Optimization in Business Trade by Using Fuzzy Incidence Graphs

Abstract

In classical graph theory, set of vertices in which every edge is incident to at least one of the vertex is called a vertex covering set and the problems of vertex covering (VC) are known as VC problems. The classical graphs do not reflect the impact of vertex on the edge and such impact is reflected in fuzzy incidence graphs (FIGs). We used optimization technique in a trade using clique covering (CC) in FIGs. This article includes some basic definitions such as strength of clique, strength of path, strength of minimum clique (SMC), acceptable strength of path and acceptable strength of clique, robust number, minimum covering number of the clique, close measure, some examples and theorems in FIGs, and new strategy of optimization to characterize and solve facility point problems by adopting the CC application of FIGs for a business alliance to get maximum total achievement by reducing the transportation cost. This procedure will be helpful to develop sustainable economic developmental goal of the world. Some already existing theorems in fuzzy graphs are also checked in FIGs.A mathematical model is defined and a real-life problem from a trade is solved keeping the fuzziness of the objects related to FIG.

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“…In the field of FCM, Sharaf (2023) stated that these methods are a necessary tool for business decision-making and problem-solving. Furthermore, fuzzy models and graphs promote the sustainable economic development of businesses (Rehman et al, 2023). The combination of quantitative data and fuzzy methods influences numerous factors of companies' performance, such as strategic decisions and managerial and promotional activities (Nezhadkian et al, 2023).…”

Some novel concepts of interval-valued picture fuzzy graphs with applications toward the Transmission Control Protocol and social networks

“…The term highly irregular BPFGs was discussed in [27]. Recently, the application of fuzzy incidence graphs toward optimizing business trade has been explored in [28]. In [29], further generalization of FGs termed intuitionistic fuzzy graphs (IFGs) was initiated.…”