Power average-based score function and extension rule of hesitant fuzzy set and the hesitant power average operators

2018 ◽  
Vol 35 (3) ◽  
pp. 3873-3882 ◽  
Author(s):  
Huchang Liao ◽  
Xingli Wu ◽  
Abazar Keikha ◽  
Arian Hafezalkotob
Keyword(s):  
Fuzzy Set ◽  
Score Function ◽  
Hesitant Fuzzy Set ◽  
Extension Rule

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.

Research on hesitant fuzzy matroid based on satisfaction function

2021 ◽  
pp. 1-10
Author(s):  
Huimin Xiao ◽  
Meiqi Wang
Keyword(s):  
Fuzzy Set ◽  
Score Function ◽  
Mapping Function ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Decision ◽  
Data Set ◽  
Satisfaction Function ◽  
Actual Event ◽  
Event Information ◽  
Fuzzy Index

In this paper, we mainly extended the study of fuzzy matroid related problems to research the fuzzy decision method. Considering the ambiguity of actual event information and evaluation, we chose hesitant fuzzy set as the extended data set. To construct the hesitant fuzzy matroid, we defined the satisfaction function of hesitant fuzzy set combining hesitant fuzzy index entropy and score function, and defined the mapping function of fuzzy matroid through this function. We also defined the algorithm of hesitant fuzzy matroid and proved the theory of rank, basis of hesitant fuzzy matroid.

Complex q-rung orthopair fuzzy Schweizer–Sklar Muirhead mean aggregation operators and their application in multi-criteria decision-making

2021 ◽  
pp. 1-23
Author(s):  
Peide Liu ◽  
Tahir Mahmood ◽  
Zeeshan Ali
Keyword(s):  
Decision Making ◽  
Comparative Analysis ◽  
Imaginary Part ◽  
Fuzzy Set ◽  
Score Function ◽  
Aggregation Operators ◽  
Unit Interval ◽  
Multi Criteria Decision Making ◽  
Accuracy Function ◽  
Special Cases

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed.

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

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.

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.

A Hesitant Intuitionistic Fuzzy Set Approach to Study Ideals of Semirings

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.

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

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
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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