In this paper, we introduce the concept of complex multi-fuzzy sets (CM k FSs) as a generalization of the concept of multi-fuzzy sets by adding the phase term to the definition of multi-fuzzy sets. In other words, we extend the range of multi-membership function from the interval [0,1] to unit circle in the complex plane. The novelty of CM k FSs lies in the ability of complex multi-membership functions to achieve more range of values while handling uncertainty of data that is periodic in nature. The basic operations on CM k FSs, namely complement, union, intersection, product and Cartesian product are studied along with accompanying examples. Properties of these operations are derived. Finally, we introduce the intuitive definition of the distance measure between two complex multi-fuzzy sets which are used to define δ-equalities of complex multi-fuzzy sets.
Contemporary research has refined systems with complex fuzzy sets in order to improve the design and model of real-life applications. Symmetry and antisymmetry are basic characteristics of binary relations used when modeling the decision maker’s preferences. A recent focus has been the analysis of a complex data set using the properties of fuzzy concept lattice and the complex soft set. We will introduce a new concept to represent the information which utilizes the time factor, called fuzzy parameterized complex multi-fuzzy soft expert set ( F P - CMFSES ), and investigate part of its fundamental properties. This F P - CMFSES model allows us to validate the information provided by an expert, at a given phase of time, using the properties of complex fuzzy sets. We then construct an algorithm based on this concept by converting it from the complex state to the real state. Eventually, we implement it to a decision-making problem to demonstrate the applicability of the suggested method. A comparison among F P - CMFSES and other existing methods is made to expose the dominance of the suggested method. Apart from that, we also propose the weighted fuzzy parameterized complex multi-fuzzy soft expert set and investigate its application to decision-making.
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