Fuzzy Soft Graphs Research Articles

Topological numbers of fuzzy soft graphs and their applications in globalizing the world by mutual trade

In this research draft, by keeping in view, the importance of Zagreb numbers, first we defined some familiar graph families and their degrees in fuzzy soft environment, and then by converting these two novel topological numbers in fuzzy soft framework, their formulae are calculated for these graphical networks. An application of international trade using two kinds of routes is also discussed in the article, and by comparing the results efficiency of both the numbers is compared and analyzed how topological descriptors are useful in examining the progress and profit in the countries, that are a part of the project. Graphs are used in the modeling of links and processes within physical, biological, social, and information systems. A fuzzy graph is the most adaptable tool in mathematics, which describes the fuzzy relationship between objects. Fuzzy graphs are very helpful to give more accuracy to the system as compared to crisp graphs. A classification of the universe with respect to certain specified parameters is known as a soft set. It is a new method for simulating ambiguity and uncertainty. Soft set theory was created by Molodtsov in 1999 as a method for simulating vagueness and uncertainty. Soft set theory is presently used widely in academia to address decision-making issues. The concept of soft graphs is used to provide a parameterized point of view for graphs. In many areas of mathematics and chemistry, as well as in network theory, spectral graph theory, and molecular chemistry, the Zagreb numbers are crucial graph parameters. Due to the importance and significance of Zagreb numbers, in this research article we define these graph parameters in fuzzy soft environment and then derived the fundamental formula for first and second Zagreb numbers of some popular graph families. Also by keeping in view the importance of graph theory in solving decision making problems in business industry, and the most generic behavior of fuzzy soft graph due to its parameterized nature we use our work in application of decision making in trade among different nations.

Topological numbers of fuzzy soft graphs and their application

The diagram kind of a graph is used to show accumulated data. Graphs can be utilized for a variety of purposes because this data can be either quantitative or qualitative. Graphs can be used to model different relationships and processes in physical, biological, and social media marketing systems, and in finding directions on a map. A graph with properties attached to its nodes and edges that emphasize its applicability to real-world systems is sometimes called a network. The idea of fuzzy sets has developed in numerous ways and across many areas since its establishment in 1965. Applications of this theory can be found in numerous fields for instance in recognition of patterns, management science, AI, computer science, medicine, also in control engineering. The progress of mathematics has reached a very high level and continues now. While classical graph theory is widely applied in several domains, there are instances where its outcomes can be subject to uncertainty. In order to address this challenge, the utilization of the fuzzy theory of graphs is adopted, as it offers more accurate outcomes. There is a lack of a parameterization tool in fuzzy graph theory, as a consequence Molodtsov introduced soft set theory, which is a rather recent way to talk about ambiguity and vagueness. It is becoming more and more popular among scholars and is a novel approach to uncertainty and ambiguity simulation. The concept of soft graphs offers a parameterized perspective on graphs. In this article, we defined some familiar graph families in a fuzzy soft (FS) environment and by calculating their degrees, derived important results for two versions of Sombor numbers. In the end, we discussed an application of calculated results and by comparison, checked the efficiency of Sombor numbers in a FS framework.

Domination in bipolar fuzzy soft graphs

The concept of domination in graphs is very ancient. Several types of notions of domination in graphs have been discussed by many researchers. In this work, the concept of domination and some notions of domination sets, minimal dominating sets, independence sets, and maximal independence sets are introduced in bipolar fuzzy soft graphs. Additionally, several properties of dominating sets are discussed and some theorems in bipolar fuzzy soft graphs are proved.

Products on interval valued pythagorean fuzzy soft graphs

Products on interval valued pythagorean fuzzy soft graphs

Decision Making Under Pythagorean Fuzzy Soft Environment

This research article illustrates the notion of strong and complete Pythagorean fuzzy soft graphs (PFSGs). Different operations on PFSGs including union of two PFSGs, join of two PFSGs, lexicographic product of two PFSGs, strong product of two PFSGs, Cartesian product of two PFSGs, composition of two PFSGs are also analysed here. Some properties related to these products are discussed here. The idea of complememt of a PFSG is also eloborated here. Moreover, we establish the application of PFSG in the decision making (DM) problem.

Applications of Interval-Valued Pythagorean Fuzzy Soft Graph in Bipolar Fuzzy Frame Works

The main contribution of this paper is to get extended ideas of various interval-valued bipolar Pythagorean fuzzy soft graphs (I-VBPFSGs) and to extend the concept of the Pythagorean fuzzy soft graph to the bipolar frameworks. Finally, in order to demonstrate, how to calculate an interval-valued Pythagorean bipolar fuzzy soft graph for a specific application, a numerical example using city data from the Yunnan province is presented.

Interval – Valued Pythagorean Fuzzy Soft Graphs

Interval-valued Pythagorean fuzzy soft sets and graph theory are combined in this essay. Then, we present notations for Pythagorean fuzzy soft graphs with interval values. On interval-valued Pythagorean fuzzy soft graphs, we also provide a variety of operations, such as Cartesian product and composition, and we look at some of their characteristics. Finally, we consider the application of I-VPFSGs for the selection of suitable houses and got the appropriate result by using score function.

Graphical Exploration of Generalized Picture Fuzzy Hypersoft Information with Application in Human Resource Management Multiattribute Decision-Making

In this study, the graphical exploration of a novel hybrid, that is, possibility of picture fuzzy hypersoft graph ( popfhs -graph) is accomplished. The popfhs -graph is more flexible and reliable in the sense that it has the ability to tackle the limitations of picture fuzzy soft graph regarding the entitlement of multiargument approximate mapping and possibility degree-based setting. Its approximate mapping considers the Cartesian product of subclasses of parameters as domain and then maps it to the power set of universal set. The possibility degree-based setting ensures the assessment of uncertain attitude of approximate elements up to the level of acceptance. First, some of elementary notions and set theoretic operations of popfhs -graph are investigated with the support of numerical examples and pictorial representations. Second, some of its variants, types of products, and composition are also discussed. Lastly, based on aggregation of the popfhs -graph, an algorithm is proposed for multiattribute decision-making problem and validated by resolving daily-life recruitment problem for the best selection of candidate.

Perfect Fuzzy Soft Tripartite Graphs and Their Complements

Fuzzy soft graphs are efficient numerical tools for simulating the uncertainty of the real world. A fuzzy soft graph is a perfect fusion of the fuzzy soft set and the graph model that is widely used in a variety of fields. This paper discusses a few unique notions of perfect fuzzy soft tripartite graphs (PFSTG), as well as the concepts of complement of perfect fuzzy soft tripartite graphs (CPFSTGs). Because soft sets are most useful in real‐world applications, the newly developed concepts of perfect soft tripartite fuzzy graphs will lead to many theoretical applications by adding extra fuzziness in analysing. We look at some of their properties and come up with a few results that are related to these concepts. Furthermore, we investigated some fundamental theorems and illustrated an application of size of perfect fuzzy soft tripartite graphs in employee selection for an institution using the perfect fuzzy soft tripartite graph.

Some studies on products of Fuzzy soft graphs

Some studies on products of Fuzzy soft graphs

An approach to decision-making via picture fuzzy soft graphs.

Fuzzy soft graphs are effective mathematical tools that are used to model the vagueness of the real world. A fuzzy soft graph is a fusion of the fuzzy soft set and the graph model and is widely used across different fields. In this current research, the concept of picture fuzzy soft graphs is presented by combining the theory of picture soft sets with graphs. The introduction of this new picture fuzzy soft graphs is an emerging concept that can be rather developed into various graph theoretical concepts. Since soft sets are most usable in real-life applications, the newly combined concepts of the picture and fuzzy soft sets will lead to many possible applications in the fuzzy set theoretical area by adding extra fuzziness in analyzing. The notions of picture soft graphs, strong and complete picture soft fuzzy graphs, a few types of product picture fuzzy soft graphs, and regular, totally regular picture fuzzy soft graphs are discussed and validated using real-world scenarios. In addition, an application of decision-making for medical diagnosis in the current COVID scenario using the picture fuzzy soft graph has been illustrated.

Inter-specific competition among trees in pythagorean fuzzy soft environment

A Pythagorean fuzzy set is very effective mathematical framework to represent parameter-wise imprecision which is the property of linguistic communication. A Pythagorean fuzzy soft graph is more potent than the intuitionistic fuzzy soft as well as the fuzzy soft graph as it depicts the interactions among the objects of a system using Pythagorean membership grades with respect to different parameters. This article addresses the content of competition graphs as well as economic competition graphs like k-competition graphs, m-step competition graphs and p-competition graphs in Pythagorean fuzzy soft environment. All these concepts are illustrated with examples and fascinating results. Furthermore, an application which describes the competition among distinct forest trees, that grow together in the mixed conifer forests of California, for plant resources is elaborated graphically. An algorithm is also designed for the construction of Pythagorean fuzzy soft competition graphs. It is worthwhile to express the competing and non-competing interactions in various networks with the help of Pythagorean fuzzy soft competition graphs wherein a variation in competition relative to different attributes is visible.

Oligopolistic competition among the wireless internet service providers of Malaysia using fuzzy soft graphs

The competitive relationship among the objects of a system often show variation when it is examined relative to different aspects or attributes. Fuzzy soft theory allows parametrization in the problems with vague data, as it inherits the properties of a fuzzy set and soft set simultaneously. This feature of fuzzy soft theory influenced us to represent the variation in competition that appears among the constituents of a system. This article presents the competition graph and economic competition graph in fuzzy soft theory; the fuzzy soft competition graph and fuzzy soft economic competition graph. Various extensions of the proposed graphs like fuzzy soft k-competition graphs, p-competition fuzzy soft graph and m-step fuzzy soft competition graphs have also been defined together with examples and some important results. An application to fuzzy soft economic competition graphs is provided that shows diverse competition among the wireless internet service providers of Malaysia. As there exist only a few mobile operators which facilitate the whole country with the wireless internet service, this competitive market structure is an oligopoly. The strength of oligopolistic (economic) competition is also manipulated. An algorithm is also established that evaluates the strength of any fuzzy soft economic competition among the sellers.

Total and Secure Domination for Corona Product of Two Fuzzy Soft Graphs

Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247–259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763–771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.

Decision-Making Approach with Fuzzy Type-2 Soft Graphs

Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory. Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship. Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters. In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory. We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles. We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples. The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems. We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services.

On total uniform fuzzy soft graphs

On total uniform fuzzy soft graphs

Granulation of ecological networks under fuzzy soft environment

The main idea of this work is the exploration of granular structures by applying the hybrid models of fuzzy soft sets and fuzzy soft graphs to discuss the indiscernibility partition of set of universe. The information granulation is examined by applying fuzzy soft theory, and the corresponding behavior of granules is reviewed. This article proposes a novel technique of formation of granular structures using fuzzy soft graphs and defines the fuzzy soft granules. Two degree-based models are introduced to explore the abstraction of these granular structure. Then, we use these two degree-based models to granulate the certain relationships between different species in an ecological system. Further, we develop and implement some algorithms of our proposed models to granulate the underconsideration networks. Finally, a comprehensive comparison of our proposed model with other existing techniques is presented to prove the applicability and effectiveness of fuzzy soft granulation.

Pythagorean fuzzy soft graphs with applications

Pythagorean fuzzy soft graphs with applications

Decision-making approach based on Pythagorean Dombi fuzzy soft graphs

A Pythagorean fuzzy set model is more useful than intuitionistic fuzzy set model to handle the imprecise information involving both membership and nonmembership degrees, and a soft set is an other parameterized point of view for handling the vagueness. A Pythagorean fuzzy soft graph is considered more capable than intuitionistic fuzzy soft graph for representing the parametric relationships between objects, and the Dombi operators with operational parameters have creditable extensibility. Based on these two notions, we propose the concept of Pythagorean Dombi fuzzy soft graph (PDFSG). We describe certain concepts of graph theory under Pythagorean Dombi fuzzy soft environment. Further, we define the degree sequence and degree set in PDFSG, and the concept of edge regular PDFSG with consequential properties. Moreover, we illustrate the examples in decision making including selection of suitable ETL software for a business intelligence project and evaluation of electronics companies. Finally, we present the comparison analysis of our proposed model to show the superiority than existing model.

Operations of Bipolar Fuzzy Soft Graph

Operations of Bipolar Fuzzy Soft Graph