Fuzzy Bi-ideals Research Articles

Normed-Bifuzzy Valued-Ideals of Semigroups

As concerning the views of T norms and T conorms, the intent of article is to define and probe the fuzzy semigroups, fuzzy ideals, fuzzy bi-ideals, bifuzzy subsemigroups, bifuzzy ideals, bifuzzy bi-ideals, fuzzy (1, 2)-ideals and bifuzzy (1, 2)-ideals in any given semigroup. Also, we indicate and study their basic properties of them in completely regular semigroups. Finally, we extend these concepts and so characterize (pre)image of them in semigroup homomorphisms.

Ordered semihyperrings characterized in terms of multipolar fuzzy hyperideals

In recent years, the m-polar fuzziness structure has attracted the attention of researchers and has been commonly applied in algebraic structures. In this article, we present the notion of multi-polar fuzzy hyperideals of ordered semihyperrings, which is a generalization of the concept of bi-polar fuzzy hyperideals of ordered semihyperrings. We investigate some of their associated properties. Furthermore, we characterized regular ordered semihyperring in terms of multi-polar fuzzy quasi-ideals and multi-polar fuzzy bi-ideals.

An efficient approach to study multi-polar fuzzy ideals of semirings

The multi polar fuzzy (m-PF) set has an extensive range of implementations in real world problems related to the multi-polar information, multi-index and multi-attributes data. This paper introduces innovative extensions to algebraic structures. We present the definitions and some important results of m-polar fuzzy subsemirings (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings. The main contributions of the paper include the derivation and proof of key theorems that shed light on the algebraic interplay and computational aspects of m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs) and m-polar fuzzy quasi-ideals (m-PFQIs) in semirings along with examples. Moreover, this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semirings by the properties of these ideals.

Hybrid Nil Rapid Fuzzy Bi-Ideals of Near Rings

In this paper, our mains focus is on exploring the concept of hybrid nil rapid fuzzy bi-ideals of near rings, including an investigation of their properties. We also delve into the hybrid intrinsic product of these bi-ideals and establish relevant theorems. Our contribution lies in advancing the field of hybrid nil rapid fuzzy bi-ideals in near rings by deepening our understanding of these concepts.

A Novel Study of Fuzzy Bi-Ideals in Ordered Semirings

In this study, by generalizing the notion of fuzzy bi-ideals of ordered semirings, the notion of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is established. We prove that (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are fuzzy bi-ideals but that the converse is not true, and an example is provided to support this proof. A condition is given under which fuzzy bi-ideals of ordered semirings coincide with (∈,∈∨(κ*,qκ))-fuzzy bi-ideals. An equivalent condition and certain correspondences between bi-ideals and (∈,∈∨(κ*,qκ))-fuzzy bi-ideals are presented. Moreover, the (κ*,κ)-lower part of (∈,∈∨(κ*,qκ))-fuzzy bi-ideals is described and depicted in terms of several classes of ordered semirings. Furthermore, it is shown that the ordered semiring is bi-simple if and only if it is (∈,∈∨(κ*,qκ))-fuzzy bi-simple.

Some Studies of Multi-Polar Fuzzy Ideals in LA-Semigroups

This article’s main goal is to investigate the concept of multi-polar fuzzy sets (MPF-sets) in LA-semi-groups, which is an extension of bi-polar fuzzy sets (BPF-sets) in LA-semigroups. The main objective of this research is to extend certain significant BPF-set results to MPF-sets results. This article introduces the concepts of multi-polar fuzzy sub LA-semigroups, multi-polar fuzzy quasi-ideals, multi-polar fuzzy bi-ideals, multi-polar fuzzy generalized bi-ideals, and multi-polar fuzzy interior ideals in LA-semigroups. This article also discusses a number of fundamental aspects of multi-polar fuzzy ideals, and we use these aspects to define regular LA-semigroups.

Fuzzy Right (Left) Ideals in Hypergroupoids and Fuzzy Bi-ideals in Hypersemigroups

Most of the results on semigroups or ordered semigroups can be transferred to hypersemigroups or to ordered hypersemigroups, respectively. The same, if we replace the word "semigroup" by "groupoid", "hypersemigroup" by "hypergroupoid". We show the way we pass from fuzzy ordered semigroups to fuzzy hypersemigroups.

Some essential bi-ideals and essential fuzzy bi-ideals in a semigroup

In this paper, we give the concepts of essential bi-ideals and essential fuzzy bi-ideals in semigroups. In the main results, we characterized regular, left regular, intra-regular, semisimple semigroups in terms of essential fuzzy ideals and essential fuzzy bi-ideals in semigroups.

A new method to evaluate regular ternary semigroups in multi-polar fuzzy environment

<abstract> <p>Theory of $m$-polar fuzzy set deals with multi-polar information. It is used when data comes from $m$ factors $\left({m \ge 2} \right)$. The primary objective of this work is to explore a generalized form of $m$-polar fuzzy subsemigroups, which is $m$-polar fuzzy ternary subsemigroups. There are many algebraic structures which are not closed under binary multiplication that is a reason to study ternary operation of multiplication such as the set of negative integer is closed under the operation of ternary multiplication but not closed for the binary multiplication. This paper, presents several significant results related to the notions of $m$-polar fuzzy ternary subsemigroups, $m$-polar fuzzy ideals, $m$-polar fuzzy generalized bi-ideals, $m$-polar fuzzy bi-ideals, $m$-polar fuzzy quasi-ideals and $m$-polar fuzzy interior ideals in ternary semigroups. Also, it is proved that every $m$- polar fuzzy bi-ideal of ternary semigroup is an $m$-polar fuzzy generalized bi-ideal of ternary semigroup but converse is not true in general. Moreover, this paper characterizes regular and intra-regular ternary semigroups by the properties of $m$-polar fuzzy ideals, $m$-polar fuzzy bi-ideals.</p> </abstract>

Regular and Intra-Regular Semigroups in Terms of m-Polar Fuzzy Environment

The central objective of the proposed work in this research is to introduce the innovative concept of an m-polar fuzzy set (m-PFS) in semigroups, that is, the expansion of bipolar fuzzy set (BFS). Our main focus in this study is the generalization of some important results of BFSs to the results of m-PFSs. This paper provides some important results related to m-polar fuzzy subsemigroups (m-PFSSs), m-polar fuzzy ideals (m-PFIs), m-polar fuzzy generalized bi-ideals (m-PFGBIs), m-polar fuzzy bi-ideals (m-PFBIs), m-polar fuzzy quasi-ideals (m-PFQIs) and m-polar fuzzy interior ideals (m-PFIIs) in semigroups. This research paper shows that every m-PFBI of semigroups is the m-PFGBI of semigroups, but the converse may not be true. Furthermore this paper deals with several important properties of m-PFIs and characterizes regular and intra-regular semigroups by the properties of m-PFIs and m-PFBIs.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

Characterisations of semigroups by the properties of their picture fuzzy bi-ideals

In this article, a new generalisation of fuzzy bi-ideals and intuitionsitic fuzzy bi-ideals of a semigroup considered so called picture fuzzy bi-ideals no a semigroup. It is well known that the intra-regular semigroups play an essential role in studying the structure, especially the decomposition, of semigroups. The purpose of this paper is to deal with the algebraic structure of semigroups by applying picture fuzzy set theory. As an application of our results we get characterisations of intra-regular regular semigroups in terms of picture fuzzy bi-ideals. We prove that a semigroup is both regular and intra-regular if and only if every picture fuzzy bi-ideal on is idempotent.

Fuzzy Bi-Ideals of Near-Rings

In this paper, we introduced the concept of - fuzzy bi-ideals and - fuzzy bi-ideals of a near-ring. Some new characterizations are also given. In particular, homomorphic behaviour of- fuzzy bi-ideals are also discussed. New type of fuzzy bi-ideals of near rings is also introduced.

Hybrid Fuzzy Bi-Ideals In Near-Rings

In this paper, we introduce the concept of hybrid fuzzy bi-ideals in near rings and give some characterizations of hybrid fuzzy bi-ideals in near rings.

SEMIGROUPS IN TERMS OF INTUITIONISTIC FUZZY BI-IDEALS

Since Zadeh introduced fuzzy sets in 1965, a lot of new theories treating imprecision and uncertainty have been introduced. Some of these theories are extensions of fuzzy set theory. The concept of 'intuitionistic fuzzy set' (IFS) was introduced by Atanassov as a generalization of the concept fuzzy set by gives both a degree of membership and the degree of non-membership. As for fuzzy sets, the degree of membership is a real number between 0 and 1. This is also the case for the degree of non-membership, and further the sum of these two degrees is not greater than 1. Since fuzzy bi-ideal play an important role in the study of semigroup structures. The purpose of this paper is to initiate and study the intuitionistic fuzzification on the concept of several ideals in a semigroups S and investigate the basic theorem of intuitionistic fuzzy bi-ideals and discuss the relationships of left (resp. right and completely regular) semigroups in terms of intuitionistic fuzzy biideals. For any homomorphisim f from a semigroup S to semigroup T if B= (μB , VB) is an intuitionistic fuzzy bi-ideal of T, then the preimage f-1(B) = (f-1(μB),f-1(VB)) of B under f is an intuitionistic fuzzy bi-ideal of semigroup S.

Prime Fuzzy Bi-Ideals in Near-Subtraction Semigroups

A study on fuzzy prime ideals in near-subtraction semigroups is already known. We have to expand the concept of prime fuzzy bi-ideals in near-subtraction semigroups and analyse some of its properties to characterize it. This will lead to learn a new type of fuzzy ideal and to develope the researcher to made their research.

Prime Fuzzy Bi-Ideals in Near-Subtraction Semigroups

A study on fuzzy prime ideals in near-subtraction semigroups is already known. We have to expand the concept of prime fuzzy bi-ideals in near-subtraction semigroups and analyse some of its properties to characterize it. This will lead to learn a new type of fuzzy ideal and to develope the researcher to made their research.

CHARACTERIZATION OF ORDERED SEMIGROUPS BASED 0N (|;qk)-QUASI-COINCIDENT WITH RELATION

Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals.

A remark on hesitant fuzzy ideals in ordered semigroups

We investigate the concept of hesitant fuzzy sets. This concept is a generalized notion of fuzzy sets. The concept of fuzzy sets can be applied to the study of ordered semigroups. It is well-known that in regular ordered semigroups, any fuzzy bi-ideal and fuzzy quasi-ideal coincide. In this paper, we illustrate that this fact does not hold for hesitant fuzzy sets. Furthermore, we provide an example illustrating that in a regular ordered semigroup, there is a hesitant fuzzy bi-ideal which is not a hesitant fuzzy quasi-ideal. Moreover, we present a class of hesitant fuzzy sets in which hesitant fuzzy bi-ideals and hesitant fuzzy quasi-ideals coincide.

Generalized Hesitant Fuzzy Ideals in Semigroups

In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals (resp. 0 , n -ideals) are introduced. Furthermore, conditions for a hesitant fuzzy m , n -ideal ( m , 0 -ideal, 0 , n -ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy m , n -ideals ( m , 0 -ideals, 0 , n -ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy m , n -ideals and hesitant fuzzy m , 0 -ideals ( 0 , n -ideals) are investigated.