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Type 2 Fuzzy Sets: An Appraisal of Theory and Applications
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1998This paper provides a guide and tutorial to type 2 fuzzy sets. Type 2 fuzzy sets allow for linguistic grades of membership thus assisting in knowledge representation. They also offer improvement on inferencing with type 1 sets. The various approaches to knowledge representation and inferencing are discussed, with worked examples, and some of the ...
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A Tour of Type-1 and Interval Type-2 Fuzzy Sets Theory
2020A succinct review of type-1 basic theory is described in this chapter and should be enough for the reader, who is not familiar with fuzzy set theory, to be able to understand these concepts (Jafelice et al. Teoria dos Conjuntos Fuzzy. Springer Briefs in Mathematics SBMAC (in Portuguese), vol 17, 2nd edn. Springer, Berlin, 2012).
Rosana Sueli da Motta Jafelice +1 more
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From Classical to Fuzzy Type Theory
2014Higher-order logic—the type theory (TT)—is a powerful formal theory that has various kinds of applications, for example, in linguistic semantics, computer science, foundations of mathematics and elsewhere. It was proved to be incomplete with respect to standard models. In fifties and sixties of the last century, L.
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Building a type-2 fuzzy regression model based on creditability theory
2013 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 2013Information in real life may have linguistically vagueness. Thus, type-1 fuzzy set was introduced to model this uncertainty. Additionally, same words will mean variously to different people, which means uncertainty also exists when associated with the membership function of a type-1 fuzzy set.
Yicheng Wei, Junzo Watada
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$\alpha$-Plane Representation for Type-2 Fuzzy Sets: Theory and Applications
IEEE Transactions on Fuzzy Systems, 2009This paper 1) reviews the alpha-plane representation of a type-2 fuzzy set (T2 FS), which is a representation that is comparable to the alpha-cut representation of a type-1 FS (T1 FS) and is useful for both theoretical and computational studies of and for T2 FSs; 2) proves that set theoretic operations for T2 FSs can be computed using very simple alpha-
Jerry M. Mendel +2 more
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Fuzzy type theory with partial functions
2019This paper is a study of fuzzy type theory (FTT) with partial functions. Out of several possibilities we decided tointroduce a special value ”∗” that represents ”undefined”. In the interpretation of FTT, this value lays outside of thecorresponding domain.
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Sea surface temperature clustering based on type-2 fuzzy theory
2010 18th International Conference on Geoinformatics, 2010Spatial data clustering is an effective method to find interesting spatio-temporal clustering patterns. There are many uncertainties in sea surface temperature (SST) clustering, so clustering methods with uncertainy must be used. Type-2 fuzzy theory takes into account the uncertainty of membership grade while fuzzy C means (FCM) not.
Kun Qin +3 more
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Statistical Fuzzy Trigonometric Korovkin-Type Approximation Theory
2011In this chapter, we consider non-negative regular summability matrix transformations in the approximation by fuzzy positive linear operators, where the test functions are trigonometric. So, we mainly obtain a trigonometric fuzzy Korovkin theorem by means of A-statistical convergence.
George A. Anastassiou, Oktay Duman
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Introduction to modelling of natural deduction based on fuzzy type theory
AIP Conference Proceedings, 2015This paper should serve as an introduction to natural deduction modelling that is based on fuzzy type theory. First the theory for the topic is explained, one of the classical logic systems is chosen (Predicate logic) then introduction to fuzzy logic is given and then fuzzy type theory is introduced and the reasons why it was chosen for this paper are ...
Zuzana Rombová, Zdenka Telnarova
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On Virtues of Many-Valued (Fuzzy) Type Theories
2010In this paper, we deal with the fuzzy type theory (FTT) — a higher-order fuzzy logic. There are several kinds of this logic depending on the chosen structure of truth values. Higher-order (fuzzy) logic is still not fully appreciated despite its high explicative power. Our goal is to point out several great virtues of it to convince the reader that this
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