Abstract
The paradigm shift prompted by Zadeh’s fuzzy sets in 1965 did not end with the fuzzy model and logic. Extensions in various lines have produced e.g., intuitionistic fuzzy sets in 1983, complex fuzzy sets in 2002, or hesitant fuzzy sets in 2010. The researcher can avail himself of graphs of various types in order to represent concepts like networks with imprecise information, whether it is fuzzy, intuitionistic, or has more general characteristics. When the relationships in the network are symmetrical, and each member can be linked with groups of members, the natural concept for a representation is a hypergraph. In this paper we develop novel generalized hypergraphs in a wide fuzzy context, namely, complex intuitionistic fuzzy hypergraphs, complex Pythagorean fuzzy hypergraphs, and complex q-rung orthopair fuzzy hypergraphs. Further, we consider the transversals and minimal transversals of complex q-rung orthopair fuzzy hypergraphs. We present some algorithms to construct the minimal transversals and certain related concepts. As an application, we describe a collaboration network model through a complex q-rung orthopair fuzzy hypergraph. We use it to find the author having the most outstanding collaboration skills using score and choice values.
Highlights
In 1965, fuzzy sets (FSs) were originally defined by Zadeh [1] as a novel approach to represent uncertainty arising in various fields
C with the incorporation of imaginary quantities, FSs have been extended to complex fuzzy sets (CFSs) by Ramot et al [2]
We present an algorithm to select an author with powerful collaboration characteristics using the score and choice values of q-rung orthopair fuzzy hypergraphs and give a brief comparison of our proposed model with CIF and CPF models
Summary
In 1965, fuzzy sets (FSs) were originally defined by Zadeh [1] as a novel approach to represent uncertainty arising in various fields. The idea of “partial membership” was questioned by many researchers at that time. The extension of crisp sets to FSs, i.e., the extension of membership function μ( x ) from {0, 1} to [0, 1], bears comparison to the generalization of Q to R. C with the incorporation of imaginary quantities, FSs have been extended to complex fuzzy sets (CFSs) by Ramot et al [2]. A CFS is characterized by a membership function μ( x ) whose range is not limited to [0,1] but extends to the unit circle in the complex plane. Μ( x ) is a complex-valued function
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