A Decision Framework under a Linguistic Hesitant Fuzzy Set for Solving Multi-Criteria Group Decision Making Problems

With fast-growing interest in sustainable healthcare management, proper selection and evaluation of hospitals become highly essential. Generally, experts/decision-makers (DMs) prefer qualitative information for rating objects. Motivated by this idea, in this paper, a linguistic hesitant fuzzy set (LHFS) is adopted for elicitation of preference information. The LHFS provides qualitative preferences of DMs as well as reflects their hesitancy, inconsistency, and vagueness. Motivated by the power of LHFS, in this paper we present a new decision framework that initially presents some operational laws and properties. Further, a new aggregation operator called simple linguistic hesitant fuzzy weighted geometry (SLHFWG) is proposed under the LHFS context that uses the strength of power operators. Some properties of SLHFWG are also investigated. Criteria weights are estimated using a newly proposed linguistic hesitant fuzzy statistical variance (LHFSV) method, and objects are ranked using the newly proposed linguistic hesitant fuzzy VIKOR (visekriterijumska optimizacijai kompromisno resenje) (LHFVIKOR) method, which is an extension of VIKOR under the LHFS context. The practicality and usefulness of the proposal are demonstrated by using a hospital evaluation example for sustainable healthcare management. Finally, the strengths and weaknesses of the proposal are realized by comparison with other methods.

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Interval-Valued Pythagorean Hesitant Fuzzy Set and Its Application to Multiattribute Group Decision-Making

Complexity ◽

10.1155/2020/1724943 ◽

2020 ◽

Vol 2020 ◽

pp. 1-26

Author(s):

Maoyin Zhang ◽

Tingting Zheng ◽

Wanrong Zheng ◽

Ligang Zhou

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Score Function ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

Interval Numbers ◽

Operational Laws ◽

Interval Valued

Pythagorean hesitant fuzzy sets are widely watched because of their excellent ability to deal with uncertainty, imprecise and vague information. This paper extends Pythagorean hesitant fuzzy environments to interval-valued Pythagorean hesitant fuzzy environments and proposes the concept of interval-valued Pythagorean hesitant fuzzy set (IVPHFS), which allows the membership of each object to be a set of several pairs of possible interval-valued Pythagorean fuzzy elements. Furthermore, we develop a series of aggregation operators for interval-valued Pythagorean hesitant fuzzy information and apply them to multiattribute group decision-making (MAGDM) problems. Then, some desired operational laws and properties of IVPHFSs are studied. Especially, considering an interval-valued Pythagorean fuzzy element (IVPHFE) is formed by several pairs of interval values, this paper proposes the concepts of score function and accuracy function in the form of two interval numbers which can retain interval-valued Pythagorean fuzzy information as much as possible. Then, the relationship among these operators is discussed by comparing the interval numbers. Eventually, an illustrative example fully shows the feasibility, practicality, and effectiveness of the proposed approach.

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Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making

Mathematics ◽

10.3390/math7070594 ◽

2019 ◽

Vol 7 (7) ◽

pp. 594 ◽

Cited By ~ 1

Author(s):

Mi Jung Son ◽

Jin Han Park ◽

Ka Hyun Ko

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Multiple Attribute Decision Making ◽

Aggregation Operators ◽

Decision Makers ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Multiple Attribute

As an extension of the fuzzy set, the hesitant fuzzy set is used to effectively solve the hesitation of decision-makers in group decision-making and to rigorously express the decision information. In this paper, we first introduce some new hesitant fuzzy Hamacher power-aggregation operators for hesitant fuzzy information based on Hamacher t-norm and t-conorm. Some desirable properties of these operators is shown, and the interrelationships between them are given. Furthermore, the relationships between the proposed aggregation operators and the existing hesitant fuzzy power-aggregation operators are discussed. Based on the proposed aggregation operators, we develop a new approach for multiple-attribute decision-making problems. Finally, a practical example is provided to illustrate the effectiveness of the developed approach, and the advantages of our approach are analyzed by comparison with other existing approaches.

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Extended TOPSIS method based on the entropy measure and probabilistic hesitant fuzzy information and their application in decision support system

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202700 ◽

2021 ◽

pp. 1-12

Author(s):

Muhammad Naeem ◽

Muhammad Ali Khan ◽

Saleem Abdullah ◽

Muhammad Qiyas ◽

Saifullah Khan

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Distance Measure ◽

Group Decision ◽

Hesitant Fuzzy Set ◽

Entropy Measure ◽

Fuzzy Information ◽

Score Functions ◽

Fuzzy Environment ◽

Basic Operating

Probabilistic hesitant fuzzy Set (PHFs) is the most powerful and comprehensive idea to support more complexity than developed fuzzy set (FS) frameworks. In this paper, it can explain a novel, improved TOPSIS-based method for multi-criteria group decision-making (MCGDM) problem through the Probabilistic hesitant fuzzy environment, in which the weights of both experts and criteria are completely unknown. Firstly, we discuss the concept of PHFs, score functions and the basic operating laws of PHFs. In fact, to compute the unknown weight information, the generalized distance measure for PHFs was defined based on the Probabilistic hesitant fuzzy entropy measure. Second, MCGDM will be presented with the PHF information-based decision-making process.

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Interval-Valued Probabilistic Hesitant Fuzzy Set Based Muirhead Mean for Multi-Attribute Group Decision-Making

Mathematics ◽

10.3390/math7040342 ◽

2019 ◽

Vol 7 (4) ◽

pp. 342 ◽

Cited By ~ 6

Author(s):

Krishankumar ◽

Ravichandran ◽

Ahmed ◽

Kar ◽

Peng

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Partial Information ◽

Programming Model ◽

Hesitant Fuzzy Set ◽

Occurrence Probability ◽

Source Selection ◽

Interval Valued

As a powerful generalization to fuzzy set, hesitant fuzzy set (HFS) was introduced, which provided multiple possible membership values to be associated with a specific instance. But HFS did not consider occurrence probability values, and to circumvent the issue, probabilistic HFS (PHFS) was introduced, which associates an occurrence probability value with each hesitant fuzzy element (HFE). Providing such a precise probability value is an open challenge and as a generalization to PHFS, interval-valued PHFS (IVPHFS) was proposed. IVPHFS provided flexibility to decision makers (DMs) by associating a range of values as an occurrence probability for each HFE. To enrich the usefulness of IVPHFS in multi-attribute group decision-making (MAGDM), in this paper, we extend the Muirhead mean (MM) operator to IVPHFS for aggregating preferences. The MM operator is a generalized operator that can effectively capture the interrelationship between multiple attributes. Some properties of the proposed operator are also discussed. Then, a new programming model is proposed for calculating the weights of attributes using DMs’ partial information. Later, a systematic procedure is presented for MAGDM with the proposed operator and the practical use of the operator is demonstrated by using a renewable energy source selection problem. Finally, the strengths and weaknesses of the proposal are discussed in comparison with other methods.

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OPERATOR-OPERATOR PADA HIMPUNAN KABUR HESITANT BERNILAI INTERVAL

Jurnal Matematika UNAND ◽

10.25077/jmu.8.1.17-25.2019 ◽

2019 ◽

Vol 8 (1) ◽

pp. 17

Author(s):

Awanda Amelia Maron ◽

Yudiantri Asdi

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Hesitant Fuzzy Set ◽

Interval Valued

Chen dan Xu memperkenalkan tentang relasi preference hesitant bernilai interval dalam proses pengambilan keputusan kelompok(Group Decision Making/GDM ) [2]. Pada proses GDM digunakan operator-operator untuk mengumpulkan informasi Interval-valued Hesitant Fuzzy Set (IVHFS) [2]. Konsep himpunan kabur hesitant bernilai interval banyak digunakan pada teori pengambilan keputusan. akan tetapi pada penelitian ini hanya dibatasi kajian aljabar yaitu dikaji tentang sifat-sifat operasi pada elemen kabur hesitant bernilai interval dan bentuk operator-operator pada IVHFS. Operasi ring sum, ring product, irisan dan gabungan pada elemen kabur hesitant bernilai interval memenuhi sifat-sifat aljabar yaitu sifat komutatif, sifat asosiatif, sifat distributif. Bentuk operator-operator pada himpunan kabur hesitant bernilai interval yaitu operator GIVHFWA, GIVHFWG dan operator GIVHFOWA, GIVHFOWG.Kata Kunci :himpunan kabur hesitant bernilai interval, sifat-sifat operasi, operator

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A BI-OBJECTIVE SCORE-VARIANCE BASED LINEAR ASSIGNMENT METHOD FOR GROUP DECISION MAKING WITH HESITANT FUZZY LINGUISTIC TERM SETS

Technological and Economic Development of Economy ◽

10.3846/20294913.2016.1275878 ◽

2018 ◽

Vol 24 (3) ◽

pp. 1125-1148 ◽

Cited By ~ 4

Author(s):

Seyed Hossein RAZAVI HAJIAGHA ◽

Meisam SHAHBAZI ◽

Hannan AMOOZAD MAHDIRAJI ◽

Hossein PANAHIAN

Keyword(s):

Decision Making ◽

Group Decision Making ◽

Group Decision ◽

Decision Makers ◽

Assignment Method ◽

Linguistic Term ◽

Criteria Weights ◽

Individual Evaluation ◽

Fuzzy Linguistic ◽

Linear Assignment

Decision makers usually prefer to express their preferences by linguistic variables. Classic fuzzy sets allowed expressing these preferences using a single linguistic value. Considering inevitable hesitancy of decision makers, hesitant fuzzy linguistic term sets allowed them to express individual evaluation using several linguistic values. Therefore, these sets improve the ability of humans to determine believes using their own language. Considering this feature, in this paper a method upon linear assignment method is proposed to solve group decision making problems using this kind of information, when criteria weights are known or unknown. The performance of the proposed method is illustrated in a numerical example and the results are compared with other methods to delineate the models efficiency. Following a logical and well-known mathematical logic along with simplicity of execution are the main advantages of the proposed method.

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Pythagorean Hesitant Fuzzy Information Aggregation and Their Application to Multi-Attribute Group Decision-Making Problems

Journal of Intelligent Systems ◽

10.1515/jisys-2017-0231 ◽

2018 ◽

Vol 29 (1) ◽

pp. 154-171 ◽

Cited By ~ 6

Author(s):

Muhammad Sajjad Ali Khan ◽

Saleem Abdullah ◽

Asad Ali ◽

Khaista Rahman

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Group Decision ◽

Information Aggregation ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Fuzzy Information ◽

New Approach ◽

Fuzzy Environment ◽

Multidimensional Evaluation

Abstract In this paper, we introduce the concept of the Pythagorean hesitant fuzzy set (PHFS), which is the generalization of the intuitionistic hesitant fuzzy set under the restriction that the square sum of its membership degrees is ≤1. In decision making with PHFSs, aggregation operators play a key role because they can be used to synthesize multidimensional evaluation values represented as Pythagorean hesitant fuzzy values into collective values. Under PHFS environments, Pythagorean hesitant fuzzy ordered weighted averaging and Pythagorean fuzzy ordered weighted geometric operators are used to aggregate the Pythagorean hesitant fuzzy values. The main advantage of these operators is that they provide more accurate and valuable results. Furthermore, these operators are applied to decision-making problems in which experts provide their preferences in the Pythagorean hesitant fuzzy environment to show the validity, practicality, and effectiveness of the new approach. Finally, we compare the proposed approach to the existing methods.

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A Novel Multi-Attribute Group Decision-Making Approach in the Framework of Proportional Dual Hesitant Fuzzy Sets

Applied Sciences ◽

10.3390/app9061232 ◽

2019 ◽

Vol 9 (6) ◽

pp. 1232 ◽

Cited By ~ 3

Author(s):

Zia Bashir ◽

Yasir Bashir ◽

Tabasam Rashid ◽

Jawad Ali ◽

Wei Gao

Keyword(s):

Decision Making ◽

Fuzzy Sets ◽

Group Decision Making ◽

Fuzzy Set ◽

Distance Measure ◽

Group Decision ◽

Traditional Approach ◽

Hesitant Fuzzy Set ◽

Flexible Tool ◽

Dual Hesitant Fuzzy Set

Making decisions are very common in the modern socio-economic environments. However, with the increasing complexity of the social, today’s decision makers (DMs) face such problems in which they hesitate and irresolute to provide their views. To cope with these uncertainties, many generalizations of fuzzy sets are designed, among them dual hesitant fuzzy set (DHFS) is quite resourceful and efficient in solving problems of a more vague nature. In this article, a novel concept called proportional dual hesitant fuzzy set (PDHFS) is proposed to further improve DHFS. The PDHFS is a flexible tool composed of some possible membership values and some possible non-membership values along with their associated proportions. In the theme of PDHFS, the proportions of membership values and non-membership values are considered to be independent. Some basic operations, properties, distance measure and comparison method are studied for the proposed set. Thereafter, a novel approach based on PDHFSs is developed to solve problems for multi-attribute group decision-making (MAGDM) in a fuzzy situation. It is totally different from the traditional approach. Finally, a practical example is given in order to elaborate the proposed method for the selection of the best alternative and detailed comparative analysis is given in order to validate the practicality.

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A Group Decision Framework for Renewable Energy Source Selection under Interval-Valued Probabilistic linguistic Term Set

Energies ◽

10.3390/en13040986 ◽

2020 ◽

Vol 13 (4) ◽

pp. 986 ◽

Cited By ~ 7

Author(s):

Raghunathan Krishankumar ◽

Arunodaya Raj Mishra ◽

Kattur Soundarapandian Ravichandran ◽

Xindong Peng ◽

Edmundas Kazimieras Zavadskas ◽

...

Keyword(s):

Decision Making ◽

Renewable Energy ◽

Group Decision ◽

Decision Framework ◽

Probabilistic Linguistic Term Set ◽

Source Selection ◽

Energy Assessment ◽

Linguistic Term ◽

Criteria Weights ◽

Interval Valued

In recent years, the assessment of desirable renewable energy alternative has been an extremely important concern that could change the environment and economic growth. To tackle the circumstances, some authors have paid attention to selecting the desirable renewable energy option by employing the decision-making assessment and linguistic term sets. With a fast-growing interest in multi-criteria group decision-making (MCGDM) problems, researchers are tirelessly working towards new techniques for better decision-making. Decision makers (DMs) generally rate alternatives linguistically with different probabilities occurring for each term. Previous studies on linguistic decision-making have either ignored this idea or have used an only a single value for representing the weight of the linguistic term. Since expression of the complete probability distribution is hard and implicit hesitation exists, representation of weights of the linguistic terms using a single value becomes imprecise and unreasonable. To avoid this challenge, an interval-valued probabilistic linguistic term set (IVPLTS) is used, which is a generalization of (probabilistic linguistic term set) PLTS. Inspired by the usefulness of IVPLTS concept, we develop a decision framework for rational decision making. Initially, some operational laws and axioms are presented. Further, a novel aggregation operator known as interval-valued probabilistic linguistic simple weighted geometry (IVPLSWG) is developed for aggregating DMs’ preferences. Also, criteria weights are determined using the newly developed interval-valued probabilistic linguistic standard variance (IVPLSV) approach and alternatives are ranked using the extended VIKOR (VlseKriterijumskaOptimizacijaKompromisnoResenje) method under IVPLTS environment. Finally, a numerical example of renewable energy assessment is demonstrated to show the practicality of the developed decision framework. Also, the strengths and weaknesses of the developed decision framework are illustrated by comparison with existing ones.

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