Fuzzy Interior Ideals Research Articles

SUP-Hesitant Fuzzy Interior Ideals in \(\Gamma\)-Semigroups

In this paper, we defined the concept \(\mathcal{SUP}\)-hesitant fuzzy interior ideals in \(\Gamma\)-semigroups, which is generalized of hesitant fuzzy interior ideals in \(\Gamma\)-semigroups. Additionally, we study fundamental properties of \(\mathcal{SUP}\)-hesitant fuzzy interior ideals in \(\Gamma\)-semigroups. Finally, we investigate characterized properties of those.

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.

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 study on ordered AG-groupoids by their fuzzy interior ideals

A study on ordered AG-groupoids by their fuzzy interior ideals

Applications of hesitant fuzzy sets to ternary semigroups

The aim of this paper is to introduce a new concept of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals on ternary semigroups. We extend the concept of fuzzy bi-ideals and fuzzy interior ideals to the context of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals, respectively. Some characterizations of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals are obtained. Moreover, we investigate relationships between hesitant fuzzy ideals and hesitant fuzzy interior ideals on ternary semigroups. Finally, we obtain necessary and sufficient conditions of hesitant fuzzy interior ideal in order to be a hesitant fuzzy ideal.

Anti Fuzzy Interior Ideals on Ordered AG-groupoids

The purpose of this paper is to investigate, the characterizations of different classes of non-associative ordered semigroups by using anti fuzzy left (resp. right, interior) ideals.

A Non-associative Ordered Semigroup Characterizated by Anti fuzzy Interior Ideals

The purpose of this paper is to investigate, the characterizations of different classes of non-associative ordered semigroups by using anti fuzzy left (resp. right, interior) ideals.

On properties of hesitant fuzzy ideals in semigroups

In this paper, we study some properties of hesitant fuzzy ideals and hesitant fuzzy bi-ideals in a semigroup and discuss their characterizations. Also we introduce hesitant fuzzy interior ideals in a semigroup and studied their properties. It is proved that in a semigroup a hesitant fuzzy ideal is a hesitant fuzzy interior ideal but the converse is not true. Moreover we prove that in regular and in intra-regular semigroups the hesitant fuzzy ideals and the hesitant fuzzy interior ideals coincide.

An Innovative Approach towards Possibility Fuzzy Soft Ordered Semigroups for Ideals and Its Application

The objective of this paper is put forward the novel concept of possibility fuzzy soft ideals and the possibility of fuzzy soft interior ideals. The various results in the form of the theorems with these notions are presented and further validated by suitable examples. In modern life decision-making problems, there is a wide applicability of the possibility fuzzy soft ordered semigroup which has also been constructed in the paper to solve the decision-making process. Elementary and fundamental concepts including regular, intra-regular and simple ordered semigroups in terms of possibility fuzzy soft ordered semigroup are presented. Later, the concept of left (resp. right) regular and left (resp. right) simple in terms of possibility fuzzy soft ordered semigroups are delivered. Finally, the notion of possibility fuzzy soft semiprime ideals in an ordered semigroup is defined and illustrated by theorems and example.

New Properties of Anti Fuzzy Ideals of Regular Semigroups

In this article, we study some properties of anti-fuzzy sub-semigroup, anti fuzzy left (right, two sided) ideal, anti fuzzy ideal, anti fuzzy generalized bi-ideal, anti fuzzy interior ideals and anti fuzzy two sided ideal of regular semigroup. Also, we characterized regular LA-semigroup in terms of their anti fuzzy ideal.

Rough approximation of a fuzzy set in semigroups based on soft relations

Binary relations play an important role in both mathematics and information sciences. In this paper, we focus our discussion on a fuzzy set which is approximated in the sense of the aftersets and foresets. To this end, a soft binary relation has been used. A new approach is being introduced to get two sets of fuzzy soft sets, called the lower approximation and upper approximation regarding the aftersets and foresets. We applied these concepts on semigroups and approximations of fuzzy subsemigroups, fuzzy left (right) ideals, fuzzy interior ideals and fuzzy bi-ideals of semigroups are studied.

(λ, µ)− Fuzzy Interior Ideals of Ordered Semirings

(λ, µ)− Fuzzy Interior Ideals of Ordered Semirings

(λ, µ)−fuzzy interior ideals of ordered Γ−semirings

In this paper we introduce the notion of (λ, µ)−fuzzy ideals and (λ, µ)−fuzzy interior ideals of ordered Γ−semiring, for all λ, µ ∈ [0, 1] such that λ < µ. We characterize the regular ordered Γ−semiring and the simple ordered Γ−semiring in terms of (λ, µ)−fuzzy interior ideals.

Bipolar Fuzzy Soft Hyperideals and Homomorphism of Gamma-Hypersemigroups

In this paper, we introduce the concept of bipolar fuzzy soft gamma hyperideals in gamma hyper semigroups. We define bipolar fuzzy soft hyper ideals, bi-ideals and interior ideals of gamma hyper semigroups and discuss some properties.

Generalised roughness in (∈,∈Vq)-fuzzy substructures of LA-semigroups

LA-semigroups are non-associative sturctures of great importance. Study of generalised roughness for fuzzy algebraic substrucures of LA-semigroups has been initiated. Many different kinds of set valued maps are needed to preserve an algebraic substrucure, while considering its lower and upper approximations. In the present paper generalised lower and upper approximations in (ϵ,ϵ Vԛ)- fuzzy ideals of LA-semigroups have been investigated. An (ϵ,ϵ Vԛ)- fuzzy subset of an LA-subsemigroup has two parts, viz. lower and upper parts. Many properties of lower and upper approximations have been given for these. In conclusion, lower and upper approximations for (ϵ,ϵ Vԛ)- fuzzy interior ideals and (ϵ,ϵ Vԛ)- fuzzy bi-ideals have been discussed in LA-semigroups.

Tripolar fuzzy interior ideals of Γ-semigroup

Tripolar fuzzy interior ideals of Γ-semigroup

Generalized roughness in fuzzy filters and fuzzy ideals with thresholds in ordered semigroups

In the present paper, concept of roughness for fuzzy filters with thresholds $$\left( u_{1},u_{2}\right) $$ in ordered semigroups is introduced. Then, this concept is extended to fuzzy bi-filters with thresholds and fuzzy quasi-filters with thresholds. Further approximations of fuzzy ideals with thresholds, fuzzy bi-ideals with thresholds, and fuzzy interior ideals with thresholds are studied. Moreover, this concept is applied to study approximations of fuzzy quasi-ideals with thresholds and semiprime fuzzy quasi-ideals with thresholds.

Some Innovative Types of Fuzzy Ideals in AG-Groupoids

Abstract AG-groupoids (non-associative structure) are basic structures in Flocks theory. This theory mainly focuses on distance optimization, motion replication, and leadership maintenance with a wide range of applications in physics and biology. In this paper, we define some new types of fuzzy ideals of AG-groupoids called (α, β)-fuzzy bi-ideals, (α, β)-fuzzy interior ideals, (β̄, ᾱ)-fuzzy bi-ideals, and (β̄, ᾱ)-fuzzy interior ideals, where α, β∈{∈γ, qδ, ∈γ∨qδ, ∈γ∧qδ} and ᾱ, β̄∈{⋶γ, q̄δ, ⋶γ∨q̄δ, ⋶γ∧q̄δ}, with α≠∈γ∧qδ and β̄≠⋶γ∧q̄δ. An important milestone achieved by this paper is providing the connection between classical algebraic structures (ordinary bi-ideals, interior ideals) and new types of fuzzy algebraic structures [(∈γ, ∈γ∨qδ)-fuzzy bi-ideals, (∈γ, ∈γ∨qδ)-fuzzy interior ideals]. Special attention is given to (∈γ, ∈γ∨qδ)-fuzzy bi-ideals and (⋶γ, ⋶γ∨q̄δ) -fuzzy bi-ideals.

Classification of Ordered Semigroups in Terms of Generalized Interval-Valued Fuzzy Interior Ideals

AbstractSeveral applied fields dealing with decision-making process may not be successfully modeled by ordinary fuzzy sets. In such a situation, the interval-valued fuzzy set theory is more applicable than the fuzzy set theory. Using a new approach of “quasi-coincident with relation”, which is a central focused idea for several researchers, we introduced the more general form of the notion of (α,β)-fuzzy interior ideal. This new concept is called interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal of ordered semigroup. As an attempt to investigate the relationships between ordered semigroups and fuzzy ordered semigroups, it is proved that in regular ordered semigroups, the interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy ideals and interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals coincide. It is also shown that the intersection of non-empty class of interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideals of an ordered semigroup is also an interval-valued$( \in ,{\rm{ }} \in \; \vee \;{{\rm{q}}_{\tilde k}})$-fuzzy interior ideal.