Fuzzy subnear-semirings and fuzzy soft subnear-semirings

Taouti, Abdelghani; Khan, Waheed Ahmad

doi:10.3934/math.2021137

Cited by 3 publications

(1 citation statement)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The notion of (α, β)soft intersectional rings and ideals along with their applications have been explored in [22]. Recently, the notions of fuzzy sub-nearsemirings and fuzzy soft sub-nearsemirings [23] have been initiated by both the authors. In a sequel, we introduce and discuss the notions of soft sub-nearsemirings, soft ideals and soft S-subsemigroups of a nearsemiring S. We also provide few characterizations of distributively generated nearsemirings in the frame of the soft sets theory.…”

Section: Introductionmentioning

confidence: 99%

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Khan

Taouti

2022

IJFIS

View full text Add to dashboard Cite

In this note, we introduce and discuss the notions of soft sub-nearsemirings, soft ideals and soft S-subsemigroups of nearsemirings. Some related properties and characterizations of these soft algebraic structures are discussed with illustrative examples. For the sake of investigations, we apply several operations of soft sets including soft intersection sum, soft product and soft uniint product. Based on these operations, we also discuss few characterizations of distributively generated nearsemirings. In due course, we investigate few relationships among these soft algebraic structures and the classical nearsemirings. We also introduce the notion of soft ideals (left and right) of nearsemirings. Firstly, we investigate these ideals by applying few operations on them. Then, we present the relationship between these soft ideals of nearsemiring with the classical ideals of nearsemirings. Moreover, we introduce the notion of soft S-homomorphism between two soft S-subsemigroups and investigate that the homomorphic image of soft S-subsemigroup is a soft S-subsemigroup. Throughout, we shift several substructures of nearsemirings towards the soft algebraic substructures of nearsemirings by utilizing different algebraic methods. Consequently, we explore a linkage among the soft set theory, classical set theory and nearsemiring theory. Mainly, our study is the interplay between soft substructures of nearsemirings and classical substructures of nearsemirings.

show abstract

Section: Introductionmentioning

confidence: 99%

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Khan

Taouti

2022

IJFIS

View full text Add to dashboard Cite

show abstract

Generalized fuzzy ideals in ordered semirings

Muhiuddin

Mahboob²,

Abughazalah

2022

Complex Intell. Syst.

View full text Add to dashboard Cite

In this paper, we introduce the concepts of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$ ( ∈ , ∈ ∨ ( κ ∗ , q κ ) ) -fuzzy left (right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$ ( ∈ , ∈ ∨ ( κ ∗ , q κ ) ) -fuzzy ideals in ordered semirings. Some correspondence between (left, right) ideals and $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$ ( ∈ , ∈ ∨ ( κ ∗ , q κ ) ) -fuzzy (left, right) ideals of ordered semirings are presented. Moreover, the notion of $$(\kappa ^*,\kappa )$$ ( κ ∗ , κ ) -lower part of $$(\in ,\in \vee (\kappa ^*,q_\kappa ))$$ ( ∈ , ∈ ∨ ( κ ∗ , q κ ) ) -fuzzy (left, right) ideals is defined and characterizations of different classes of ordered semirings are given.

show abstract

Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications

Zhu,

Liu

2023

MATH

View full text Add to dashboard Cite

<abstract><p>Picture fuzzy sets (PFSs) are a versatile generalization of fuzzy sets and intuitionistic fuzzy sets (IFSs), providing a robust framework for modeling imprecise, uncertain, and inconsistent information across various fields. As an advanced extension of PFSs, interval-valued picture fuzzy sets (IvPFSs) offer superior capabilities for handling incomplete and indeterminate information in various practical applications. Distance measures have always been an important topic in fuzzy sets and their variants. Some existing distance measures for PFSs have shown limitations and may yield counterintuitive results under certain conditions. Furthermore, there are currently few studies on distance measures for IvPFSs. To solve these problems, in this paper we devised a series of novel distance measures between PFSs and IvPFSs inspired by the Hellinger distance. Specifically, all the distance measures were divided into two parts: One considered the positive membership degree, neutral membership degree and negative membership degree, and the other added the refusal membership degree. Moreover, the proposed distance measures met some important properties, including boundedness, non-degeneracy, symmetry, and consistency, but also showed superiority compared to the existing measures, as confirmed through numerical comparisons. Finally, the proposed distance measures were validated in pattern recognition and medical diagnosis applications, indicating that the proposed distance measures can deliver credible, reasonable results, particularly in similar cases.</p></abstract>

show abstract

Fuzzy subnear-semirings and fuzzy soft subnear-semirings

Cited by 3 publications

References 25 publications

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Soft Sub-nearsemirings, Soft Ideals and Soft S-Subsemigroups of Nearsemirings

Generalized fuzzy ideals in ordered semirings

Distance measures of picture fuzzy sets and interval-valued picture fuzzy sets with their applications

Contact Info

Product

Resources

About