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