Single and Interval-Valued Hybrid Enthalpy Fuzzy Sets and a TOPSIS Approach for Multicriteria Group Decision Making

The concept of entropy is one of the most important notions of the information theory. Entropy quantifies the amount of uncertainty involved in the value of a random variable or the outcome of a random process. Shannon's entropy is one of the most useful entropy types. The notion of enthalpy is the information energy expressed by the complement of Shannon's entropy. In this paper, we propose the concept of interval-valued hybrid enthalpy fuzzy set by modifying single and interval-valued fuzzy multisets. In this context, an interval-valued hybrid enthalpy fuzzy set contains information about both the data and their entropy. We also provide a cosine similarity measure between interval-valued hybrid enthalpy fuzzy sets. Using this cosine similarity measure, we propose a TOPSIS approach for multicriteria group decision making. Moreover, we apply the proposed TOPSIS method to a research assistant selection problem, and we compare the result with the result of a classical TOPSIS method.