Abstract
A graph structure is a useful framework to solve the combinatorial problems in various fields of computational intelligence systems and computer science. In this research article, the concept of fuzzy sets is applied to the graph structure to define certain notions of fuzzy graph structures. Fuzzy graph structures can be very useful in the study of various structures, including fuzzy graphs, signed graphs, and the graphs having labeled or colored edges. The notions of the fuzzy graph structure, lexicographic-max product, and degree and total degree of a vertex in the lexicographic-max product are introduced. Further, the proposed concepts are explained through several numerical examples. In particular, applications of the fuzzy graph structures in decision-making process, regarding detection of marine crimes and detection of the road crimes, are presented. Finally, the general procedure of these applications is described by an algorithm.
Highlights
Decision-making is a process of solving problems for choosing the best alternative
Multicriteria decision-making (MCDM) can be explicated as a discipline of operation research in which the satisfactory solution is opted regarding some significant factors which can be considered as conflicting criteria for the decision-making problems. e concept of MCDM is widely used in medical, economics, engineering, and social sciences
Fuzzy graph structures are more advantageous than graph structures to cope with uncertainty
Summary
Decision-making is a process of solving problems for choosing the best alternative. Multicriteria decision-making (MCDM) can be explicated as a discipline of operation research in which the satisfactory solution is opted regarding some significant factors which can be considered as conflicting criteria for the decision-making problems. e concept of MCDM is widely used in medical, economics, engineering, and social sciences. A fuzzy set, proposed by Zadeh [1], is the class of objects with continuity of grades of membership It is characterized by the membership function that assigns each element grade of membership between zero and one. Dinesh [38] worked on fuzzy graph structures and discussed few related concepts. The concept of fuzzy sets is applied to a graph structure to define certain notions of fuzzy graph structures. Applications of the fuzzy graph structures in decision-making process, regarding detection of marine crimes and detection of the road crimes, are presented. E contents of this article are as follows: In Section 2, some fundamental concepts of graph structures and fuzzy graphs are reviewed. E certain notions of fuzzy graph structures are defined, and their interesting properties are investigated in the same section.
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