Analytical Formulations for the Level Based Weighted Average Value of Discrete Trapezoidal Fuzzy Numbers

TL;DR

This paper derives analytical formulas for calculating the Level Based Weighted Average (WABL) of discrete trapezoidal fuzzy numbers, enhancing decision-making flexibility by incorporating decision maker strategies.

Contribution

It provides the first analytical formulas for WABL of discrete trapezoidal fuzzy numbers, facilitating easier computation and application in fuzzy decision-making.

Findings

Derived formulas for WABL of trapezoidal fuzzy numbers

Validated formulas with computational examples

Enhanced decision-making flexibility through WABL

Abstract

In fuzzy decision-making processes based on linguistic information, operations on discrete fuzzy numbers are commonly performed. Aggregation and defuzzification operations are some of these often used operations. Many aggregation and defuzzification operators produce results independent to the decision makers strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take into account the level weights and the decision makers optimism strategy. This gives flexibility to the WABL operator and, through machine learning, can be trained in the direction of the decision makers strategy, producing more satisfactory results for the decision maker. However, in order to determine the WABL value, it is necessary to calculate some integrals. In this study, the concept of WABL for discrete trapezoidal fuzzy numbers is investigated, and analytical formulas have been proven to facilitate the calculation of WABL value for these fuzzy numbers. Trapezoidal and their special form, triangular fuzzy numbers, are the most commonly used fuzzy number types in fuzzy modeling, so in this study, such numbers have been studied. Computational examples explaining the theoretical results have been performed.