Hesitant Fuzzy Set and Its Extensions

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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A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

International Journal of Fuzzy System Applications ◽

10.4018/ijfsa.2021070101 ◽

2021 ◽

Vol 10 (3) ◽

pp. 1-17

Author(s):

Debabrata Mandal

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Cartesian Product ◽

Intuitionistic Fuzzy Set ◽

Ideal Theory ◽

Hesitant Fuzzy Set ◽

Neutrosophic Set ◽

Intuitionistic Fuzzy ◽

Interval Valued ◽

The Ideal

The classical set theory was extended by the theory of fuzzy set and its several generalizations, for example, intuitionistic fuzzy set, interval valued fuzzy set, cubic set, hesitant fuzzy set, soft set, neutrosophic set, etc. In this paper, the author has combined the concepts of intuitionistic fuzzy set and hesitant fuzzy set to study the ideal theory of semirings. After the introduction and the priliminary of the paper, in Section 3, the author has defined hesitant intuitionistic fuzzy ideals and studied several properities of it using the basic operations intersection, homomorphism and cartesian product. In Section 4, the author has also defined hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals of a semiring and used these to find some characterizations of regular semiring. In that section, the author also has discussed some inter-relations between hesitant intuitionistic fuzzy ideals, hesitant intuitionistic fuzzy bi-ideals and hesitant intuitionistic fuzzy quasi-ideals, and obtained some of their related properties.

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Interval-valued probabilistic hesitant fuzzy set and its application in the Arctic geopolitical risk evaluation

International Journal of Intelligent Systems ◽

10.1002/int.22069 ◽

2018 ◽

Vol 34 (4) ◽

pp. 627-651 ◽

Cited By ~ 7

Author(s):

Chenyang Song ◽

Hua Zhao ◽

Zeshui Xu ◽

Zhinan Hao

Keyword(s):

Fuzzy Set ◽

Risk Evaluation ◽

Hesitant Fuzzy Set ◽

The Arctic ◽

Interval Valued

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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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Convexity of hesitant fuzzy sets based on aggregation functions

Computer Science and Information Systems ◽

10.2298/csis200428045h ◽

2020 ◽

pp. 45-45

Author(s):

Pedro Huidobro ◽

Pedro Alonso ◽

Vladimír Janis ◽

Susana Montes

Keyword(s):

Fuzzy Sets ◽

Fuzzy Set ◽

Fuzzy Optimization ◽

Hesitant Fuzzy Set ◽

Hesitant Fuzzy Sets ◽

Geometric Properties ◽

Aggregation Functions ◽

Definition Of

Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

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