Relations and compositions between interval-valued complex fuzzy sets and applications for analysis of customers’ online shopping preferences and behavior

Analyzing the relations and patterns that exist in complex data sets is an integral part of the research in complex fuzzy set theory. The main object of study in this paper is the interval-valued complex fuzzy set (IV-CFS) model. This adaptation of complex fuzzy sets can handle datasets with a time-periodic feature, and the partial ignorance that exists in the data as well as the process of assigning values for the membership functions, in addition to modeling multi-dimensional data. This paper focuses on finding the patterns and relations between complex data sets using the properties of interval-valued complex fuzzy sets (IV-CFSs). To achieve this objective, this paper establishes the concept of relations and the composition operation for IV-CFSs using the extensive properties of the Cartesian product. Some of the algebraic properties of the relations and compositions are also introduced to define the equivalence relation between IV-CFSs. The proposed method is then applied to an MCDM problem related to customers’ online shopping preferences and behavior. A detailed case study of this MCDM problem is then presented through the interpretation of the results that were obtained. A brief comparison is then presented between our proposed method and other methods in literature used to analyze patterns between complex data sets.