Domination in m− polar soft fuzzy graphs

In this paper, we have introduced dominating set, minimal dominating set, independent dominating set, maximal independent dominating set in m − polar soft fuzzy graphs. We proved theorems and also some properties of dominating set in m− polar soft fuzzy graphs

Interval-valued intuitionistic fuzzy soft graphs with application

The concept of interval-valued intuitionistic fuzzy soft sets and fuzzy graphs structure together constitute a new structure called an interval-valued intuitionistic fuzzy soft graph. The definitions of interval-valued intuitionistic fuzzy soft subgraph and strong interval-valued intuitionistic fuzzy soft graph are introduced with suitable examples. The degree of the good influence of a parameter in a fuzzy network and there is no influence by an interval number in the same system. Similarly, the effectiveness and non-effectiveness of the other fuzzy system on other parameters is measured by the concept of soft graphs in this article. Also, several different types of operations, including Cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs are presented. Some related properties of these operations are investigated. Finally, we give a real-life application of interval-valued intuitionistic fuzzy soft graphs on social media and find out the most affected person in social media.Publisher's Versio

Interval-valued intuitionistic fuzzy soft graph

One of the theories designed to deal with uncertainty is the soft set theory. These collections were used due to a lack of membership functions in the fields of decision-making, systems analysis, classification, data mining, medical diagnosis, etc. Fuzzy graphs based on soft sets were developed alongside fuzzy graphs. Studying these graphs, examining the properties and operators on it, give special flexibility in dealing with indeterminate problems. In particular, most of the issues around us are mixed and operations are conveniently used in many combinatorial applications. Therefore, the study of operations have a significant effect on solving problems based on decisionmaking, medical, etc. In this paper, we introduce the notion of interval-valued intuitionistic fuzzy soft graphs, by combine concepts of interval-valued intuitionistic fuzzy graphs and fuzzy soft graphs. We also present several different types of operations including cartesian product, strong product and composition on interval-valued intuitionistic fuzzy soft graphs and investigate some properties of them.Publisher's Versio

Some Operations on Complex Fuzzy Graphs

In this paper we discussed about some types of complex fuzzygraphs which is the extension of fuzzy graph. As the membershipvalue of elements of fuzzy graph is in between 0 and 1. In complexfuzzy graph it will be extended to unit circle of complex plane. Someoperations such as union, intersection, composition, cartesian productof two complex fuzzy graphs are introduced. Some basic theoremswith respect to the above mentioned operations are proved with examples

International Journal of Mathematical Combinatorics, Vol.6

The International J.Mathematical Combinatorics (ISSN 1937-1055) is a fully refereed international journal, sponsored by the MADIS of Chinese Academy of Sciences and published in USA quarterly comprising 460 pages approx. per volume, which publishes original research papers and survey articles in all aspects of Smarandache multi-spaces, Smarandache geometries, mathematical combinatorics, non-euclidean geometry and topology and their applications to other sciences

Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives.

Vector optimization problems over a fuzzy combinatorial set of permutations are investigated. Based on the properties of the convex hull of a fuzzy combinatorial set of permutations, modifications of multicriteria choice methods are developed and substantiated for a fuzzy feasible combinatorial set. Mathematical models of some application problems are presented

Vector optimization problems with linear criteria over a fuzzy combinatorial set of alternatives.

Vector optimization problems over a fuzzy combinatorial set of permutations are investigated. Based on the properties of the convex hull of a fuzzy combinatorial set of permutations, modifications of multicriteria choice methods are developed and substantiated for a fuzzy feasible combinatorial set. Mathematical models of some application problems are presented

Pythagorean fuzzy incidence graphs with application in illegal wildlife trade

Chemical engineers can model numerous interactions in a process using incidence graphs. They are used to methodically map out a whole network of interconnected processes and controllers to describe each component's impact on the others. It makes it easier to visualize potential process paths or a series of impacts. A Pythagorean fuzzy set is an effective tool to overcome ambiguity and vagueness. In this paper, we introduce the concept of Pythagorean fuzzy incidence graphs. We discuss the incidence path and characterize the strongest incidence path in Pythagorean fuzzy incidence graphs. Furthermore, we propose the idea of Pythagorean fuzzy incidence cycles and Pythagorean fuzzy incidence trees in Pythagorean fuzzy incidence graphs and give some essential results. We illustrate the notions of Pythagorean fuzzy incidence cut vertices, Pythagorean fuzzy incidence bridges, and Pythagorean fuzzy incidence cut pairs. We also establish some results about Pythagorean fuzzy incidence cut pairs. Moreover, we study the types of incidence pairs and determine some crucial results concerning strong incidence pairs in the Pythagorean fuzzy incidence graph. We also obtain the characterization of Pythagorean fuzzy incidence cut pairs using $\alpha$-strong incidence pairs and find the relation between Pythagorean fuzzy incidence trees and $\alpha$-strong incidence pairs. Finally, we provide the application of Pythagorean fuzzy incidence graphs in the illegal wildlife trade