An extended Pythagorean fuzzy VIKOR method with risk preference and a novel generalized distance measure for multicriteria decision-making problems

This study aims to extend classic VIKOR technique for multicriteria decision-making (MCDM) problems within Pythagorean fuzzy (PF) scenario. First, judgments from decision makers (DMs) are expressed by PF sets that can describe more uncertain and ambiguous information than available fuzzy sets. Second, PF point operators are applied to denote the risk preference of the DM who may express an attitude toward an emerging science and technology. Third, a new generalized distance measurement formula considering all the characteristics of PF sets is proposed, and some attractive properties of distance measure, which outperforms available distance measures, are proved. Fourth, the novel generalized distance measure is employed to relative distance to identify the optimum and worst PF values and then employed in Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{p}$$\end{document}-metric VIKOR formula to accurately gain the group utility, individual regret, and compromise index. The novel PF-VIKOR algorithm considering DM’s risk preference and a novel distance measure is described in detail, and a blockchain technology solution selection problem is utilized to validate the feasibility of our technique. Then, the sensitivity analysis is implemented to test stability of our PF-VIKOR technique when the parameters in risk preferences and generalized distance measure are adjusted. Fifth, the comparison among various PF-MCDM techniques is performed to validate superiority and practicability of our presented technique.