Optimized data manipulation methods for intensive hesitant fuzzy set with applications to decision making

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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New aggregation operators of single-valued neutrosophic hesitant fuzzy set and their application in multi-attribute decision making

Pattern Analysis and Applications ◽

10.1007/s10044-017-0635-6 ◽

2017 ◽

Vol 22 (2) ◽

pp. 417-427 ◽

Cited By ~ 12

Author(s):

Chun-fang Liu ◽

Yue-Sheng Luo

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Aggregation Operators ◽

Hesitant Fuzzy Set ◽

Multi Attribute Decision Making

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Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽

10.3390/math6120280 ◽

2018 ◽

Vol 6 (12) ◽

pp. 280 ◽

Cited By ~ 21

Author(s):

Harish Garg ◽

Gagandeep Kaur

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Weight Vector ◽

Aggregation Operators ◽

Distance Measures ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Maximum Deviation ◽

Dual Hesitant Fuzzy Set ◽

Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

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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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Multiple-attribute Decision-Making Method under a Single-Valued Neutrosophic Hesitant Fuzzy Environment

Journal of Intelligent Systems ◽

10.1515/jisys-2014-0001 ◽

2015 ◽

Vol 24 (1) ◽

pp. 23-36 ◽

Cited By ~ 48

Author(s):

Jun Ye

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Intuitionistic Fuzzy Set ◽

Multiple Attribute Decision Making ◽

Weighted Averaging ◽

Hesitant Fuzzy Set ◽

Neutrosophic Set ◽

Fuzzy Environment ◽

Cosine Measure ◽

Multiple Attribute

AbstractOn the basis of the combination of single-valued neutrosophic sets and hesitant fuzzy sets, this article proposes a single-valued neutrosophic hesitant fuzzy set (SVNHFS) as a further generalization of the concepts of fuzzy set, intuitionistic fuzzy set, single-valued neutrosophic set, hesitant fuzzy set, and dual hesitant fuzzy set. Then, we introduce the basic operational relations and cosine measure function of SVNHFSs. Also, we develop a single-valued neutrosophic hesitant fuzzy weighted averaging (SVNHFWA) operator and a single-valued neutrosophic hesitant fuzzy weighted geometric (SVNHFWG) operator and investigate their properties. Furthermore, a multiple-attribute decision-making method is established on the basis of the SVNHFWA and SVNHFWG operators and the cosine measure under a single-valued neutrosophic hesitant fuzzy environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

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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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