Abstract
A complex neutrosophic set is a useful model to handle indeterminate situations with a periodic nature. This is characterized by truth, indeterminacy, and falsity degrees which are the combination of real-valued amplitude terms and complex-valued phase terms. Hypergraphs are objects that enable us to dig out invisible connections between the underlying structures of complex systems such as those leading to sustainable development. In this paper, we apply the most fruitful concept of complex neutrosophic sets to theory of hypergraphs. We define complex neutrosophic hypergraphs and discuss their certain properties including lower truncation, upper truncation, and transition levels. Furthermore, we define T-related complex neutrosophic hypergraphs and properties of minimal transversals of complex neutrosophic hypergraphs. Finally, we represent the modeling of certain social networks with intersecting communities through the score functions and choice values of complex neutrosophic hypergraphs. We also give a brief comparison of our proposed model with other existing models.
Highlights
Fuzzy sets (FSs) were originally defined by Zadeh [1] as a novel approach to represent uncertainty arising in various fields that was questioned by many researchers at that time
A complex neutrosophic sets (CNSs) extends the concept of single-valued neutrosophic sets (SVNSs) from real unit interval [0, 1] to the complex plane and is used to represent two-dimensional imprecise and indeterminate information
A CNS plays a vital role in modeling the real-life applications where the truth, indeterminacy, and falsity degrees of given data are periodic in nature
Summary
Fuzzy sets (FSs) were originally defined by Zadeh [1] as a novel approach to represent uncertainty arising in various fields that was questioned by many researchers at that time. A CNS is characterized by a complex-valued truth t( x ), complex-valued indeterminate i ( x ), and complex-valued falsity f ( x ) membership functions, whose range is extended from [0, 1] to the unit disk in the complex plane They proposed set theoretic operations such as complement, union, intersection, complex neutrosophic product, Cartesian product, distance measure, and δ-equalities of CNSs and presented an application of CNSs in signal processing. To handle periodic nature of falsity degrees in IFGs, Yaqoob et al [19] defined complex intuitionistic fuzzy graphs (CIFGs) They studied the homomorphisms of CIFGs and provided an application of CIFGs in cellular network provider companies for the testing of their proposed approach.
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