Hybrid Soft Computing Models Applied to Graph Theory

Akram, Muhammad; Zafar, Fariha

doi:10.1007/978-3-030-16020-3

Cited by 32 publications

(16 citation statements)

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“…ere are known solutions of the assignment problems using the methods of graph theory in fuzzy conditions defined by the fuzzy bipartite graphs. e task is solved by "selecting the optimal (by the defined criterion) maximum fuzzy part from the initial defined fuzzy graph" [17,18].…”

Section: Target Assignment Model Graph Theory Uses Methodsmentioning

confidence: 99%

Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution

Beloglazov

Finaev

Soloviev

et al. 2020

Journal of Robotics

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The paper discusses the solution of the assignment task between two groups of mobile (MR) objects. The assignment task is to determine the purpose of MR to each other when playing football. This article analyzes well-known works devoted to the tasks of assignments, and the relevance of research in this area is noted. The task of target distribution is successfully solved with a small degree of uncertainty. The urgency of further research to solve the problem of target distribution in conditions of uncertainty is substantiated. The model of target assignment is considered. The basis of the model is a bipartite graph. The vertices of a bipartite graph are defined by the properties of MR. One group of MR is assigned red color and the other one group is blue. The properties of the mobile objects are formally determined by the membership grades given by the experts. Identification of a bipartite graph is a solution to the assignment problem. When the problem of target distribution on a bipartite graph is solved, the criterion of the maximum degree of bipartite is applied. Formulas are given to determine the degree of bipartite, taking into account the number of vertices in the graph and the weight of each edge in two fractions of the graph. The study of the target distribution model was carried out by the simulation method. A program is developed to solve the problem of assignments. Properties and degrees of belonging of properties of red and blue MR are set for carrying out researches. The program allows you to produce research and under equality of red and blue MR, and under their inequality. The analysis of modeling results is carried out.

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Section: Target Assignment Model Graph Theory Uses Methodsmentioning

confidence: 99%

Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution

Beloglazov

Finaev

Soloviev

et al. 2020

Journal of Robotics

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“…The fuzzy graphs theory is finding an increasing number of applications for modeling real-time systems, where the level of information inherent in the system depends on different levels of accuracy. The Different types of intuitionistic fuzzy graphs were considered in literature in order to cope with a diversity of practical cases: intuitionistic fuzzy competition graphs, intuitionistic fuzzy neighborhood graphs, intuitionistic fuzzy rough graphs, and others [13,14] were introduced to analyze the ecosystems and to represent the relations of competition among the species in the food web. Some properties and features of intuitionistic fuzzy graphs were considered [15], for example, edge irregular intuitionistic fuzzy graphs, edge totally irregular intuitionistic fuzzy graphs, and others are introduced and the intuitionistic fuzzy genus graph with its genus value, strong and weak intuitionistic fuzzy genus graph are defined, as well as the isomorphism properties on intuitionistic fuzzy genus graph are discussed [16].…”

Section: Introductionmentioning

confidence: 99%

On Computing Domination Set in Intuitionistic Fuzzy Graph

Bozhenyuk¹,

Belyakov²,

Knyazeva³

et al. 2021

IJCIS

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In this paper, the concept of minimal intuitionistic dominating vertex subset of an intuitionistic fuzzy graph was considered, and on its basis, the notion of a domination set as an invariant of the intuitionistic fuzzy graph was introduced. A method and an algorithm for finding all minimal intuitionistic dominating vertex subset and domination set was proposed. This method is the generalization of Maghout's method for fuzzy graphs. The example of finding the domination set of the intuitionistic fuzzy graph were considered as well.

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“…Thong and Son [32] explored multivariable fuzzy forecasting using PF clustering and the PF rule interpolation technique. Akram and Zafer [33] contributed fascinatingly to readers. Akram et al [34] presented and tested the Dijkstra algorithm using a TPFN of a picture fuzzy environmental network.…”

Section: Introductionmentioning

confidence: 99%

Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

Parimala¹,

Prakash²,

Topal

2021

Complex Intell. Syst.

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An elongation of the novel intuitionistic fuzzy set is a picture fuzzy set theory. The demonstration of this has been used to deal with the abstinence criteria in a decision-making problem. The uncertainty in nature occurs sometimes in real-world problems and amidst them, the prominent one is the shortest path problem (SPP) solving. In the last few years, one of the best algorithms on the network for finding SPP is Bellman–Ford. Due to uncertainty in the decision-making process, it becomes difficult for decision-makers for communicating their point of view and judgment with certainty. We conceive of SPP in this contribution via Bellman's algorithm (BA) for a network with trapezoidal picture fuzzy numbers (TPFNs). We introduce a new algorithm to stand the shortest picture fuzzy path between each pair of nodes. A TPFN is considered for the length of all edges. A numerical example for the validation of the presented algorithm has also been proposed. There has also been relative research with existing techniques showing the benefits of the new algorithm.

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Hybrid Soft Computing Models Applied to Graph Theory

Cited by 32 publications

References 0 publications

Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution

Methods Research and Software Development for Parameters Formalization of the Assignment Task Applicable to the Target Distribution

On Computing Domination Set in Intuitionistic Fuzzy Graph

Bellman–Ford algorithm for solving shortest path problem of a network under picture fuzzy environment

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