Pythagorean theorem

Entropy (arrow of time)

Electrical engineering

Physics

Mathematical optimization

Engineering

Artificial intelligence

VIKOR method

Renewable energy

Geometry

Mathematics

Computer science

Fuzzy logic

Thermodynamics

Journal of Cleaner Production

The utilization of renewable energy sources or technologies has grown huge attention from the last few decades. The selection of renewable energy technologies is a laborious task for decision-makers. Therefore, the present study develops a new method using novel divergence and entropy measures of Pythagorean Fuzzy Sets (PFSs) and the Vlsekriterijumska Optimizacija I KOmpromisno Resenje (VIKOR) to evaluate renewable energy technologies. Recently, several studies have been presented regarding PFSs. However, there is very less investigation about the entropy measure of PFSs, particularly there is no study presented for a divergence measure of PFSs in the available literature. Consequently, this paper firstly develops novel information measures for PFSs. Next, the VIKOR method is extended to solve The Multiple-Criteria Decision Making (MCDM) problems with PFSs which the information of criteria weights is completely unidentified. To achieve the significant degrees of the Decision-Experts (DEs) and the criteria, new approaches are determined with the help of two developed measures including Pythagorean fuzzy-entropy and Pythagorean fuzzy-divergence. Moreover, an operation is utilized to PF weighted averaging operator for integrating the individual decision information into a group decision matrix. Further, the proposed PF-divergence measure is implemented to determine the particular measure of closeness of the alternatives in the present method. Finally, to exemplify the efficiency of the proposed approach, a selection problem of renewable energy technologies is presented where the evaluation of the energy alternatives versus each criterion is expressed in terms of Pythagorean Fuzzy Numbers (PFNs). The results of this study demonstrated that the proposed PF-VIKOR was effective to select and evaluate renewable energy technologies.

A novel VIKOR approach based on entropy and divergence measures of Pythagorean fuzzy sets to evaluate renewable energy technologies in India