Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

Abstract

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.

Prioritization of thermal energy storage techniques based on Einstein-ordered aggregation operators of q-rung orthopair fuzzy hypersoft sets

“…They also introduced the Einstein-ordered geometric operator and used it to establish the MAGDM technique (Zulqarnain et al, 2022b). Athira et al (2022) extended SMs for PFSSs with fundamental results and used their developed similarity measures for clustering analysis. Hussain et al (2020) expanded the PFSS to a q-ROFSS and developed the AOs based on algebraic operational laws.…”