Interval-valued probabilistic hesitant fuzzy set-based framework for group decision-making with unknown weight information

2020 ◽  
Author(s):  
Raghunathan Krishankumar ◽  
Kattur Soundarapandian Ravichandran ◽  
Amir H. Gandomi ◽  
Samarjit Kar
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Interval Valued

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

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 342 ◽  
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.

scholarly journals OPERATOR-OPERATOR PADA HIMPUNAN KABUR HESITANT BERNILAI INTERVAL

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

Interval-valued probabilistic hesitant fuzzy set for multi-criteria group decision-making

2018 ◽  
Vol 23 (21) ◽  
pp. 10853-10879 ◽  
Author(s):  
R. Krishankumar ◽  
K. S. Ravichandran ◽  
Samarjit Kar ◽  
Pankaj Gupta ◽  
Mukesh Kumar Mehlawat
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Interval Valued

scholarly journals An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0252115
Author(s):  
Qasim Noor ◽  
Tabasam Rashid ◽  
Syed Muhammad Husnine
Keyword(s):  
Decision Making ◽  
At Risk ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Value At Risk ◽  
Group Decision ◽  
Hesitant Fuzzy Set ◽  
Stock Selection ◽  
Decision Making Model ◽  
Interval Valued

Generally, in real decision-making, all the pieces of information are used to find the optimal alternatives. However, in many cases, the decision-makers (DMs) only want “how good/bad a thing can become.” One possibility is to classify the alternatives based on minimum (tail) information instead of using all the data to select the optimal options. By considering the opportunity, we first introduce the value at risk (VaR), which is used in the financial field, and the probabilistic interval-valued hesitant fuzzy set (PIVHFS), which is the generalization of the probabilistic hesitant fuzzy set (PHFS). Second, deemed value at risk (DVaR) and reckoned value at risk (RVaR) are proposed to measure the tail information under the probabilistic interval-valued hesitant fuzzy (PIVHF) environment. We proved that RVaR is more suitable than DVaR to differentiate the PIVHFEs with example. After that, a novel complete group decision-making model with PIVHFS is put forward. This study aims to determine the most appropriate alternative using only tail information under the PIVHF environment. Finally, the proposed methods’ practicality and effectiveness are tested using a stock selection example by selecting the ideal stock for four recently enrolled stocks in China. By using the novel group decision-making model under the environment of PIVHFS, we see that the best stock is E4 when the distributors focus on the criteria against 10% certainty degree and E1 is the best against the degree of 20%, 30%, 40% and 50% using the DVaR method. On the other hand when RVaR method is used then the best alternative is E4 and the worst is E2 against the different certainty degrees. Furthermore, a comparative analysis with the existing process is presented under the PHF environment to illustrate the effectiveness of the presented approaches.

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

Complexity ◽  
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.

scholarly journals Interval-Valued Intuitionistic Hesitant Fuzzy Aggregation Operators and Their Application in Group Decision-Making

2013 ◽  
Vol 2013 ◽  
pp. 1-33 ◽  
Author(s):  
Zhiming Zhang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Set ◽  
Group Decision ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Mathematical Tool ◽  
Fuzzy Information ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modelling people’s hesitancy in daily life. In this paper, we extend the hesitant fuzzy set to interval-valued intuitionistic fuzzy environments and propose the concept of interval-valued intuitionistic hesitant fuzzy set, which allows the membership of an element to be a set of several possible interval-valued intuitionistic fuzzy numbers. The aim of this paper is to develop a series of aggregation operators for interval-valued intuitionistic hesitant fuzzy information. Then, some desired properties of the developed operators are studied, and the relationships among these operators are discussed. Furthermore, we apply these aggregation operators to develop an approach to multiple attribute group decision-making with interval-valued intuitionistic hesitant fuzzy information. Finally, a numerical example is provided to illustrate the application of the developed approach.

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

2019 ◽  
Vol 9 (6) ◽  
pp. 1232 ◽  
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.

scholarly journals Multiple Attributes Group Decision-Making Approaches Based on Interval-Valued Dual Hesitant Fuzzy Unbalanced Linguistic Set and Their Applications

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Xiaowen Qi ◽  
Junling Zhang ◽  
Changyong Liang
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Hesitant Fuzzy Set ◽  
Linguistic Term ◽  
Multiple Attributes ◽  
Interval Valued ◽  
Power Aggregation Operator

Aiming at multiple attributes group decision-making (MAGDM) problems that characterize uncertainty nature and decision hesitancy, firstly, we propose the interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) in which two sets of interval-valued hesitant fuzzy membership degrees and nonmembership degrees are employed to supplement the most preferred unbalanced linguistic term, as an effective hybrid expression tool to elicit complicate preferences of decision-makers more comprehensively and flexibly than existing tools based on classic linguistic term set. Basic operations for IVDHFUBLS are further defined; also a novel distance measure is developed to avoid potential information distortion that could be brought about by traditional complementing methodology for hesitant fuzzy set and its derivatives. In view of the fundamental role of aggregation operators in MAGDM modelling, we next develop some extended power aggregation operators for IVDHFUBLS, including power aggregation operator, weighted power aggregation operator, and induced power ordered weighted aggregation operator; their desirable properties and special cases are also analyzed theoretically. Subsequently, with support of the above methods, we develop two effective approaches for our targeted complex decision-making problems and verify their effectiveness and practicality by numerical studies.

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