%0 Journal Article %1 Mendel15insk %A Mendel, Jerry M. %D 2015 %J Informatik-Spektrum %K 01614 springer paper ai knowledge processing fuzzy logic theory %N 6 %P 523--532 %R 10.1007/s00287-015-0927-4 %T Type-2 Fuzzy Sets and Systems: a Retrospective %V 38 %X This article provides a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. It explains how type-2 fuzzy sets can be used to model membership function uncertainties, and how by doing this smoother performance can be obtained than by using type-1 fuzzy sets. It also summarizes the notation that should be used for type-2 fuzzy sets, describes four important mathematical representations for these fuzzy sets, explains the differences between type-1 and type-2 fuzzy logic systems and which of the four representations is most useful when designing an optimal type-2 fuzzy logic system, provides a very useful strategy for optimal designs of fuzzy logic systems -- one that guarantees performance improvement as one goes from a type-1 fuzzy logic system to a type-2 fuzzy logic system design -- , and describes four methods for simplifying the designs of type-2 fuzzy logic systems. Finally, it explains why type-2 fuzzy sets can capture two kinds of linguistic uncertainties simultaneously (the uncertainty of an individual and the uncertainties of a group about a word), whereas type-1 fuzzy sets cannot, and that such type-2 fuzzy set word models are what should be used to implement Zadeh's Computing With Words paradigm.

@article{Mendel15insk, abstract = {This article provides a high-level retrospective of type-2 fuzzy sets and fuzzy logic systems. It explains how type-2 fuzzy sets can be used to model membership function uncertainties, and how by doing this smoother performance can be obtained than by using type-1 fuzzy sets. It also summarizes the notation that should be used for type-2 fuzzy sets, describes four important mathematical representations for these fuzzy sets, explains the differences between type-1 and type-2 fuzzy logic systems and which of the four representations is most useful when designing an optimal type-2 fuzzy logic system, provides a very useful strategy for optimal designs of fuzzy logic systems -- one that guarantees performance improvement as one goes from a type-1 fuzzy logic system to a type-2 fuzzy logic system design -- , and describes four methods for simplifying the designs of type-2 fuzzy logic systems. Finally, it explains why type-2 fuzzy sets can capture two kinds of linguistic uncertainties simultaneously (the uncertainty of an individual and the uncertainties of a group about a word), whereas type-1 fuzzy sets cannot, and that such type-2 fuzzy set word models are what should be used to implement Zadeh's Computing With Words paradigm.}, added-at = {2016-05-22T09:53:02.000+0200}, author = {Mendel, Jerry M.}, biburl = {https://www.bibsonomy.org/bibtex/2276d4d84456c0a1b40e43bf9598dd58d/flint63}, doi = {10.1007/s00287-015-0927-4}, file = {SpringerLink:2015/Mendel15insk.pdf:PDF}, groups = {public}, interhash = {31e2d501bc1fcbf882470ab31cade528}, intrahash = {276d4d84456c0a1b40e43bf9598dd58d}, issn = {0170-6012}, journal = {Informatik-Spektrum}, keywords = {01614 springer paper ai knowledge processing fuzzy logic theory}, month = {#dec#}, number = 6, pages = {523--532}, timestamp = {2018-04-16T12:08:45.000+0200}, title = {Type-2 {Fuzzy} Sets and Systems: a Retrospective}, username = {flint63}, volume = 38, year = 2015 }