ELECTRE TRI-C with Hesitant Fuzzy Sets and Interval Type 2 Trapezoidal Fuzzy Numbers Using Stochastic Parameters: Application to a Brazilian Electrical Power Company Problem

Abstract

ELECTRE TRI-C is a method for sorting problems with imprecise evaluations and stable criteria weights, typically for a single decision-maker. While some extensions have addressed uncertain criteria weights and outranking functions using hesitant fuzzy sets (HFS) and interval type 2 trapezoidal fuzzy numbers (IT2TrfN), there is a gap in handling situations where multiple decision-makers provide uncertain information. This paper presents an extension of the ELECTRE TRI-C method incorporating a stochastic framework to model HFS and IT2TrfN, thereby accommodating subjective judgments from multiple decision-makers. The extended method was validated by sorting 49 projects based on their criticality in a Brazilian electrical power company, involving three decision-makers. The application shows strong correlations in project rankings among decision-makers, but with some exceptions. However, significant variations in acceptability ratings for sorting among decision-makers lead to notable error dispersion, highlighting differences between ranking and sorting outcomes. The key contributions of our approach are as follows: (1) Integration of subjective judgments from multiple decision-makers using IT2TrFN and Monte Carlo Simulation for constructing outranking functions; (2) Aggregation of preferences from multiple decision-makers using HFS; (3) Stochastic processing of both quantitative and qualitative criteria; (4) Integration of linear equations to represent weight constraints; and (5) Introduction of a novel visualization method for comprehensive analysis of stochastic results, enhancing robustness analysis. The proposal’s advantages over alternative methods are also highlighted.