Decision-Making Application Based on Aggregations of Complex Fuzzy Hypersoft Set and Development of Interval-Valued Complex Fuzzy Hypersoft Set

Abstract

Hypersoft set, an extension of soft set, deals with disjoint attribute-valued sets corresponding to distinct attributes. In this study, the innovation of complex fuzzy hypersoft set (CFH-set) is conferred, which can tackle with uncertainties and vagueness that lie in the data by taking into account the amplitude and phase terms of the complex numbers at the same time. This model establishes a gluing framework of the fuzzy set and hypersoft set characterized in the complex plane. This structure is more flexible and useful as it consents a broad range of values for membership function by expanding them to the unit circle in a complex plane through the characterization of the fuzzy hypersoft set to consider the periodic nature of the information and the attributes can further be classified into attribute-values sets for vivid understanding. With the characterization of its some fundamental properties and operations, aggregations of complex fuzzy hypersoft set: matrix, cardinal set, cardinal matrix of cardinal set, aggregation operator/set and matrix of aggregation set, are conceptualized
along with application in decision-making. Moreover, complex interval-valued fuzzy hypersoft set is developed and some of its fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic operations i.e. compliment, union, intersection etc. are investigated.