Fuzzy Entropy Measure with an Applications in Decision Making Under Bipolar Fuzzy Environment based on TOPSIS Method

Abstract

In this paper, based on the concept of Havrda-Charvat-Tsallis entropy, fuzzy entropy measure is introduced in the setting of fuzzy set theory. The properties of the new fuzzy measure are investigated in a mathematical view point. Several examples are applied to illustrate the performance of the proposed fuzzy measure. Comparison with several existing entropies indicates that the proposed fuzzy information measure has a greater ability in discrimaniting different fuzzy sets. Lastly, the proposed fuzzy information measure is applied to the problem of MCDM (multi criteria decision making) based on TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method under bipolar fuzzy environment. Two models are constructed to obtain the attribute weights in the cases that the information attribute weights is partially known and completely unknown. An example is employed to show the effectiveness of the new MCDM method.