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COMMUTATIVE RINGS DERIVED FROM FUZZY HYPERRINGS
Davvaz, Bijan,Firouzkouhi, Narjes The Honam Mathematical Society 2020 호남수학학술지 Vol.42 No.2
The fundamental relation on a fuzzy hyperring is defined as the smallest equivalence relation, such that the quotient would be the ring, that is not commutative necessarily. In this paper, we introduce a new fuzzy strongly regular equivalence on fuzzy hyperrings, where the ring is commutative with respect to both sum and product. With considering this relation on fuzzy hyperring, the set of the quotient is a commutative ring. Also, we introduce fundamental functor between the category of fuzzy hyperrings and category of commutative rings and some related properties. Eventually, we introduce α-part in fuzzy hyperring and determine some necessary and sufficient conditions so that the relation α is transitive.
A Note on Essential Soft Submodules
Bijan Davvaz,Jing Ma,Chengxiz Sun 한국지능시스템학회 2019 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.19 No.1
In this paper, we investigate the property of essential soft submodule and give an equivalent condition of essential soft submodule. Then the concept of the socle of a soft module is introduced, basic properties of such soft submodules are investigated, several equivalent definitions of the socle and the radical of a soft module are given respectively. Also, examples of these related soft submodules are given.
IDEAL THEORY OF SUBTRACTION SEMIGROUPS BASED ON (3, 2)-FUZZY SETS
( Bijan Davvaz ),( John Britto Princivishvamalar ),( Neelamegarajan Rajesh ),( Balasubramaniyan Brundha ) 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.3
In this paper, we define the notions of (3, 2)-fuzzy ideal of subtraction semigroup and near subtraction semigroup. Also, we discuss some of its properties with examples.
DERIVATION AND ACTOR OF CROSSED POLYMODULES
Bijan Davvaz,Murat Alp 한국수학교육학회 2018 純粹 및 應用數學 Vol.25 No.3
An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.
CONSTRUCTION OF ORDERED REGULAR EQUIVALENCE RELATIONS ON ORDERED SEMIHYPERRINGS
Omidi, Saber,Davvaz, Bijan The Honam Mathematical Society 2018 호남수학학술지 Vol.40 No.4
In the present paper, we construct an ordered regular equivalence relation on an ordered semihyperring by 2-hyperideals such that the corresponding quotient structure is also an ordered semihyperring.
STUDY ON CLEAN ORDERED RINGS DERIVED FROM CLEAN ORDERED KRASNER HYPERRINGS
Saber Omidi,Bijan Davvaz 한국수학교육학회 2018 純粹 및 應用數學 Vol.25 No.2
In this paper, we introduce the notion of a clean ordered Krasner hy-perring and investigate some properties of it. Now, let (R;+,;≤) be a clean ordered Krasner hyperring. The following is a natural question to ask: Is there a strongly regular relation σ on R for which R/σ is a clean ordered ring? Our motivation to write the present paper is reply to the above question.
Heart and Complete Parts of (R,S)-hyper Bi-module
M. Nooranian,Bijan Davvaz 한국수학교육학회 2022 純粹 및 應用數學 Vol.29 No.3
In this article, we investigate several aspects of $(R,S)$-hyper bi-modules and describe some their properties. The concepts of fundamental relation, completes part and complete closure are studied regarding to $(R,S)$-hyper bi-modules. In particular, we show that any complete $(R,S)$-hyper bi-module has at least an identity and any element has an inverse. Finally, we obtain a few results related to the heart of $(R,S)$-hyper bi-modules
On Soft Topological Polygroups and Their Examples
Rasoul Mousarezaei,Bijan Davvaz 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.1
Polygroups are a special subclass of hypergroups that satisfies group-like axioms. A polygroup is a multigroup that is completely regular and reversible in itself. A topological polygroup is a polygroup P with a topology on P that satisfies certain conditions. Moreover, the concept of soft sets is a general mathematical tool for dealing with uncertainty. In this study, we investigate soft topological polygroups over a polygroup. The ideas presented in this article can be used to build more polygroups and soft topological polygroups.
CONSTRUCTION OF ORDERED REGULAR EQUIVALENCE RELATIONS ON ORDERED SEMIHYPERRINGS
Saber Omidi,Bijan Davvaz 호남수학회 2018 호남수학학술지 Vol.40 No.4
In the present paper, we construct an ordered regular equivalence relation on an ordered semihyperring by 2-hyperideals such that the corresponding quotient structure is also an ordered semihyperring.
MANY VALUED LOGIC AND INTUITIONISTIC FUZZY SETS: A STONE THEOREM GENERALIZATION
AMROUNE, ABDELAZIZ,DAVVAZ, BIJAN The Honam Mathematical Society 2015 호남수학학술지 Vol.37 No.3
Atanassov introduced another fuzzy object, called intu- itionistic 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 Łukasiewicz-Moisil algebras by using the notion of intuitionistic fuzzy sets.