Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment.

In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions.

Estimation of most effected cycles and busiest network route based on complexity function of graph in fuzzy environment.

Connectivity and strength has a major role in the field of network connecting with real world life. Complexity function is one of these parameter which has manifold number of applications in molecular chemistry and the theory of network. Firstly, this paper introduces the thought of complexity function of fuzzy graph with its properties.

New concepts of inverse fuzzy mixed graphs and its application.

Fuzzy mixed graph (FMG) can be used to model some graphical intercommunication network systems if there are many directed and undirected relations between some vertices. In inverse fuzzy graph, the membership value of edges are greater than or equal to the minimum of the membership value of the corresponding vertices. In inverse fuzzy mixed graph (IFMG), directed and undirected relations exist between some vertices and it can be used to analyze many graphical problems of real life such that the membership values of edges are greater than or equal to the minimum of the membership value of the corresponding pair of vertices.

A New Group Decision-Making Technique under Picture Fuzzy Soft Expert Information.

As an extension of intuitionistic fuzzy sets, the theory of picture fuzzy sets not only deals with the degrees of rejection and acceptance but also considers the degree of refusal during a decision-making process; therefore, by incorporating this competency of picture fuzzy sets, the goal of this study is to propose a novel hybrid model called picture fuzzy soft expert sets by combining picture fuzzy sets with soft expert sets for dealing with uncertainties in different real-world group decision-making problems. The proposed hybrid model is a more generalized form of intuitionistic fuzzy soft expert sets. Some novel desirable properties of the proposed model, namely, subset, equality, complement, union and intersection, are investigated together with their corresponding examples.

Computing -index, coindex and Zagreb polynomials of the th generalized transformation graphs.

In chemical graph theory, forgotten topological index or -index plays a crucial role to collect information about the properties of chemical compounds. The th generalized transformation graphs of a molecular graph preserve the entire information on the molecular topology contained in the relevant molecular graph. In this paper, some exact expressions of the F-index and its co-index for the th generalized transformation graphs are obtained.

Some isomorphic properties of -polar fuzzy graphs with applications.

The theory of graphs are very useful tool in solving the combinatorial problems in different areas of computer science and computational intelligence systems. In this paper, we present a frame work to handle -polar fuzzy information by combining the theory of -polar fuzzy sets with graphs. We introduce the notion of weak self complement -polar fuzzy graphs and establish a necessary condition for -polar fuzzy graph to be weak self complement.