Hesitant fuzzy soft topology and its applications to multi-attribute group decision-making
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METHODOLOGIES AND APPLICATION
Hesitant fuzzy soft topology and its applications to multi-attribute group decision-making Muhammad Riaz1 • Bijan Davvaz2 • Atiqa Fakhar1 • Atiqa Firdous1
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The purpose of this research study is to extend the multi-attribute group decision-making (MAGDM) methods to hesitant fuzzy soft set (HFS-set), hesitant fuzzy soft topology (HFS-topology) and HFS-Hausdorff spaces in group decision-making environment, as HFS-set is more superior tool to capture vagueness, hesitancy and incompleteness in individual evaluations. In order to obtain optimal decisions in MAGDM, we present two algorithms based on hesitant fuzzy soft set and hesitant fuzzy soft topology. Lastly, we present MAGDM method by using HFS-Hausdorff space to deal with hesitancy and uncertainty. The developed methods have the ability to solve MADGM problems in which the assessment information on available alternatives, provided by the experts, is presented by hesitant fuzzy soft sets. Furthermore, the efficiency of proposed algorithms is shown by applying them to the real-world problems. We use reduct, optimum reduct, aggregate HFS-sets and weight vector according of given alternatives, priority of the attributes and customer demand for best MAGDM in the selection of car. Keywords Hesitant fuzzy set (HF-set) Hesitant fuzzy soft set (HFS-set) HFS-topology MAGDM
1 Introduction The analytical modelling and conferring of various types of uncertainties has become an issue of great importance in solving certain problems originating in different fields such as artificial intelligence, computational intelligence, image processing, signal processing, medicine, social sciences, economics and engineering. Although a number of mathematical models such as fuzzy set theory, rough set theory and interval mathematics are efficient tools to deal with Communicated by V. Loia. & Muhammad Riaz [email protected] Bijan Davvaz [email protected] Atiqa Fakhar [email protected] Atiqa Firdous [email protected] 1
Department of Mathematics, University of the Punjab, Lahore, Pakistan
2
Department of Mathematics, Yazd University, Yazd, Iran
uncertainties, all these theories have their own limitations. One major deficiency of these theories is the possible use of parameterization tools. Abualigah and Hanandeh (2015) applied genetic algorithms to information retrieval using vector space model. Genetic algorithms are usually used in information retrieval systems (IRs) to enhance the information retrieval process. Abualigah et al. (2017) introduced a new feature selection method to improve the document clustering using particle swarm optimization algorithm. Abualigah and Khader (2017b) introduced unsupervised text feature selection technique based on hybrid particle swarm optimization algorithm with genetic operators for the text clustering. Abualigah et al. (2018) introduced the idea of hybrid clustering analysis using imp
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