Decision Making with Uncertainty Using Hesitant Fuzzy Sets

Faizi, Shahzad; Rashid, Tabasam; Sałabun, Wojciech; Zafar, Sohail; Wątróbski, Jarosław

doi:10.1007/s40815-017-0313-2

Cited by 160 publications

(79 citation statements)

References 50 publications

(51 reference statements)

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“…. Using this notation, the interval [2,4] is the proper interval ( [2,4] , ∃) and the interval [3,1] is the improper interval ( [1,3] , ∀). A pointwise interval can be considered as either proper or improper.…”

Section: Modal Intervalsmentioning

confidence: 99%

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A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba

Adillon

2017

Symmetry

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Abstract:We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name "modal interval trapezoidal fuzzy numbers". In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers.

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Section: Modal Intervalsmentioning

confidence: 99%

“…Nowadays, we can find applications of fuzzy sets in the most part of scientific disciplines, such as decision-making [2][3][4], probability [5], control theory [6], medical sciences [7], characterization of complex systems [8], among others.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba

Adillon

2017

Symmetry

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“…Generally, decision making is a cognitive process based on different mental and reasoning processes that lead to the choice of a suitable alternative from a set of possible alternatives in a decision situation [1][2][3][4][5]. Because of the inherent complexity and uncertainty of the decision situation or the existence of multiple and conflicting objectives, decision-making problems are complex and difficult; particularly in the era of big data, decision making becomes more complicated because the huge amounts of decision information and alternatives are continuously growing.…”

Section: Introductionmentioning

confidence: 99%

A New Hesitant Fuzzy Linguistic TOPSIS Method for Group Multi-Criteria Linguistic Decision Making

2017

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Hesitant fuzzy linguistic decision making is a focus point in linguistic decision making, in which the main method is based on preference ordering. This paper develops a new hesitant fuzzy linguistic TOPSIS method for group multi-criteria linguistic decision making; the method is inspired by the TOPSIS method and the preference degree between two hesitant fuzzy linguistic term sets (HFLTSs). To this end, we first use the preference degree to define a pseudo-distance between two HFLTSs and analyze its properties. Then we present the positive (optimistic) and negative (pessimistic) information of each criterion provided by each decision maker and aggregate these by using weights of decision makers to obtain the hesitant fuzzy linguistic positive and negative ideal solutions. On the basis of the proposed pseudo-distance, we finally obtain the positive (negative) ideal separation matrix and a new relative closeness degree to rank alternatives. We also design an algorithm based on the provided method to carry out hesitant fuzzy linguistic decision making. An illustrative example shows the elaboration of the proposed method and comparison with the symbolic aggregation-based method, the hesitant fuzzy linguistic TOPSIS method and the hesitant fuzzy linguistic VIKOR method; it seems that the proposed method is a useful and alternative decision-making method.

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“…In recent years, various methods, such as utility additive method (UTA) [2], robust ordinal regression (ROR) [3], analytic hierarchy process (AHP) [4], analytic network process (ANP) [5], primitive cognitive network process (P-CNP) [6], step-wise weight assessment ratio analysis (SWARA) [7,8], weighted aggregated sum product assessment (WASPAS) [9], factor relationship (FARE) method [10], the visekriterijumska optimizacija i kompromisno resenje (VIKOR) method [11], the characteristic objects method (COMET) [12], and COMET with hesitant fuzzy sets (HFS COMET) [13,14] have been proposed to handle MADM problems. Among these methods, AHP has been increasingly studied by plenty of researchers and applied in various applications due to its simplicity and practicability [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

The Interval Cognitive Network Process for Multi-Attribute Decision-Making

Yin

Cheng

et al. 2017

Symmetry

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Aiming at combining the good characteristics of a differential scale in representing human cognition and the favorable properties of interval judgments in expressing decision-makers' uncertainty, this paper proposes the interval cognitive network process (I-CNP) to extend the primitive cognition network process (P-CNP) to handle interval judgments. The key points of I-CNP include a consistency definition for an interval pairwise opposite matrix (IPOM) and a method to derive interval utilities from an IPOM. This paper defines a feasible region-based consistency definition and a transitivity based consistency definition for an IPOM. Both of the two definitions are equivalent to the consistency definition for a crisp pairwise opposite matrix (POM) when an IPOM is reduced to a POM. Two methods that are able to derive interval utilities from both consistent and inconsistent IPOMs are developed based on the two definitions. Four numerical examples are used to illustrate the proposed methods and to compare I-CNP to interval analytic hierarchy process (IAHP). The results show that I-CNP reflects the decision-makers' cognition better, and that the suggestions provided by I-CNP are more convincing. I-CNP provides new useful alternative tools for multi-attribute decision-making problems.

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Decision Making with Uncertainty Using Hesitant Fuzzy Sets

Cited by 160 publications

References 50 publications

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

A New Hesitant Fuzzy Linguistic TOPSIS Method for Group Multi-Criteria Linguistic Decision Making

The Interval Cognitive Network Process for Multi-Attribute Decision-Making

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