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## Publications

Publications (660)

Many uncertainties arise in real-world problems, making them impossible to solve using conventional approaches. Researchers all over the world have developed new mathematical theories like fuzzy set theory and rough set theory to better understand the uncertainties that occur in various fields. Soft set theory, which was recently introduced, offers...

We study the lattice structure of fuzzy A-ideals in an mv-module M (fai (M), symbolically) and show that it is a complete Heyting lattice and so the set of its pseudocomplements forms a Boolean algebra. In the sequel, the properties of fuzzy congruences in an mv-module are investigated and using them some structural theorems are stated and proved....

In this paper, we establish some equivalent conditions for a semigroup to be regular and intra-regular, in terms of hybrid ideals and hybrid bi-ideals. We also characterize the left and right simple and the completely regular semigroups utilizing hybrid ideals and hybrid bi-ideals. We show that a semigroup S is left simple if and only if it is hybr...

With the aim of applying the Dokdo structure to BE-algebra, the notions of (weak) Dokdo BE-subalgebra and Dokdo BE-filter are introduced, and their properties are investigated. The relationship between weak Dokdo BE-subalgebra, Dokdo BE-subalgebra and Dokdo BE-filter is established. The conditions under which Dokdo structure can be weak Dokdo BE-su...

The concept of a positive implicative makgeolli ideal in BCK-algebras is introduced, and its properties are investigated. The relationship between a makgeolli ideal and a positive implicative makgeolli ideal is established. The conditions under which a makgeolli ideal can be a positive implicative makgeolli ideal are explored. Characterizations of...

The scheme of rough sets is an effective procedure that handle ambiguous, inexact or uncertain information configuration. Rough set theory for algebraic structures like semigroups is a formal approximation space consisting of a universal set and an equivalence relation. This article achieves a new utilization of rough sets in the theory of semigrou...

The notion of (right) left mapping on equality algebras is introduced, and related properties are investigated. In order for the kernel of (right) left mapping to be filter, we investigate what conditions are required. Relations between left mapping and →-endomorphism are investigated. Using left mapping and →-endomorphism, a characterization of po...

In this paper, our aim was making a metric space on hoop algebras, because of that, we introduced the notion of valuation maps from F-quasi-valuation map based on hoops and related properties of them are investigated. By using these notions, we introduced a quasi-metric space. The continuity of operations of a hoop is studied with topology induced...

The aim of this paper is to define the concept of makgeolli structures on hoops. For this aim, we use the notions and results in fuzzy and soft set theory and apply them to hoops.
Then, we introduce the notion of makgeolli algebra and makgeolli filter in hoops and study
some properties of them. Some equivalence definitions of makgeolli filter and s...

In this paper, the notions of maximal GE-filter and prime GE-filter of a GE-algebra are introduced and the relation between them is given. Some characterizations of prime GE-filters of a transitive GE-algebra are given in terms of the GE-filter generated by a subset of a transitive GE-algebra. We generalized Stone’s theorem to transitive GE-algebra...

In this paper, the notions of normal m-dominating set, normal m-domination number, inverse normal domination set (number) and inverse normal m-domination number are introduced, and some the related results are investigated. Finally, a utilization relevant to decision-making based on influencing factors the company’s efficiency is presented.

In this paper, the notions of ideals in NBCK-algebras are presented and some properties of such ideals are analyzed. Essentially, our approach is to define NBCK-algebras of all cosets by considering an operation on the set of all cosets defined via ideals. Afterwards, our aim is to study ideal theorems on NBCK-algebras.

We define the notions of annihilators in hoops and study some related attributes of them, and we show that annihilators are ideals of hoop. In addition, we show that all ideals of hoop are a bounded distributive pseudo-complement lattice, and we use this result and demonstrate that the collection of all annihilators of hoop is a Boolean algebra. Al...

For the purpose of applying the concept of Lukasiewicz fuzzy set to ideals in BE-algebras, Lukasiewicz fuzzy ideal is introduced, and its properties are studied. The relationship between fuzzy ideal and Lukasiewicz fuzzy ideal is discussed. Conditions for the Lukasiewicz fuzzy set to be a Lukasiewicz fuzzy ideal are provided, and characterizations...

By applying the concept of Lukasiewicz fuzzy set to BE-algebras, the notions of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are introduced, and their properties are investigated. Characterizations of Lukasiewicz fuzzy BE-algebra and Lukasiewicz fuzzy BE-filter are discussed, and the relationship between fuzzy BE-algebra (resp., fuz...

In this paper, we study the intuitionistic (T, S)−fuzzy ideals of a nearring and investigate some of their properties. Some of the recent results obtained by S. D. Kim and S. K. Kim in 1996 on fuzzy ideals of nearrings are generalized. For a intuitionistic (T, S)−fuzzy ideal A = (µ A , λ A) of a nearring R, we prove a normalization theorem for such...

The concept of forceable weak eGE-algebras is introduced, and its associated properties are investigated. The structure of GE-filters in the GE-algebras derived from weak eGE-algebras is discussed. The relationship between an eGE-algebra and a forceable weak eGE-algebra is considered, and the characterization of an eGE-filter in weak eGE-algebras i...

In general, models of universe problems in almost all fields, such as engineering, mathematics, medical sciences, computer science, physics, management sciences, artificial intelligence, and operations research, are practically full of complexities and include various types of uncertainties when dealing with them on numerous occasions. Different th...

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.

Recently, in Borzooei et al. [Inverse fuzzy graphs with applications, to appear in New Mathematics and Natural Computation], we defined the concept of inverse fuzzy graph as a generalization of graph, which is able to answer some problems that graph theory and fuzzy graph theory cannot explain. Now, in this paper, we define the notions of dominatin...

We are fully aware that an ordered semigroup has a very close relation with theoretical computer science, especially with the theory of pattern recognition, decision processes, artificial intelligence, information retrieval and so on. We are eager to introduce the new concepts of hybrid interior ideals and hybrid simple in an ordered semigroup in t...

The notions of an interior GE-filter, a weak interior GE-filter and a belligerent interior GE-filter are introduced, and their relations and properties are investigated. Example of a GE-filter which is neither an interior GE-filter nor a weak interior GE-filter is provided. Relations between a weak interior GE-filter and an interior GE-filter are d...

First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra, and several properties are investigated. The relationship between crossing cubic ideal and commutat...

The concept of a neutrosophic set, which is a generalization of an intuitionistic fuzzy set and a para consistent set etc., was introduced by F. Smarandache. Since then, it has been studied in various applications. In considering a generalization of the neutrosophic set, Mohseni Takallo et al. used the interval valued fuzzy set as the indeterminate...

As a generalization of BE-algebras, the pseudo BE-algebra was introduced by Borzooei et al., and the notions of pseudo subalgebras and pseudo filters in pseudo BE-algebras were defined, and some related properties were investigated. In order to further study pseudo subalgebras and pseudo filters in pseudo BE-algebras, concepts of pseudo atom, atomi...

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 notion of DFS-filter (double-framed soft filter) in lattice implication algrebras is introduced and characteristics of DFS-filters are discussed and related result are investigated. We defined IDFS-filter (implicative double-framed soft filter) and extension property for IDFS-filters is established. We made PIDFS-filter (positive implicative do...

The concept of a (strong) set-valued BCK/BCI-morphism in BCK/BCI-algebras is considered, and several properties are investigated. Conditions for a set-valued mapping to be a set-valued BCK/BCI-morphism are given. Using the concept of generalized approximation space, generalized rough subalgebra (ideal) in BCK/BCI-algebras are introduced, and invest...

The concept of a hybrid structure in X -semimodules, where X is a semiring, is introduced in this paper. The notions of hybrid subsemimodule and hybrid right (resp., left) ideals are defined and discussed in semirings. We investigate the representations of hybrid subsemimodules and hybrid ideals using hybrid products. We also get some interesting r...

In this paper, the concept of an implicative equality algebra is defined and related properties are investigated. Characterizations of an implicative equality algebra and the relation among implicative and positive implicative equality algebras are discussed. Also, we define the notion of annihilator of equality algebras and investigate some traits...

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...

The concept of a prominent interior GE-filter (of type 1 and type 2) is introduced, and their properties are investigated. The relationship between a prominent GE-filter and a prominent interior GE-filter and the relationship between an interior GE-filter and a prominent interior GE-filter are discussed. Examples to show that any interior GE-filter...

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...

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...

The notion of an m-polar \((\in ,\) \(\in )\)-fuzzy a-ideal is introduced, and its properties are investigated. The relationship between m-polar fuzzy subalgebra, m-polar fuzzy ideal, and m-polar \((\in ,\) \(\in )\)-fuzzy a-ideal is examined. Conditions for an m-polar fuzzy ideal to be an m-polar \((\in ,\) \(\in )\)-fuzzy a-ideal are provided. Th...

In this paper, we define the notions of intuitionistic fuzzy filters and intuitionistic fuzzy implicative (positive implicative, fantastic) filters on hoops. Then we show that all intuitionistic fuzzy filters make a bounded distributive lattice. Also, by using intuitionistic fuzzy filters we introduce a relation on hoops and show that it is a congr...

In this article, we give a number of important properties of meet-commutative UP-algebras. In the class of these UP-algebras, we introduce and analyze the concepts of prime and irreducible UP-filters.

The MBJ-neutrosophic set is applied to the implicative ideal of BCK-algebra to introduce the concept of implicative MBJ-neutrosophic ideal. Several properties are investigated. The relationship between implicative MBJ-neutrosophic ideal and each MBJ-neutrosophic subalgebra, (positive implicative, commutative) MBJ-neutrosophic ideal is established....

In this article, a new idea of BMBJ-neutrosophic hyper-BCK-algebras is introduced and some of its properties are investigated. Here, BMBJ-neutrosophic hyper-BCK-ideal, BMBJ-neutrosophic weak hyper-BCK-ideal, BMBJ-neutrosophic s-weak hyper-BCK-ideal, and BMBJ-neutrosophic strong hyper-BCK-ideal are presented, and some relevant results and relations...

The notion of commutative MBJ-neutrosophic ideal is introduced, and several properties are investigated. Relations between MBJ-neutrosophic ideal and commutative MBJ-neutrosophic ideal are considered. Characterizations of commutative MBJ-neutrosophic ideal are discussed.

The notion of strong GE-filters and GE-ideals (generated) is introduced, and the related properties are investigated. The intersection of strong GE-filters (resp., GE-ideals) is proved to be a strong GE-filter (resp., GE-ideal), and the union of strong GE-filters (resp., GE-ideals) is generally not a strong GE-filters (resp., GE-ideal) by example....

In this paper, we want to investigate some theorems about [Formula: see text]-cubic sets in [Sh. Rashid, M. Gulistan, Y. B. Jun, S. Khan and S. Kadry, [Formula: see text]-cubic sets and aggregation operators, J. Intell. Fuzzy Syst. 37(4) (2019) 5009–5023] and while correcting these theorems, we get new results in this issue and at the end we presen...

UP-algebra was introduced by Iampan 2017 as a generalization of KU-algebra. In such logical-algebraic structures, many types of UP-filters have been introduced and analyzed in 2019, such as implicative, comparative, allied and shift UP-filters by Iampan and Jun. Also, the concept of weak implicative UP-filters was introduced in 2020 by Romano and J...

UP-algebra was introduced by Iampan 2017 as a generalization of KU-algebra. In such logical-algebraic structures, many types of UP-filters have been introduced and analyzed in 2019, such as implicative, comparative, allied and shift UP-filters by Iampan and Jun. Also, the concept of weak implicative UP-filters was introduced in 2020 by Romano and J...

Given a set [Formula: see text], conditions for the neutrosophic quadruple [Formula: see text]-set to be a (positive implicative) neutrosophic quadruple [Formula: see text]-algebra are considered. The notion of (positive implicative) neutrosophic quadruple ideal is introduced, and the extended neutrosophic quadruple [Formula: see text]-algebra is e...

A characterization of cubic subalgebra is established. The notion of internal and external cubic subalgebra in BCK/BCI-algebra and several properties are investigated. The R-union, R-intersection, P-union, and P-intersection of internal and external cubic subalgebras in BCK/BCI-algebra are discussed.

The notion of a [Formula: see text]-polar [Formula: see text] [Formula: see text]-fuzzy [Formula: see text]-ideal is introduced, and its properties are investigated. The relationship between [Formula: see text]-polar fuzzy subalgebra, [Formula: see text]-polar fuzzy ideal, and [Formula: see text]-polar [Formula: see text] [Formula: see text]-fuzzy...

Relations between a transitive GE-algebra, a belligerent GE-algebra, an antisymmetric GE-algebra, and a left exchangeable GE-algebra are displayed. A new substructure, so called imploring GE-filter, is introduced, and its properties are investigated. The relationship between a GE-filter, an imploring GE-filter, a belligerent GE-filter, and a promin...

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 concepts of (commutative, transitive, left exchangeable, belligerent, antisymmetric) interior GE-algebras and bordered interior GE-algebras are introduced, and their relations and properties are investigated. Many examples are given to support these concepts. A semigroup is formed using the set of interior GE-algebras. An example is given that...

The falling shadow theory is applied to subhoops and filters in hoops. The notions of falling fuzzy subhoops and falling fuzzy filters in hoops are introduced, and several properties are investigated. Relationship between falling fuzzy subhoops and falling fuzzy filters are discussed, and conditions for a falling fuzzy subhoop to be a falling fuzzy...

Fuzzy soft positive implicative hyper BCK-ideal of types (<<,≤,≤), (<<,<<,≤) and (≤,<<,≤) are introduced, and their relations are investigated. Relations between fuzzy soft strong hyper BCK-ideal and fuzzy soft positive implicative hyper BCK-ideal of types (<<,≤,≤) and (<<,<<,≤) are discussed. We prove that the level set of fuzzy soft positive impl...

Using the belongs to relation (∈) and quasi-coincident with relation (q) between fuzzy points and fuzzy sets, the notions of an (∈, ∈)- fuzzy sub-hoop, an (∈, ∈ ∨ q)-fuzzy sub-hoop and a (q, ∈ ∨ q)-fuzzy sub- hoop are introduced, and several properties are investigated. Characterizations of an (∈, ∈)-fuzzy sub-hoop and an (∈, ∈ ∨ q)-fuzzy sub-hoop...

The concept of an imploring interior GE-filter is introduced, and their properties are investigated. The relationship between an interior GE-filter and an imploring interior GE-filter are discussed. Example to show that any interior GE-filter is not an imploring interior GE-filter is provided. Conditions for an interior GE-filter to be an imploring...

Your article is protected by copyright and all rights are held exclusively by The National Academy of Sciences, India. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may furth...

1 2 3 Your article is protected by copyright and all rights are held exclusively by The National Academy of Sciences, India. This e-offprint is for personal use only and shall not be self-archived in electronic repositories. If you wish to self-archive your article, please use the accepted manuscript version for posting on your own website. You may...

The notions of (implicative) soju filters in a hoop algebra are introduced, and related properties are investigated. Relations between a soju sub-hoop, a soju filter and an implicative soju filter are discussed. Conditions for a soju filter to be implicative are displayed, and characterizations of an implicative soju filters are considered. The ext...

Given i, j, k ∈ {1, 2, 3, 4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebra...

The generalization of N-structure is introduced first and then applied to BCH-algebra for research. The concepts of k-folded N-subalgebra, k-folded N-closed ideal and (closed) k-folded N-filter are introduced, and then their relations and several properties are investigated. Conditions for the k-folded N-subalgebra to be k-folded N-closed ideal are...

Given i, j, k ∈ {1, 2, 3, 4}, the notion of (i, j, k)-length neutrosophic subalgebras in BCK/BCI-algebras is introduced, and their properties are investigated. Characterizations of length neutrosophic subalgebras are discussed by using level sets of interval neutrosophic sets. Conditions for level sets of interval neutrosophic sets to be subalgebra...

The notions of (quasi, pseudo) star-shaped sets are introduced, and several related properties are investigated. Characterizations of (quasi) star-shaped sets are considered. The translation of (quasi, pseudo) star-shaped sets are discussed. Unions and intersections of quasi star-shaped sets are conceived. Conditions for a quasi (or, pseudo) star-s...

In this paper, we define the notions of i-octahedron groupoid and i-OLI [resp., i-ORI and i-OI], and study some of their properties and give some examples. Also we deal with some properties for the image and the preimage of i-octahedron groupoids [resp., i-OLI, i-ORI and i-OI] under a groupoid homomorphism. Next, we introduce the concepts of i-octa...