Hesitant fuzzy N -soft ELECTRE-II model: a new framework for decision-making
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ORIGINAL ARTICLE
Hesitant fuzzy N-soft ELECTRE-II model: a new framework for decisionmaking Muhammad Akram1 • Arooj Adeel2 • Ahmad N. Al-Kenani3 • Jose´ Carlos R. Alcantud4 Received: 19 September 2020 / Accepted: 28 October 2020 Springer-Verlag London Ltd., part of Springer Nature 2020
Abstract In the modelization of frameworks for multi-attribute decision-making, hesitancy embodies a convenient attitude toward undetermined or vague knowledge provided by distinct experts from a group. Hesitant fuzzy N-soft sets are a functional improvement in hesitant fuzzy sets with the practical spirit of N-soft sets. This analytical model accommodates the hesitant situations with evaluations by grades (e.g., in terms of star ratings) and partial degrees of membership. In this article, we approach the problem of selecting alternatives that are described by this model. We advocate for the use of an adapted form of the ELECTRE-II method, that we describe under the name ‘‘hesitant fuzzy N-soft ELECTRE-II method.’’ With the aim of designing this novel method, we first characterize the notion of hesitant fuzzy N-soft concordance and discordance sets and then construct strong and weak outranking relation, which allow us to rank the objects of the reference set. A practical example concerning the ranking of hotels based on star ratings is fully developed in order to illustrate the applicability of this method. Furthermore, an exhaustive comparison with the hesitant fuzzy N-soft ELECTRE-I and bipolar fuzzy ELECTRE-I methods is performed. Keywords Star ratings Decision-making Hesitant fuzzy N-soft sets ELECTRE-II
1 Introduction
& Jose´ Carlos R. Alcantud [email protected] Muhammad Akram [email protected] Arooj Adeel [email protected] Ahmad N. Al-Kenani [email protected] 1
Department of Mathematics, University of the Punjab, New Campus, Lahore 4590, Pakistan
2
Department of Mathematics, University of Education, Bank Road Campus, Lahore 4590, Pakistan
3
Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80219, Jeddah 21589, Saudi Arabia
4
BORDA Research Unit and IME, University of Salamanca, 37007 Salamanca, Spain
As a practical groundwork, multi-criteria decision-making (MCDM), also called multi-attribute decision-making (MADM), has intended to systematize the decisions among the objects from a reference set possessing multiple attributes or criteria. In several actually existing problems, a challenging task for decision-makers is to assign precise evaluations for objects with particularly blurry characteristics. When one wants to classify the decision opportunities for loosely defined MCDM problems, fuzzy sets [1] have been particularly convenient in order to illustrate some types of uncertainties [2]. Their importance is not limited to this field: For example, for solving fuzzy Fredholm–Volterra integro-differential equations and for the numerical solutions of fuzzy differential equations, the readers are referred to [3, 4]. Correspondin
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