A similarity measure under Pythagorean fuzzy soft environment with applications

A novel similarity measure (SM) based upon cosine similarity measure and Frobenius inner product of matrices, and a weighted SM for Pythagorean fuzzy soft sets (PFS-sets/PFSSs) are coined in this article. Some fundamental characteristics of the proposed SM are also brought into light, including that SM of any two PFS-sets equals unity iff the two PFS-sets coincide. Employing this SM, a relation $$\thickapprox ^\lambda $$ amongst two PFS-sets is demarcated. Further, it is demonstrated that this relation does not enjoy the status of an equivalence relation. Moreover, the efficacy of the proposed SM is established with the aid of numerical examples. Comparison analysis of the proposed method with some of the prevailing similarity measures is also given, both numerically and diagrammatically. In the end, an application from psychological disorder accompanied by algorithm and flow chart have been put on display through a conjectural case study.