Inverse Graphs in m-Polar Fuzzy Environments and Their Application in Robotics Manufacturing Allocation Problems with New Techniques of Resolvability

Abstract

The inverse in crisp graph theory is a well-known topic. However, the inverse concept for fuzzy graphs has recently been created, and its numerous characteristics are being examined. Each node and edge in m-polar fuzzy graphs (mPFG) include m components, which are interlinked through a minimum relationship. However, if one wants to maximize the relationship between nodes and edges, then the m-polar fuzzy graph concept is inappropriate. Considering everything we wish to obtain here, we present an inverse graph under an m-polar fuzzy environment. An inverse mPFG is one in which each component’s membership value (MV) is greater than or equal to that of each component of the incidence nodes. This is in contrast to an mPFG, where each component’s MV is less than or equal to the MV of each component’s incidence nodes. An inverse mPFG’s characteristics and some of its isomorphic features are introduced. The α-cut concept is also studied here. Here, we also define the composition and decomposition of an inverse mPFG uniquely with a proper explanation. The connectivity concept, that is, the strength of connectedness, cut nodes, bridges, etc., is also developed on an inverse mPF environment, and some of the properties of this concept are also discussed in detail. Lastly, a real-life application based on the robotics manufacturing allocation problem is solved with the help of an inverse mPFG.