A novel possibility measure to interval-valued intuitionistic fuzzy set using connection number of set pair analysis and its applications

2019 ◽  
Vol 32 (8) ◽  
pp. 3337-3348 ◽  
Author(s):  
Harish Garg ◽  
Kamal Kumar
Keyword(s):  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Set Pair Analysis ◽  
Possibility Measure ◽  
Connection Number ◽  
Intuitionistic Fuzzy ◽  
Pair Analysis ◽  
Interval Valued

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.

MAGDM Problems with Correlation Coefficient of Triangular Fuzzy IFS

2017 ◽  
pp. 154-192
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Decision Making ◽  
Correlation Coefficient ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Multiple Attribute ◽  
Decision Making Models ◽  
Magdm Problems ◽  
Interval Valued

Correlation coefficient of Intuitionistic Fuzzy Set (IFS), Interval valued IFS, Triangular IFS and Trapezoidal IFS are already present in the literature. This paper proposes the correlation coefficient for Triangular Fuzzy Intuitionistic Fuzzy set (TrFIFS). The method on uncertain Multiple Attribute Group Decision Making (MAGDM) problems based on aggregating intuitionistic fuzzy information is investigated for TrFIFSs. The Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Averaging (TrFIFOWA) operator is proposed for TrFIFSs and the Triangular Fuzzy Intuitionistic Fuzzy Ordered Weighted Geometric (TrFIFOWG) operator is utilized for decision making models where expert weights are completely unknown. Based on these operators and the correlation coefficient defined for the TrFIFSs, new decision making models are proposed with numerical illustrations. Some comparisons are also made with existing ranking methods for validity.

scholarly journals Distance Based Entropy Measure of Interval-Valued Intuitionistic Fuzzy Sets and Its Application in Multicriteria Decision Making

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Tabasam Rashid ◽  
Shahzad Faizi ◽  
Sohail Zafar
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Set ◽  
Multicriteria Decision Making ◽  
Fuzzy Entropy ◽  
Entropy Measure ◽  
Multicriteria Decision ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Fuzzy entropy means the measurement of fuzziness in a fuzzy set and therefore plays a vital role in solving the fuzzy multicriteria decision making (MCDM) and multicriteria group decision making (MCGDM) problems. In this study, the notion of the measure of distance based entropy for uncertain information in the context of interval-valued intuitionistic fuzzy set (IVIFS) is introduced. The arithmetic and geometric average operators are firstly used to aggregate the interval-valued intuitionistic fuzzy information provided by the decision makers (DMs) or experts corresponding to each alternative, and then the fuzzy entropy of each alternative is calculated based on proposed distance measure. Several numerical examples are solved to demonstrate the application to MCDM and MCGDM problems to show the effectiveness of the proposed approach.

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