIONAL E-CONFERENCE ON PURE AND APPLIED MATHEMATICAL SCIENCES, 04-06 May 2022,Tunisia
- 2022-01-01
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2022-01-01
f-aggregation Operators on a Bounded Lattice
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.
Citation
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
- 2021-06-26
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2021-06-26
Algebraic operations on ordered structures
In the present paper, we study an extended structure of a lattice (trellis, for short) by considering sets with a reflexive and antisymmetric, but not necessarily transitive relation. Of course, by postulating the existence of least upper bounds and greatest lower bounds of each pair of elements similarly to the case of lattices. Also, we present some properties analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity
Citation
Abdelkrim Mehenni , ,(2021-06-26), Algebraic operations on ordered structures,National Conference on Applied Mathematics and Didactics NCAMD2021, Constantine-Algeria. 26 Juin, 2021.,Constantine-Algeria.
- 2021-05-26
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2021-05-26
Some properties of trellises
In the present paper, we study an extended structure of a lattice (trellis, for short) by considering sets with a reflexive and antisymmetric, but not necessarily transitive relation. Of course, by postulating the existence of least upper bounds and greatest lower bounds of each pair of elements similarly to the case of lattices. Also, we present some properties analogous to nearly all the basic theorems of lattice theory, thus demonstrating the superfluity of the assumption of associativity
Citation
Abdelkrim Mehenni , ,(2021-05-26), Some properties of trellises,The First Online International Conference on Pure and Applied Mathematics IC-PAM’21 May 26-27, 2021, Ouargla, ALGERIA,Ouargla, Algeria
- 2019-11-23
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2019-11-23
On faggregation operators on a bounded lattice
In the present work, we introduce the notion of f-aggregation operator on a bounded lattice as a generalization of an aggregation operator and present the possibility to see weakest conditions for the aggregation operator with respect to a function on a bounded lattice and showed a necessary and sufficient condition under which a binary operation is an faggregation operator, for any function f defined on bounded lattice.
Citation
Abdelkrim Mehenni , ,(2019-11-23), On faggregation operators on a bounded lattice,Rencontre d’Analyse Mathematique et Applications ´ RAMA11,University of Sidi Bel Abbès
- 2018-12-17
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2018-12-17
On f-aggregation operators
Binary operations are among the oldest fundamental concepts in algebraic structures. A binary operation on a non-empty set X is any function from the Cartesian product X × X into X. The concept of aggregation or aggregation operator (as a particular concept of a binary operation on a bounded Lattice verified certain conditions) was generalized in a bounded lattice by Magda Komornkov and Radko Mesiar in 2010 . Several authors have also studied the aggregation operators in some lattices and their applications. In this work, we propose the following notion of an f-aggregation operator as a generalization of an aggregation operator. Also this notion give us the possibility to see weakest conditions for the aggregation operator.
Citation
Abdelkrim Mehenni , ,(2018-12-17), On f-aggregation operators,Workshops on Pure and Applied Mathematics December 17-18, 2018,University of Msila