Abstract:

The idea of Pythagorean fuzzy sets (PFSs) was originally given by Yager in 2013, to handle incomplete and indistinct information in everyday life more effectively with reasonable accuracy than Fuzzy sets and Intuitionistic fuzzy sets, respectively. Distance and similarity measures are dual concepts which are used to check the difference and resemblance respectively between PFSs. As far as our knowledge is concerned, no one has transformed PFSs to intervalued Pythagorean fuzzy sets (IVPFSs) so far. So, in this article, we suggest a novel distance and similarity measure between Pythagorean fuzzy sets based on the transformation from PFSs to IVPFSs. We construct axiomatic definition based on proposed distance and similarity measure between IVPFSs. Furthermore, we present some examples interconnected to pattern recognition and multicriteria decision making (MCDM) to exhibit the accuracy and applicability of our proposed distance and similarity measure. We construct an algorithm for ELECTRE (Elimination and Choice Expressing Reality) method using our proposed method to handle complex multicriteria decision-making problems related to daily life. Our final results exhibit that the suggested method is rational and authentic to treat different complex problems linked to our everyday life situation especially in MCDM situations.

Keywords:  Pythagorean  fuzzy  sets,  Inter  valued  Pythagorean  fuzzy  sets,  Distance  and

Similarity measures, Pattern recognition, ELECTRE, Multi-criteria decision making.