New Concepts of Intuitionistic Fuzzy Trees with Applications

Abstract

It is known that Intuitionistic fuzzy models give more precision, flexibility and compatibility to the system as compared to the classic and fuzzy models. Intuitionistic fuzzy tree has an important role in neural networks, computer networks, and clustering. In the design of a network, it is important to analyze connections between the levels. In addition, the intuitionistic fuzzy tree is becoming increasingly significant as it is applied to different areas in real life. The study proposes the novel concepts of intuitionistic fuzzy graph (IFG) and some basic definitions. We investigate the types of arcs, for example, $$\alpha _{\mu }$$ α μ -strong, $$\beta _{\mu }$$ β μ -strong, and $$\delta _{\mu }$$ δ μ -arc in an intuitionistic fuzzy graph, and introduce some of their properties. In particular, the present work develops the concepts of intuitionistic fuzzy bridge (IFB), intuitionistic fuzzy cut nodes (IFCN) and some important properties of an intuitionistic fuzzy bridge. Next, we define an intuitionistic fuzzy cycle (IFC) and an intuitionistic fuzzy tree (IFT). Likewise, we discuss some properties of the IFT and the relationship between an intuitionistic fuzzy tree and an intuitionistic fuzzy cycle. Finally, an application of intuitionistic fuzzy tree is illustrated in other sciences.

Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat

“…In 2021, Akram et al [ 25 ] presented the concept of strong edges for m -polar FGs. Rao et al [ 26 ] introduced the concept of different types of arcs in intuitionistic fuzzy graph. The connectivity index ( ) for IFGs was studied by Naeem et al [ 27 ], in 2021.…”

Operations on Complex Intuitionistic Fuzzy Graph

“…Hossein et al [2] showed the rationality of some operation are defined on intuitionistic fuzzy graph are Direct product, Lexicographic product, Strong product. Yongsheng Rao et al [20] derived types of arcs in an intuitionistic fuzzy graph and intuitionistic fuzzy tree. Also studies the intuitionistic fuzzy bridge, intuitionistic fuzzy cutnode, intuitionistic fuzzy cycle, intuitionistic fuzzy tree.…”

Two-Sided Matching Decision-Making in an Incomplete and Heterogeneous Context: A Optimization-Based Method

“…The TSDM problems have been widely existed in diverse applications, such as marriage matching [1,2], college admission matching [3,4], roommate matching [5,6], firm and employee matching [7,8], and task and volunteer teams [9]. In practical TSDM problem, it is common that the individuals express the demand information via the preference ordering and linguistic evaluation [10][11][12][13][14][15][16][17][18].…”

“…For example, Sertel and özkal-Sanver [10] aimed to two-sided matching problem with complete strict preference ordering information, considered the endowments of two-sided matching party and proposed a matching rule maximizing consumption. Alkan and Gale [17] studied the two-sided matching problem with complete strict preference ordering, in which the unrevealed preference behavior of two-sided matching party is considered. Furthermore, an extension of Gale-Shapley algorithm is developed to solve this problem.…”