Abstract
Graphs allow us to study the different patterns of inside the data by making a mental image. The aim of this paper is to develop a neutrosophic cubic graph structure, which is the extension of neutrosophic cubic graphs. As neutrosophic cubic graphs are defined for one set of edges between vertices, while neutrosophic cubic graphs structures are defined for more than one set of edges. Further, we defined some basic operations, such as Cartesian product, composition, union, join, cross product, strong product, and lexicographic product of two neutrosophic cubic graph structures. Several types of other interesting properties of neutrosophic cubic graph structures are discussed in this paper. Finally, a decision-making algorithm based on the idea of neutrosophic cubic graph structures is constructed. The proposed decision-making algorithm is applied in a decision-making problem to check the validity.
Highlights
Fuzzy sets: The extension of classical set theory in the form of fuzzy sets was given by Zadeh in 1965 in his seminal paper [1]
COMPARATIVE ANALYSIS AND CONCLUSIONS All versions of neutrosophic sets like, single valued neutrosophic set, interval valued neutrosophic set and neutrosophic cubic set are used in literature so far for the applications of neutrosophic sets
On the other sides we have the comparison between the different types of graphs as shown the following table: So, we used the concept of neutrosophic cubic sets in this paper with the concept of neutrosophic cubic structures
Summary
Fuzzy sets: The extension of classical set theory in the form of fuzzy sets was given by Zadeh in 1965 in his seminal paper [1]. Various theories like theory of probability, fuzzy set theory, intuitionistic fuzzy sets, rough set theory etc., are consistently being used as powerful constructive tools to deal with multiform uncertainties and imprecision enclosed in complex systems All these above theories do not model undetermined information adequately. M. Gulistan et al.: Novel Neutrosophic Cubic Graphs Structures With Application in Decision Making Problems the generalization of a fuzzy sets and intutionistic fuzzy set. The idea of NS generates the theory of neutrosophic sets by giving representation to indeterminates This theory is considered as complete representation of almost every model of all real-world problems. If uncertainty is involved in a problem we use fuzzy theory while dealing indeterminacy, we need neutrosophic theory This theory has several applications in many different fields like control theory, databases, medical diagnosis problem and decision-making problems. At the end we discuss the application of neutrosophic cubic graphs in decision making problems
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