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

Abstract

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.

Risk Assessment Method for Ship Based on Improved Fuzzy Multicriteria Decision-Making

“…In view of this, the paper endeavors to propose a new method to solve the problems arising from multicriteria decision-making based on the intuitionistic fuzzy number, peer-to-peer consensus model, nonlinear programming model, and MULTIMOORA. First, intuitionistic fuzzy number is introduced to resolve the limitation of the experts' cognitive uncertainty expression under limited information, and a triangular intuitionistic fuzzy number (IFN) evaluation table of risk sources is established [24]; second, the transfer of expert opinions is weighted by the Markov chain on fnite state spaces, and then a consensus model is formed by group analytic hierarchy process (AHP) to obtain the expert weight [25]; the nonlinear programming model [26] is introduced to determine the weight of risk factors using the experts' preference; the triangular intuitionistic fuzzy number is applied to the fre risk assessment, and combined with the MULTIMOORA method, a ship risk assessment method based on improved fuzzy multicriteria decisionmaking is proposed to identify key risk factors; fnally, the fuzzy number quantitative calculation method [27] with intuitionistic attributes is adopted to identify the fnal ranking of alternatives and improve the efectiveness of the model. Te proposed model is then verifed by using the engine room fre risk assessment of a ship as an example.…”