Entropy for intuitionistic fuzzy sets

By Eulalia Szmidt, Janusz Kacprzyk. Fuzzy Sets Syst., 2001

908 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c9393405c329fdccd6840f0d8bc970f0b1f62477

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Citations in the corpus

On similarity and entropy of neutrosophic sets (2013, neutral): “Szmidt & Kacprzyk [11] studied the entropy of intuitionistic fuzzy sets.”
A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets (2009, background): “Szmidt and Kacprzyk [27] derived an interval cardinality for intuitionistic fuzzy sets (IFS) [1].”
TOPSIS-Based Nonlinear-Programming Methodology for Multiattribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets (2010, methodology): “This idea was first put forward by Szmidt and Kacprzyk [25] when they studied the entropy in the context of IF events.”
Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making (2011, background): “…Gau et al., 1993; Grzegorzewski, 2004; Hong & Choi, 2000; Li, 2004; Li, 2005, 2008; Li & Cheng, 2002; Lin, Yuan, & Xia, 2007; Liu, 2007; Li, Wang, Liu, & Shan, 2009; Szmidt & Kacprzyk, 1996a, 1996b, 1996c, 1997, 2000, 2001a, 2001b, 2002, 2003; Tan & Chen, 2010; Wang, 2009; Wei, 2008; Ye, 2009b).”
Some geometric aggregation operators based on intuitionistic fuzzy sets (2006, background): “Szmidt and Kacprzyk (2001) proposed a non-probabilistic-type entropy measure for intuitionistic fuzzy sets.”
Intuitionistic Fuzzy Information Measures with Application in Rating of Township Development (2016, background): “The trigonometric intuitionistic fuzzy information measures h1(A) and h2(A) satisfy the following axiomatic requirements [34]: (P1): h1(A) = h2(A) = 0 (minimum) ⇔ A is a crisp set; (P2): h1(A) = h2(A) = 1 (maximum) ⇔ μA(xi) = νA(xi) for all xi ∈ X; (P3): h1(A) ≤ h1(B) and h2(A) ≤ h2(B) if A is less ”
Intuitionistic fuzzy information - Applications to pattern recognition (2007, methodology): “Definition 6 (Szmidt and Kacprzyk, 2001a).”
Intuitionistic Fuzzy Aggregation Operators (2007, background): “Szmidt and Kacprzyk [10] proposed a nonprobabilistic-type entropy measure for A-IFSs.”
Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making (2007, neutral): “2000; De et al., 2001; Deschrijver & Kerre, 2003; Grzegorzewski, 2004; Mondal & Samanta, 2001, 2002; Szmidt & Kacprzyk, 2000, 2001 ), and has been applied in different fields, including decision making (Atanassov, Pasi & Yager, 2005; Chen & Tan, 1994; Hong & Choi, 2000; Szmidt & Kacprzyk, 2002; Xu ”
Uncertainty measures for interval type-2 fuzzy sets (2007, background): “Note that Szmidt and Kacprzyk’s [62] deﬁnition and Cornelis and Kerre’s [16] deﬁnition are proposed for IFSs.”
Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets (2013, methodology): “Lots of studies have been done on this issue, for instance, Szmidt and Kacprzyk [20], Hong and Kim [8], Hung and Yang [9] and Xu and Chen [32] independently proposed various similarity measures based on different distance measures for IFSs.”
Hesitant fuzzy entropy and cross‐entropy and their use in multiattribute decision‐making (2012, background): “Szmidt and Kacprzyk 18 proposed a nonprobabilistic entropy measure for intuitionstic fuzzy sets.”
Supplier selection for development of petroleum industry facilities, applying multi-criteria decision making techniques including fuzzy and intuitionistic fuzzy TOPSIS with flexible entropy weighting (2016, methodology): “The second method (termed IFT-2 here) uses an entropy computation based upon that proposed by Szmidt & Kacprzyk (2001): EðCiÞ ¼ 1 n Xn j¼1 min mijðCiÞ; yijðCiÞ þ pijðCiÞ max mijðCiÞ; yijðCiÞ þ pijðCiÞ where i ¼ 1;2…;m; j ¼ 1;2…;n (28) The IFT-2 entropy values are then normalized and an entropy…”