Abstract
The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.
Highlights
Multi-criteria decision-making (MCDM), as an essential framework for comparison, has always been used to select the most desirable one from a set of alternatives, which are evaluated by some finite and predefined attributes
Zadeh [1] presented the theory of fuzzy set (FS), which is an essential tool to deal with fuzzy information
Atanassov [3] presented intuitionistic FS (IFS) which can be successfully applied in different awkward fields because it is characterized by the values of positive grade and negative grade and their sum must be restricted to [0,1]
Summary
Multi-criteria decision-making (MCDM), as an essential framework for comparison, has always been used to select the most desirable one from a set of alternatives, which are evaluated by some finite and predefined attributes. Yager [6] proposed Pythagorean FS (PFS) in which the sum of the square of positive grade and square of negative grade is restricted to [0,1], PFS becomes an essential tool to cope with awkward and difficult fuzzy information, and many researchers utilized it to solve the decision-making problems [7, 8]. Yager [9] presented q-rung orthopair FS (q-ROFS) in which the sum of the q-power of positive grade and the q-power of negative grade is restricted to [0,1], where q is greater than 1 Since it was established, it has received the attention of Complex & Intelligent Systems many researchers and it is utilized in the environments of aggregation operators, similarity measures, hybrid aggregation operators and so on. Xing et al [13] established point weighted aggregation operators based on QROFSs
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