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.
Highlights
In fuzzy decisionmaking models based on linguistic information, usually operations on discrete fuzzy numbers are performed [2, 3].In [2], in order to merge subjective evaluations, a compensatory class of aggregation functions on the finite chain from [4] is used
A more sophisticated form of this approach based on the Weighted Average Based on Levels (WABL) defuzzification operator is investigated
We handle the discrete fuzzy numbers that are used in various type of fuzzy decision-making systems with linguistic information
Summary
The most general representative of the last group of methods is the Weighted Average Based on Levels method (WABL) This method is based on the study about the mean value of the fuzzy number proposed in the pioneer study [10]. The basic forms of fuzzy numbers such as triangular and trapezoidal fuzzy numbers with discrete universe of levels and with different patterns of level weights are investigated in this study and some analytical formulas to calculate the WABL values are presented. 5, the WABL values for discrete leveled trapezoidal FN with various levels’ weights patterns are investigated and some analytical formulas are proven Using this formulas give us a way for simple calculation of the WABL value of a fuzzy number without using more complicated integral calculations. The conclusion part highlighting benefits of this study completes the paper
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
