Pythagorean Fuzzy N-Soft Groups

Hameed, Muhammad Shazib; Mukhtar, Salman; Nawaz, Khan, Haq; Ali, Shahbaz; Mateen, M. Haris; Gulzar, Muhammad

doi:10.11591/ijeecs.v21.i2.pp1030-1038

Cited by 5 publications

(2 citation statements)

References 19 publications

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“…In upcoming research, to utilize some new ideas and operators, we will review the theory of complex intuitionistic fuzzy soft sets [28], complex spherical fuzzy sets [29], linear Diophantine fuzzy information [30,31], fuzzy N-soft sets [32], complex Pythagorean fuzzy N-soft sets [33], spherical fuzzy N-soft expert sets [34], and decision making [3,31,[35][36][37], which are very important extensions in the field of fuzzy sets and their generalizations.…”

Section: Future Directionsmentioning

confidence: 99%

Aggregation Operators Based on Algebraic t-Norm and t-Conorm for Complex Linguistic Fuzzy Sets and Their Applications in Strategic Decision Making

2022

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Aggregation operators perform a valuable and significant role in various decision-making processes. Averaging and geometric aggregation operators are both used for capturing the interrelationships of the aggregated preferences, even if the preferences are independent. The purpose of this paper is to analyze the theory of complex linguistic fuzzy (CLF) sets and their important laws, such as algebraic laws, score values, and accuracy values, and to describe the relationship between the score and accuracy values with the help of their properties. Additionally, based on the proposed CLF information, we introduce the theory of CLF weighted averaging (CLFWA), CLF ordered weighted averaging (CLFOWA), CLF hybrid averaging (CLFHA), CLF weighted geometric (CLFWG), CLF ordered weighted geometric (CLFOWG), and CLF hybrid geometric (CLFHG) operators. The fundamental properties and some valuable results of these operators are evaluated, and their particular cases are described. Based on the presented operators, a technique for evaluating the “multi-attribute decision-making” (MADM) problems in the consideration of CLF sets is derived. The superiority of the derived technique is illustrated via a practical example, a set of experiments, and significant and qualitative comparisons. The illustration results indicate that the derived technique can be feasible and superior in evaluating CLF information. Further, it can be used for determining the interrelationships of attributes and the criteria of experts. Moreover, it is valuable and capable of evaluating the MADM problems using CLF numbers.

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Section: Future Directionsmentioning

confidence: 99%

Aggregation Operators Based on Algebraic t-Norm and t-Conorm for Complex Linguistic Fuzzy Sets and Their Applications in Strategic Decision Making

2022

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“…Later on, Athira et al [4,5] studied the entropy and distance measure of PFSS. Recently, topological and group structures on PFSS are introduced and that can be seen in [25,13] also Athira and Sunil proposed the incomplete PFSS [3].…”

Section: Introductionmentioning

confidence: 99%

Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

2022

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Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure.

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

Bashir,

Alharbi,

Mazhar

et al. 2024

Sci Rep

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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.

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Pythagorean Fuzzy N-Soft Groups

Cited by 5 publications

References 19 publications

Aggregation Operators Based on Algebraic t-Norm and t-Conorm for Complex Linguistic Fuzzy Sets and Their Applications in Strategic Decision Making

Aggregation Operators Based on Algebraic t-Norm and t-Conorm for Complex Linguistic Fuzzy Sets and Their Applications in Strategic Decision Making

Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

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

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