ANALYTICAL FORMULATIONS FOR THE LEVEL
BASED WEIGHTED AVERAGE VALUE OF
DISCRETE TRAPEZOIDAL FUZZY NUMBERS
Resmiye Nasiboglu1* , Rahila Abdullayeva2
1Department of Computer Science, Dokuz Eylul University, Izmir, Turkey
2Department of Informatics, Sumgait State University, Sumgait, Azerbaijan
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 decisionmaker’s
strategy. On the other hand, the Weighted Average Based on Levels (WABL) approach can take
into account the level weights and the decision maker's "optimism" strategy. This gives flexibility to the
WABL operator and, through machine learning, can be trained in the direction of the decision maker's
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.
KEYWORDS
Fuzzy number;Trapezoidal; Weighted level-based averaging; Defuzzification.
Original Source URL : http://aircconline.com/ijsc/V9N3/9318ijsc01.pdf
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