Operations on type-2 fuzzy sets

By Nilesh N. Karnik, Jerry M. Mendel. Fuzzy Sets Syst., 2001

738 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c471fa1c73ccc90050da4a021976eb4f25c54f79

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Citations in the corpus

Decision-making in fuzzy environment (2012, background): “Also Corneils et al. (2006) and Karnik and Mendel (2001) noted that the main reason for proposing this new concept is the fact that, in the linguistic modeling of a phenomenon, the presentation of the linguistic expression in the form of ordinary fuzzy sets is not clear enough.”
Einstein Geometric Aggregation Operators using a Novel Complex Interval-valued Pythagorean Fuzzy Setting with Application in Green Supplier Chain Management (2021, background): “For example, interval-valued FS was explored by Zadeh (1975), Torra (2010) elaborated the principle of hesitant FS (HFS), Karnik and Mendel (2001) utilized certain operational laws based on type-2 FS (T-2FS), Mendel and John (2002) developed T2FS made simple, and Mahmood (2020) developed the theory…”
Toward General Type-2 Fuzzy Logic Systems Based on zSlices (2010, methodology): “The intersection operation for general type-2 fuzzy sets can be computed by discretizing the respective sets into vertical slices and performing the meet operation as described in [10].”
Equalization of nonlinear time-varying channels using type-2 fuzzy adaptive filters (2000, background): “For the proof of this theorem see [13].”
Computing derivatives in interval type-2 fuzzy logic systems (2004, methodology): “For an interval singleton type-2 FLS, it is possible to obtain closed-form formulas for all of these quantities, and these results are given in Section A.2 of Appendix A; they are obtained by using well-known closed-form formulas for the join and meet of interval sets (e.g., [ 1 ] and [6]).”
Modification of the Best-Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers (2018, background): “In addition, Grattan-Ginis (1975) and Karnik and Mendel (2001) consider that these linguistic expressions with the help of classic fuzzy sets (fuzzy sets type-1) are not sufficiently clear and precise.”
Advances in type-2 fuzzy sets and systems (2007, background): “When all MFs are Gaussian, then Karnik and Mendel [28] have an approximation for computing the meet under product t-norm, one that leads to another Gausssian MF, so that the approximate meet is ‘‘reproducing’’, and can be expanded in multi-argument form.”
Extension of fuzzy TOPSIS method based on interval-valued fuzzy sets (2009, background): “[16] and Karnik and Mendel [17] noted that the main reason for proposing this new concept is the fact that in the linguistic modeling of a phenomenon, the presentation of the linguistic expression in the form of ordinary fuzzy sets is not clear enough.”
An integrated multi-criteria decision-making methodology based on type-2 fuzzy sets for selection among energy alternatives in Turkey (2015, background): “Such sets are fuzzy sets whose membership grades themselves are type-1 fuzzy sets; they are very useful in circumstances where it is difficult to determine an exact membership function for a fuzzy set; hence, they are useful for incorporating linguistic uncertainties [25].”
Pythagorean Membership Grades in Multicriteria Decision Making (2014, background): “Most notable among these have been the introduction of intuitionistic [5]–[7] and interval valued [8], [9] fuzzy subsets.”