Distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric

By P. Grzegorzewski. Fuzzy Sets Syst., 2004

640 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/ce33297c548dd70a809a690aca93ca84d10479f8

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Citations in the corpus

The interval-valued fuzzy TOPSIS method and experimental analysis (2008, methodology): “For measuring distances between IVFSs, we adopt several popular definitions proposed by Atanassov [4], Szmidt and Kacprzyk [16] and Grzegorzewski [8], including the generalizations of Hamming distance, Euclidean distance and their normalized counterparts.”
Extension of VIKOR method for decision making problem based on hesitant fuzzy set (2013, methodology): “As a generalization of fuzzy set [11–20], Torra and Narukawa [21] and Torra [22] proposed the hesitant fuzzy set which permitted the membership having a set of possible values and discussed the relationship between hesitant fuzzy set and intuitionistic fuzzy set.”
Distance and similarity measures for hesitant fuzzy sets (2011, methodology): “Hung and Yang [11] and Grzegorzewski [10] suggested a lot of similarity measures for IFSs and interval-valued fuzzy sets based on the Hausdorff metric.”
Some geometric aggregation operators based on intuitionistic fuzzy sets (2006, methodology): “Grzegorzewski (2004) suggested some methods for measuring distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets, based on the Hausdorff metric.”
An Extension of the Electre I Method for Group Decision-Making Under a Fuzzy Environment (2011, methodology): “There are generally two approaches in the literature: Hamming distance and Euclidean distance [121,122].”
TOPSIS-Based Nonlinear-Programming Methodology for Multiattribute Decision Making With Interval-Valued Intuitionistic Fuzzy Sets (2010, methodology): “Grzegorzewski [27] proposed some distance measures, which are based on Hausdorff metric.”
Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting (2012, background): “Grzegorzewski [24] proposed some distances between intuitionistic fuzzy sets and/or interval-valued fuzzy sets based on the Hausdorff metric.”
On distance and correlation measures of hesitant fuzzy information (2011, background): “8 For example, Grzegorzewski 9 proposed a distance measure between intuitionistic fuzzy sets 10 and/or interval-valued fuzzy sets 11 based on the Hausdorff metric.”
Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making (2007, positive): “Based on the Hausdorff metric, Grzegorzewski (2004) suggested some methods for measuring distances between IFSs.”
Handbook of Granular Computing (2008, methodology): “Other kinds of reducts are preserving: (i) the distance between attribute value vectors for any two objects if this distance is greater than a given threshold [89]; (ii) the distance between entropy distributions between any two objects if this distance exceeds a given threshold [90]; or (iii) the s”
Gray relational analysis method for intuitionistic fuzzy multiple attribute decision making (2011, background): “…& Burillo, 1996; Bustince, Kacprzyk, & Mohedano, 2000; Chen & Tan, 1994; De, Biswas, & Roy, 2000; Deschrijver & Kerre, 2007; 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;…”