Characterizations of Certain Types of Type 2 Soft Graphs

Abstract

The vertex-neighbors correspondence has an essential role in the structure of a graph. The type 2 soft set is also based on the correspondence of initial parameters and underlying parameters. Recently, type 2 soft graphs have been introduced. Structurally, it is a very efficient model of uncertainty to deal with graph neighbors and applicable in applied intelligence, computational analysis, and decision-making. The present paper characterizes type 2 soft graphs on underlying subgraphs (regular subgraphs, irregular subgraphs, cycles, and trees) of a simple graph. We present regular type 2 soft graphs, irregular type 2 soft graphs, and type 2 soft trees. Moreover, we introduce type 2 soft cycles, type 2 soft cut-nodes, and type 2 soft bridges. Finally, we present some operations on type 2 soft trees by presenting several examples to demonstrate these new concepts.

Another View of Aggregation Operators on Group-Based Generalized Intuitionistic Fuzzy Soft Sets: Multi-Attribute Decision Making Methods

“…It can be seen that, using AND operation, the importance of IFVs for υ 2 and υ 3 are diminished in Equations (11) and (12). The importance of IFVs for υ 3 are diminished in Equation (13).…”

“…By virtue of robustness of fuzzy soft set theory in dealing with uncertain data, many researchers serve to integrate it with inductive learning techniques for better results. In recent past, fuzzy sets, soft sets and fuzzy soft sets are applied to evaluate vagueness in decision makings [7][8][9][10][11][12][13][14][15][16][17][18], algebraic structures [19,20], medical diagnosis [21] and differential equations [22]. Some hybrid models of fuzzy soft sets have been introduced and applied in several fields [23,24].…”

Study on Neutrosophic Graph with Application on Earthquake Response Center in Japan

“…Khizar Hayat et al [26] determinant and adjoint of neutrosophic matrices with interval values are defined using the permanent function as a basis. On underlying subgraphs of a simple graph, type 2 soft graphs were characterized by Khizar Hayat et al [27]. Faruk Karaaslan and Khizar Hayat [28] gave verires matrices of neutrosophic sets.…”

Parameter reductions in N‐soft sets and their applications in decision‐making

“…Once this is done, we justify its applicability in decision making, inclusive of an example of use. For more terminologies, not discussed in the paper, the readers are addressed to Bera, Roy, Karaaslan, and Çagman (2017), Hayat, Ali, Karaaslan, Cao, and Shah (2020), Hayat, Cao, Ali, Karaaslan, and Qin (2018), Hayat, Ali, Cao, and Karaaslan (2018), and Karaaslan (2016b).…”