# Arsham Borumand SaeidShahid Bahonar University of Kerman · Department of Mathematics

Arsham Borumand Saeid

Ph.D

Editor-in-Chief:
Journal of Mahani Mathematical Research &
Transactions on Fuzzy Sets and Systems

## About

370

Publications

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2,678

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Introduction

Additional affiliations

June 2019 - present

## Publications

Publications (370)

In this paper, first (by the notions which defined,) we get some new properties and characterizations in MV-modules. We show that there exits an one to one corresponding between P-prime A-ideals of an A-module M and P_S –prime A_S-ideals of M_S, where S is a closed subset of A and P is a prime ideal of A such that P⋂S=∅. After that we introduced so...

The main objective of this study is to introduce Sheffer stroke R0−algebra (for
short, SR0− algebra). Then it is stated that the axiom system of a Sheffer stroke R0−algebra is independent. It is indicated that every Sheffer stroke R0−algebra is R0−algebra but specific conditions are necessarily for the inverse. Afterward, various ideals of a Sheffe...

The study of topological indices for fuzzy graphs is beneficial for fuzzy multi-criteria decision-making problems and various connected fuzzy networks. In this paper, we discuss two fuzzy topological indices, namely fuzzy Randic index and fuzzy harmonic index. We establish several upper bounds for these fuzzy indices. We also present the lower boun...

In this paper, we define modal operators in residuated skew lattices and prove some fundamental properties of monotone modal operators on residuated skew lattices (RSL). We prove that the composition of two modal operators is a modal operator if and only if they commute. We investigate strong modal operators in RSL and get a characterization of the...

The main objective of the study is to introduce a hesitant fuzzy structures on Sheffer
stroke BCK-algebras related to their subsets (subalgebras as possible as). Then it is
proved that every hesitant fuzzy ideal of a Sheffer stroke BCK-algebra related to the
subset is the hesitant fuzzy subalgebra. By defining a hesitant fuzzy maximal ideal in
this...

In this study, we give some fundamental set-theoretical solutions of Yang-Baxter equation in triangle algebras and state triangle algebras. We prove that the necessary and sufficient condition for certain mappings to be set theoretical solutions of Yang-Baxter equation on these structures is that these structures must be also MTL-(state) triangle a...

In this paper we introduce Sheffer stroke BE-algebras (briefly, SBE-algebras) and investigate a relationship between SBE-algebras and BE-algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-algebra, it is shown that any SBE-filter of a SBE-algebra is a SBE-subalgebra but the converse of this statement is not true. Beside...

The Markov Weighted Fuzzy Time Series (MWFTS) is a method for making predictions based on developing a fuzzy time series (FTS) algorithm. The MWTS has overcome certain limitations of FTS, such as repetition of fuzzy logic relationships and weight considerations of fuzzy logic relationships. The main challenge of the MWFTS method is the absence of s...

In this article, we introduce dual hesitant q$$ q $$‐rung orthopair fuzzy 2‐tuple linguistic set (DHq‐ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2‐tuple linguistic term into dual hesitant q$$ q $$‐rung orthopair fuzzy set (DHq‐ROFS). DHq‐ROFTLS is a better way to deal with uncertain and imprecise information in the dec...

The concept of ₦-structures was initiated by Jun et al. in 2009. Later, Young Bae Jun extended this concept as ₦-hyper sets and dealt its associated outcomes. In particular, four types of ₦-substructures with relevant properties have been investigated which leads to the introduction of the notion of ₦-hyper [Formula: see text]subalgebra in this stu...

This study aims to introduce the concept of (anti) fuzzy ideals of a Sheffer stroke BCK-algebra. After describing an anti fuzzy subalgebra and an anti fuzzy (sub-implicative) ideal of a Sheffer stroke BCK-algebra, the relationships of these notions are demonstrated. Also, a t-level cut and complement of a fuzzy subset are defined, and some of the p...

In this paper, as a further generalization of fuzzy ideals, we introduce the notion of a fuzzy (soft) quasi-interior ideals of semirings and characterize regular semiring in terms of fuzzy (soft) quasi-interior ideals of semirings. We prove that (μ,A) is a fuzzy soft left quasi-interior ideal over a regular semiring M, if and only if (μ,...

We know that Γ−ring, Γ−incline, Γ−semiring, Γ−semigroup are generalizations of ring, incline, semiring and semigroup respectively. In this paper, we introduce the concept of Γ−BCK-algebras as a generalization of BCK-algebras and study Γ−BCK-algebras. We also introduce subalgebra, ideal, closed ideal, normal subalgebra, normal ideal and construct qu...

The purpose of this paper is to introduce a novel notion of hypergraph-based codes, L.C-hypergraphs and codeable hypergraphs with respect to binary (linear) codes. In order to realize the article’s goals, we define the concepts of code-based graphs, consider them as complex networks and construct them from binary (linear) codes via an equivalence r...

The main objective of this study is to introduce a neutrosophic N− subalgebra (ideal) of Lalgebras and to investigate some properties. It is shown that the level-set of a neutrosophic N−subalgebra (ideal) of an L-algebra is its subalgebra (ideal), and the family of all neutrosophic N−subalgebras of an L-algebra forms a complete distributive modular...

In this study, fuzzy subalgebras and ideals with t-conorms on Sheffer stroke Hilbert algebras are discussed. We state and prove relationships between the level-set of a fuzzy subalgebra with a t-conorm T (briefly, T-fuzzy subalgebra) and a subalgebra of a Sheffer stroke Hilbert algebra. Then the composition of T-fuzzy subalgebras and homomorphisms...

In this paper, we introduce and study the notion of a [Formula: see text]positive implicative[Formula: see text] left ray in groupoids, and we show that every normal subgroup of a group is a left ray of a group, and in every finite group, left rays are normal subgroups. Further, left absorptive subsets of groupoids are discussed and several example...

The notion of a belligerent GE-filter in a GE-algebra is introduced, and the relationships between a GE-filter and a belligerent GE-filter will be given. Conditions for a GE-filter to be a belligerent GE-filter are provided. The product and the union of GE-algebras are discussed and its properties are investigated.

In this paper, Sheffer stroke BL-algebra and its properties are investigated. It is shown that a Cartesian product of two Sheffer stroke BL-algebras is a Sheffer stroke BL-algebra. After describing a filter of Sheffer stroke BL-algebra, a congruence relation on a Sheffer stroke BL-algebra is defined via its filter, and quotient of a Sheffer stroke...

Nowadays, wireless sensor networks (WSNs) are used to monitor and collect data in various environments. One of the main challenges in WSNs is the energy consumption due to the deployed sensor nodes in WSNs are energy-constrained. Clustering method is a solution for this problem and the cluster head (CH) selection process is a major part of the clus...

The conditions of β−algebra is enforced into the structure of cubic intuitionistic fuzzy settings. Furthermore, the concept of cubic intuitionistic β− subalgebra is expressed and its pertinent properties were explored. Also, discussed about the level set of cubic intuitionistic β−subalgebras and furnished some fascinating results on the cartesian p...

A complex intuitionistic fuzzy set (CIFS) has an ability to represent the problems with intuitionistic uncertainty and periodicity, simultaneously. In this paper, we present a new framework for handling complex intuitionistic fuzzy information by combining the CIFSs with competition graphs. We first introduce the concept of complex intuitionistic f...

Different extensions of fuzzy sets like intuitionistic, picture, Pythagorean, and spherical have been proposed to model uncertainty. Although these extensions are able to increase the level of accuracy, imposing rigid restrictions on the grades are the main problem of them. In these types of fuzzy sets, the value of grades and also the sum of them...

In this paper, we study MV?algebra of continuous functions C(X) and maximal ideals of C(X). Furthermore, Z?ideal and Z??ideal of C(X) are introduced and proved that every Z??ideal in C(X) is a Z?ideal but the converse is not true and every finitely generated Z?ideal is a basic Z??ideal. Also, we investigate meet and join of two Z?ideals (Z??ideal)...

In this paper, we propose a new intuitionistic entropy measurement for multi-criteria decision-making (MCDM) problems. The entropy of an intuitionistic fuzzy set (IFS) measures uncertainty related to the data modelling as IFS. The entropy of fuzzy sets is widely used in decision support methods, where dealing with uncertain data grows in importance...

In this study, new properties of various filters on a Sheffer stroke BL-algebra are studied. Then some new results in filters of Sheffer stroke BL-algebras are given. Also, stabilizers of nonempty subsets of Sheffer stroke BL-algebras are defined and some properties are examined. Moreover, it is shown that the stabilizer of a filter with respect to...

AbstractAs generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic structures (or NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike the classical algebraic structures, where all operations are well defined and all axioms are totally true, in NeutroAlgebras and An...

The purpose of this paper was to introduce the concepts of very thin multigroup, nondistributive (very thin) multirings, zero-divisor elements of multirings and zero-divisor graphs based on zero-divisor elements of multirings. In order to realize the article’s goals, we consider the relationship between finite nondistributive (very thin) multirings...

Recently, a number of researches studied relationship between codes and BCK-algebras, dealing with the category codes in a BCK-algebra have not been considered in earlier works. This paper investigates a code constructed by a BCK-algebra and also a BCK-algebra constructed based on code. The suggested rendered algorithm constructs the code based on...

The notions of \({{\mathcal {N}}}\)-ideal of types \((\in , \in )\) and \((\in , \in \! \vee \, {q})\), soft \({\mathcal N}_{\in }\)-set, soft \({{\mathcal {N}}}_{q}\)-set, soft \({{\mathcal {N}}}_{\in \! \vee \, {q}}\)-set, soft \({{\mathcal {N}}}\)-subalgebra and soft \({{\mathcal {N}}}\)-ideal in BCK/BCI-algebra are introduced, and several prope...

In this article, we introduce the variety of monadic MTL-algebras as MTL-algebras equipped with two monadic operators. After a study of the basic properties of this variety, we define and investigate monadic filters in monadic MTL-algebras. By using the notion of monadic filters, we prove the subdirect representation theorem of monadic MTL-algebras...

As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the NeutroAlgebraic Structures (or
NeutroAlgebras) and AntiAlgebraic structures (or AntiAlgebras). Unlike
the classical algebraic structures, where all operations are well-defined and all
axioms are totally true, in NeutroAlgebras and AntiAlgebr...

This study aims to investigate [Formula: see text]-valued GFA from algebraic and topological perspectives, where [Formula: see text] stands for residuated lattice and B is a set of propositions about the general fuzzy automata, in which its underlying structure is a complete infinitely distributive lattice. Further, the concepts of [Formula: see te...

In this paper, we introduce the notion of state monadic BL-algebras and we investigate their properties. We define the concept of state monadic filters and study certain types of state monadic filters; we define and charaterize maximal and prime state monadic filters. Characterizations of local, simple and semisimple state monadic BL-algebras are a...

As generalizations and alternatives of classical algebraic structures there have been introduced in 2019 the Neutro Algebraic Structures (or Neutro Algebras) and Anti Algebraic structures (or Anti Algebras). Unlike the classical algebraic structures, where all operations are well-defined and all axioms are totally true, in Neutro Algebras and Anti...

In this paper, some types of fuzzy filters of a strong Sheffer stroke
non-associative MV-algebra (for short, strong Sheffer stroke NMV-algebra) are
introduced. By presenting new properties of filters, we define a prime filter in
this algebraic structure. Then (prime) fuzzy filters of a strong Sheffer stroke
NMV-algebra are determined and some featu...

The aim of the study is to present (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets on Sheffer stroke UP-algebra (in short, SUP-algebra). After defining (sup-hesitant) fuzzy SUP-subalgebras and fuzzy duplex SUP-sets of a SUP-algebra, we give their some properties and analyse whether the intersection or union of these subalgebras is a...

In this study, Sheffer stroke Nelson algebras (briefly, s-Nelson algebras), (ultra) ideals, quasi-subalgebras and quotient sets on these algebraic structures are introduced. The relationships between s-Nelson and Nelson algebras are analyzed. Also, it is shown that a s-Nelson algbera is a bounded distributive modular lattice, and the family of all...

In this article, we study ideals in residuated lattice and present a characterization theorem for them. We investigate some related results between the obstinate ideals and other types of ideals of a residuated lattice, likeness Boolean, primary, prime, implicative, maximal and ʘ-prime ideals. Characterization theorems and extension property for ob...

In this paper, we introduce the notion of a wRM/eRM-algebra as a generalization of a RM-algebra. These structures are studied in details. Also, we derived an eRM-algebra from a RM-algebra and vice versa. The concept of a positive implicative eRM-algebra is defined and we discussed on the medial filters.

In recent years, mobile ad-hoc networks have been used widely due to advances in wireless technology. These networks are formed in any environment that is needed without a fixed infrastructure or centralized management. Mobile ad-hoc networks have some characteristics and advantages such as wireless medium access, multi-hop routing,
low cost devel...

In this paper, Sheffer stroke BCK-algebra is defined and its features are investigated. It is indicated that the axioms of a Sheffer stroke BCK-algebra are independent. The relationship between a Sheffer stroke BCK-algebra and a BCK-algebra is stated. After describing a commutative, an implicative and an involutory Sheffer stroke BCK-algebras, some...

The present study aimed to propose the similarity triangle algebra and prove the completeness of the similarity triangle logic. The similarity was defined on triangle algebra. Similarity triangle algebra is a triangle algebra endowed with a binary operation S, which verifies specific additional properties. These properties and a class of all the si...

In this paper, we introduce the notion of states and state operators on residuated skew lattices and investigate some related properties of them. The relationships between state operators and states on residuated skew lattices are discussed. We prove that every Bosbach state on a residuated skew lattice is a Riecan state and with an example we show...

In this study, a neutrosophic N−subalgebra and a level set of a neutrosophic N−structure are defined on Sheffer stroke Hilbert algebras. By determining a subalgebra on Sheffer stroke Hilbert algebras, it is proved that the level set of neutrosophic N-subalgebras on this algebra is its subalgebra and vice versa. It is stated that the family of all n...

In this paper we introduce Sheffer stroke BE-algebras (briefly, SBE-algebras) and investigate a relationship between SBE-algebras and BE-algebras. By presenting a SBE-filter, an upper set and a SBE-subalgebra on a SBE-algebra, it is shown that any SBE-filter of a SBE-algebra is a SBE-subalgebra but the converse of this statement is not true. Beside...

A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted a...

In the online published article, the third author’s “A. Borumand Saeid” affiliation is updated as following “Dept. of Pure Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran”.

In this paper, at first we study strong Sheffer stroke NMV-algebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient strong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

The relationship between a transitive GE-algebra and a belligerent GE-algebra (also, between an antisymmetric GE-algebra and a left exchangeable GE-algebra) is displayed. A condition for the trivial GE-filter to be a belligerent GE-filter is provided. The least GE-filter containing a given GE-filter and one element is formed. Conditions under which...

The notions of Ɲ -ideal of types (∈,∈) and (∈,∈Vq), soft Ɲ ∈ -set, soft Ɲ q -set, soft Ɲ ∈vq -set, soft Ɲ -subalgebra and soft Ɲ -ideal in BCK|BCI -algebra are introduced, and several properties are investigated. Characterizations of Ɲ -subalgebra of types (∈,∈) and (∈,∈Vq), Ɲ -ideal of types (∈,∈) and (∈,∈Vq), soft Ɲ -subalgebra and soft Ɲ -ideal...

This paper computes eigenvalues of discrete complete hypergraphs and partitioned hypergraphs. We define positive equivalence relation on hypergraphs that establishes a connection between hypergraphs and graphs. With this regards it makes a connection between spectrum of graphs and spectrum of quotient of any hypergraphs. Finally, this study tries t...

We introduce and investigate central lifting property (CLP) for orthomodular lattices as a property whereby all central elements can be lifted modulo every p-ideal. It is shown that prime ideals, maximal ideals and finite p-ideals have CLP. Also Boolean algebras, simple chain finite orthomodular lattices, subalgebras of an orthomodular lattices gen...

Inspired by the analysis of soft sets and fuzzy sets, in this paper, we study the relevance and interrelationship of the equivalence and congruence relation of lattice ordered fuzzy soft groups(l-FSGs). Moreover, we analyze some of the innate algebraic results accrued out of it theoretically. We construct l-FSG congruence class and l-FSG quotient s...

Nowadays, the most important aspects of wireless sensor networks (WSNs) are to make optimal use of and direct the limited energy of sensor nodes towards the desired application and prolong the network lifetime for that application. Although a few studies exist that have addressed these special goals, they have been mostly focused on the process of...

The main objects of supply chain management are reducing the risk of supply chain and production cost, increasing the income, improving the customer services, optimizing the achievement level and business processes, which would increase the ability, competency, customer satisfaction and profitability. Further, the process of selecting an appropriat...

The aim of this study is to introduce fuzzy filters of Sheffer stroke Hilbert algebra. After defining fuzzy filters of Sheffer stroke Hilbert algebra, it is shown that a quotient structure of this algebra is described by its fuzzy filter. In addition to this, the level filter of a Sheffer stroke Hilbert algebra is determined by its fuzzy filter. So...

In this paper, we introduce the concepts of (internal, external) IVI-octahedron sets, and study some of their properties and give some examples. Also, we define Type $i$-order, Type $i$-intersection, Type $i$-union ($i=1,~2,~3,~4$) and obtain their some properties. Second, we define an IVI-octahedron point and deal with the characterizations of Typ...

In this paper, we introduce Sheffer Stroke UP-algebra (in short, SUP-algebra) and study its properties. We demonstrate that the Cartesian product of two SUP-algebras is a SUP-algebra. After presenting SUP-subalgebras, we define SUP-homomorphisms between SUP-algebras.

Hilbert algebras are important tools for certain investigations in intuitionistic logic and other non-classical logic and as a generalization of Hilbert algebra a new algebraic structure, called a GE-algebra (generalized exchange algebra), is introduced and studied its properties. We consider filters, upper sets and congruence kernels in a GE-algeb...

In this study, some (fuzzy) filters of a Sheffer stroke BL-algebra and its properties are presented. To show a relationship between a filter and a fuzzy filter of Sheffer stroke BL-algebra, we prove that f is a fuzzy (ultra) filter of C if and only if f_{p} is either empty or a (ultra) filter of C for each p in [0, 1], and it is satisfied for p = f...

In this paper, we have introduced the notion of local and semilocal triangle algebras and propose the theorems that characterize these algebraic structures. Additionally, we have established the new properties of these algebraic structures and discussed the relations between local triangle algebras and some interval valued residuated lattice (IVRL)...

We consider pseudofinite MV-algebras. As a main result, we show that an infinite MV-algebra is pseudofinite if and only if it is definably well founded, improving a result of a previous paper. Moreover, we show that the theory of pseudofinite MV-algebras has a partial form of elimination of quantifiers. Further, we show that the class of pseudofini...

We introduce Engel elements in a BCI-algebra by using left and right normed commutators, and some properties of these elements are studied. The notion of $n$-Engel BCI-algebra as a natural generalization of commutative BCI-algebras is introduced, and we discuss Engel BCI-algebra, which is defined by left and right normed commutators. In particular,...

In this paper, at first we study strong Sheffer stroke NMValgebra. For getting more results and some classification, the notions of filters and subalgebras are introduced and studied. Finally, by a congruence relation, we construct a quotient stroong Sheffer stroke NMV-algebra and isomorphism theorems are proved.

In this paper, we focus on investigating some types of (skew) filters such as weak (positive) implicative (skew) filters on pseudo residuated skew lattices and obtain some properties of these (skew) filters. The relationship between these (skew) filters and other types of (skew) filters are discussed. It is shown that any weak positive implicative...

In this paper, pseudo residuated skew lattices are defined as a non-commutative generalization of residuated skew lattices and their properties are investigated. It is shown that the class of all conormal pseudo residuated skew lattices forms a variety under some conditions. Dense, regular and strong elements are studied in a pseudo residuated skew...

The present study aimed to introduce $n$-fold interval valued residuated lattice (IVRL for short) filters in triangle algebras. Initially, the notions of $n$-fold (positive) implicative IVRL-extended filters and $n$-fold (positive) implicative triangle algebras were defined. Afterwards, several characterizations of the algebras were presented, and...

This paper introduces the hypergraphs as complex hyper networks based on codes.
Indeed hypergraphs are securated.

In this paper, at first median algebras and the Yang-Baxter equation are studied, some of their properties are presented. After giving some solutions to the set-theoretical Yang-Baxter equation by using these properties, it is found a solution that is not usually a solution to the set-theoretical Yang-Baxter equation in median algebras but it is th...

In this paper, congruences and (order, prime and compatible) filters are introduced in Sheffer stroke basic algebras. They are interrelated with each other. Also some relationships between filters and congruences by focusing on their properties in these structures are given. In addition to these, a basic algebra is constructed by the help of compat...

In this paper, we introduce a Sheffer stroke Hilbert algebra by giving definitions of Sheffer stroke and a Hilbert algebra.
After it is showed that the axioms of Sheffer stroke Hilbert algebra are independent, it is given some properties of this algebraic
structure. Then it is stated the relationship between Sheffer stroke
Hilbert algebra and Hilbe...

Knowing the applications of logical algebras in various fields, such as artificial intelligence or coding theory, in this paper, we study some properties of a special class of such algebras, namely finite Wajsberg algebras. For this purpose, we give a representation theorem for finite Wajsberg algebras and give a formula for the number of non-isomo...

The notions of (2;2 _q)-cubic p- (a- and q-) ideals of BCI-algebras
are introduced and some related properties are investigated. Several characterizations
for these generalized (2;2 _q)-cubic ideals are defined and relationship
between (2;2 _q)-cubic p-ideals, (2;2 _q)-cubic q-deals and (2;2 _q)-cubic
a-ideals of BCI-algebras are discussed.

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residua...

This paper defines the concept of partitioned hypergraphs, and enumerates the number of these hypergraphs and discrete complete hypergraphs. A positive equivalence relation is defined on hypergraphs, this relation establishes a connection between hypergraphs and graphs. Moreover, we define the concept of (extended) derivable graph. Then...

Graph operations produce new classes of graphs from initial ones which in turn may be useful for the modeling and recognition of computer network designs. A Pythagorean fuzzy set-based model offers more flexibility to cope with human evaluation information as compared to intuitionistic fuzzy model. The main objective of this research study is to ex...