M. AMROUNE عمرون Abdelaziz عبد العزيز

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Mathematics Department

Research Interests

Specialized in Mathematics Department. Focused on academic and scientific development.

Contact Info

University of M'Sila, Algeria

Email : abdelaziz.amroune@univ-msila.dz

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Recent Publications

2024-09-17

On picture fuzzy sets

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*.
Citation

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

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2024-07-03

MORE ON PICTURE FUZZY SETS AND THEIR PROPERTIES

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2024-07-03), "MORE ON PICTURE FUZZY SETS AND THEIR PROPERTIES", [national] Turkish World Mathematical Society Journal of Applied and Engineering Mathematics , Isik University

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2023-09-26

EXTENSION OF SOME OF ATANASSOV’S MODULAR OPERATORS ON PICTURE FUZZY SETS

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.
Citation

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

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2023-07-18

Integrations on lattices.

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2023-07-18), "Integrations on lattices.", [national] Miskolc Mathematical Notes , UNIV MISKOLC INST MATH

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2023-06-01

ON PICTURE FUZZY RELATIONS AND THEIR PROPERTIES

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2023-06-01), "ON PICTURE FUZZY RELATIONS AND THEIR PROPERTIES", [national] The 4th Mathematics National Seminar , Constantine

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2022-10-26

ON PICTURE FUZZY SETS

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.
Citation

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

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2022-02-25

HOMODERIVATIONS ON A LATTICE,

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2022-02-25), "HOMODERIVATIONS ON A LATTICE,", [national] Jordan Journal of Mathematics and Statistics (), 15(2), 2022, pp , Yarmouk University

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2022

(F,G)-Derivations on a Lattice

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Mourad Yettou, , (2022), "(F,G)-Derivations on a Lattice", [national] Kragujevac Journal of Mathematics , University of Kragujevac, Kragujevac, Serbia

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2021-06-30

Representation and Construction of Intuitionistic Fuzzy T- Preorders and Fuzzy Weak T –Orders,

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2021-06-30), "Representation and Construction of Intuitionistic Fuzzy T- Preorders and Fuzzy Weak T –Orders,", [national] Discussiones Mathematicae-General Algebra and Applications , Sciendo

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2019-09-04

On the aggregation of some fuzzy relations and their related structures

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
Citation

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

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2019

On the Aggregating of Some Fuzzy Relations and their Related Structures

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.
Citation

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

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More on intuitionistic fuzzy lattices and their filters

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Brahim Ziane, , (2019), "More on intuitionistic fuzzy lattices and their filters", [national] Facta Universitatis, Series: Mathematics and Informatics , University of Niš, Serbia

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f-Fixed points of isotone f-derivations on a lattice

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Yettou Mourad, , (2019), "f-Fixed points of isotone f-derivations on a lattice", [national] Discussiones Mathematicae-General Algebra and Applications , University of Zielona Góra, Poland

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A binary operation-based representation of a lattice

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
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Mourad Yettou, , (2019), "A binary operation-based representation of a lattice", [national] KYBERNETIKA , Nakladatelstvi Academia

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2018

More on fuzzy lattice and their filters

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Ali Oumhani, , (2018), "More on fuzzy lattice and their filters", [national] journal Ann. Univ. Oradea, fasc. Math , Department of Mathematics and Computer Science, Faculty of Sciences, University of Oradea, Romania

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Aggregating Fuzzy Binary Relations and Fuzzy Filters

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Aissa Bouad, , (2018), "Aggregating Fuzzy Binary Relations and Fuzzy Filters", [national] DiscussionesMathematicae-General Algebra and Applications , FACULTY OF MATHEMATICS, COMPUTER SCIENCE AND ECONOMETRICS UNIVERSITY OF ZIELONA GORA

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A representation theorem for bounded distributive hyperlattices

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Ali Oumhani, , (2018), "A representation theorem for bounded distributive hyperlattices", [national] Quasigroups and Related Systems , Institute of Mathematics of the Moldovian Academy of Sciences until 1992 ...

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2017

On fuzzy lattices and their filters

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.
Citation

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

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A representation theorem for infinite fuzzy distributive lattices

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Ali Oumhani, , (2017), "A representation theorem for infinite fuzzy distributive lattices", [national] Journal of Intelligent & Fuzzy Systems , IOS Press

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Kinds of t-fuzzy Filters of Fuzzy Lattices

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2017), "Kinds of t-fuzzy Filters of Fuzzy Lattices", [national] Fuzzy Information and Engineering , Taylor & Francis

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2016

Representation theorem for finite intuitionistic fuzzy perfect distributive lattices

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Oumhani Ali, , (2016), "Representation theorem for finite intuitionistic fuzzy perfect distributive lattices", [national] Journal of Fuzzy Set Valued Analysis , ISPACS

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Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras,

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
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Bijan davvaz, , (2016), "Many-Valued Logic and Zadeh’s Fuzzy Sets: A Stone Representation Theorem for Interval-Valued Łukasiewicz–Moisil Algebras,", [national] Journal of Intelligent Systems , De Gruyter

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2015

Many valued logic and intuitionistic fuzzy sets: A stone representation theorem generalisation

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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, Bijan Davvaz, , (2015), "Many valued logic and intuitionistic fuzzy sets: A stone representation theorem generalisation", [national] Honam Mathematical J , Honam Mathematical Society

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Szpilrajn theorem for intuitionistic fuzzy orderings

, 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.
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, ZEDAM Lemnaouar, BijanDavvaz, , (2015), "Szpilrajn theorem for intuitionistic fuzzy orderings", [national] Annals of Fuzzy Mathematics and Informatics , Kyung Moon Sa

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2010

Representation of T-fuzzy finite distributive lattices by means of T-fuzzy Priestley spaces

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

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2010), "Representation of T-fuzzy finite distributive lattices by means of T-fuzzy Priestley spaces", [national] The journal of fuzzy mathematics , Los Angeles, USA : International Fuzzy Mathematics Institute, ©1993

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2005

20. Which role plays the condition of continuity in the representation of L-M algebra

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
Citation

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2005), "20. Which role plays the condition of continuity in the representation of L-M algebra", [national] Fart , Ed , PushpaPublishing House

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PRIESTLEY DUALITY FOR MV-ALGEBRAS

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

M. AMROUNE عمرون Abdelaziz عبد العزيز, Lemnaouar Zedam, , (2005), "PRIESTLEY DUALITY FOR MV-ALGEBRAS", [national] Far East Journal of Mathematical Sciences (FJMS) , Pushpa Publishing House

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2004

Representation of involutive many valued Moisil- Łukasiewicz algebras by means of Priestley spaces

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

M. AMROUNE عمرون Abdelaziz عبد العزيز, (2004), "Representation of involutive many valued Moisil- Łukasiewicz algebras by means of Priestley spaces", [national] Far East Journal of Mathematical Sciences (FJMS) , Pushpa Publishing House

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2003

Priestley Duality and Representation of Heyting Algebra

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

M. AMROUNE عمرون Abdelaziz عبد العزيز, Messoud Gheboli, Lemnaouar Zedam, , (2003), "Priestley Duality and Representation of Heyting Algebra", [national] Far East Journal of Mathematical Sciences (FJMS) , Pushpa Publishing House

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