M. MEHENNI Abdelkrim

MCB

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Department

Mathematics Department

Research Interests

LATTICE THEORY WEACLY ASSOCIATIVE LATTICE ALGEBRAIC OPERATIONS Mathematics

Contact Info

University of M'Sila, Algeria

Email : abdelkrim.mehenni@univ-msila.dz

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Recent Publications

2024-10-04

The first training season on Python language

The first training season on Python language in univ m'sila
Citation

M. MEHENNI Abdelkrim, (2024-10-04), "The first training season on Python language", [national] Training season on Python language , univ m'sila

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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

M. MEHENNI Abdelkrim, (2023-12-06), "OPERATIONS ON NON-ASSOCIATIVE ALGEBRAIC STRUCTURES", [international] The Second International Workshop on Applied Mathematics 2nd-IWAM'2023 , Constantine, ALGERIA.

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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

M. MEHENNI Abdelkrim, (2023-11-08), "Triangular norms on algebraic structures", [national] National Conference on Mathematics and its Applications (NCMA'2023) 7-8 November 2023 , Setif

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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

M. MEHENNI Abdelkrim, (2023-10-12), "Weakly associative Lattices", [international] 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

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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

M. MEHENNI Abdelkrim, (2023-05-25), "Pseudo triangular norms on bounded trellises", [national] arXiv , arXiv éditeur

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2023-01-21

Certificat English

course supporte indiv English
Citation

M. MEHENNI Abdelkrim, (2023-01-21), "Certificat English", [national] Univ M'sila

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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

M. MEHENNI Abdelkrim, (2022-11-30), "Class of NonAssociative Algebraic Structures", [national] National Conference on Mathematics and Applications NCMA 2022 Mila , Abdelhafid Boussouf, University Center of Mila

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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

M. MEHENNI Abdelkrim, (2022-11-17), "Algebraic operations on ordered structures", [national] University of Science and Technology Houari Boumediene (USTHB)

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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

M. MEHENNI Abdelkrim, (2022-05-24), "Trellis theory and some new results", [international] 2nd International Symposium on Current Developments in Fundamental and Applied Mathematics Sciences , Turkey

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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

M. MEHENNI Abdelkrim, (2022-05-05), "Weakly associative lattices", [international] INTERNATIONAL E-CONFERENCE ON PURE AND APPLIED MATHEMATICAL SCIENCES, 04-06 May 2022 , Tunisia

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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

M. MEHENNI Abdelkrim, (2022-01-01), "f-aggregation Operators on a Bounded Lattice", [national] Azerbaijan Journal of Mathematics , Institute of Mathematics and Mechanics NAS of Azerbaijan

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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

M. MEHENNI Abdelkrim, (2021-05-26), "Some properties of trellises", [international] The First Online International Conference on Pure and Applied Mathematics IC-PAM’21 May 26-27, 2021, Ouargla, ALGERIA , Ouargla, Algeria

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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

M. MEHENNI Abdelkrim, (2019-11-23), "On faggregation operators on a bounded lattice", [national] Rencontre d’Analyse Mathematique et Applications ´ RAMA11 , University of Sidi Bel Abbès

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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

M. MEHENNI Abdelkrim, (2018-12-17), "On f-aggregation operators", [national] Workshops on Pure and Applied Mathematics December 17-18, 2018 , University of Msila

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