Distances between intuitionistic fuzzy sets
By Eulalia Szmidt, Janusz Kacprzyk. Fuzzy Sets Syst., 2000
1,570 citations recorded by the source corpus.
Subfields: Artificial Intelligence, Management Science and Operations Research
View Paper: https://www.semanticscholar.org/paper/53c3482fe49277ab25f441699df3dc4b9eac7ece
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In Artificial Intelligence
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Citations in the corpus
- Intuitionistic Fuzzy Analytic Hierarchy Process (2014, background): “In order to rank the IFVs, Szmidt and Kacprzyk [44] proposed a function, which is in the mathematic form: ρ(α) = 0.5(1 + πα )(1 − μα ) (10) The smaller the value of ρ(α), the greater the IFV α in the sense of the amount of positive information included and reliability of information.”
- Picture fuzzy sets - A new concept for computational intelligence problems (2013, methodology): “Some of the defined operations are extensions of the FS operations [6], [11] , [12] and of some of operations for IFSs and IvIFSs [1 – 4], [10] and [13].”
- Using the OWA Operator in the Minkowski Distance (2008, methodology): “For the formulation used in fuzzy set theory see fo r example [31]–[33].”
- Distance and similarity measures for hesitant fuzzy sets (2011, methodology): “Some authors [17,24,29,30,35,39] improved Li and Cheng’ method [15].”
- On distance and correlation measures of hesitant fuzzy information (2011, background): “Szmidt and Kacprzyk 15 discussed a concept of correlation for data represented as intuitionistic fuzzy set adopting the concepts from statistics, proposed a formula for measuring the correlation coefficient (lying in [ − 1 , 1]) of intuitionistic fuzzy sets and showed the importance to take into acco”
- Picture fuzzy sets (2015, methodology): “Distance between picture fuzzy sets The following definition is an extension of the distances between intuitionistic fuzzy sets given by Szmidt and Kacprzyk in [15].”
- Intuitionistic and interval-valued intutionistic fuzzy preference relations and their measures of similarity for the evaluation of agreement within a group (2009, background): “Let X = { x 1 , x 2 , . . . , x n } be a finite universe of discourse, A and B be two IFSs in X , then Szmidt and Kacprzyk (2000) defined the normalized Hamming distance between A and B as below: By (4), we have: thus, (6) can be rewritten as: is called the normalized Hamming distance between α 1 and…”
- TOPSIS-Based Nonlinear-Programming Methodology for Multiattribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets (2010, background): “This idea was first put forward by Szmidt and Kacprzyk [25] when they studied the entropy in the context of IF events.”
- GRA method for multiple attribute decision making with incomplete weight information in intuitionistic fuzzy setting (2010, background): “Szmidt and Kacprzyk [16] proposed some solution concepts in group decision making with intuitionistic fuzzy preference relations, such as intuitionistic fuzzy core and consensus winner, etc. Szmidt and Kacprzyk [17] investigated the consensus-reaching process in group decision making based on indivi”