Type-2 fuzzy sets made simple

Mendel, Jerry M.; John, Robert

doi:10.1109/91.995115

Cited by 2,263 publications

(1,134 citation statements)

References 35 publications

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“…Whereas for FSs the membership degree of an element of a set is determined by a value in the interval [0, 1], the membership degree of an element for T2FSs is a fuzzy set in [0,1], that is, a T2FS is determined by a membership function µ : X → M, where M = [0, 1] [0, 1] is the set of functions from [0,1] to [0,1] (see [11], [14], [15], [19]). In this paper we will get results for T2FSs with membership degrees in M = [0, 1] [0,1] (set of functions from [0,1] to [0,1]) and also in the subset L of normal and convex functions of M. Because the membership degree of T2FSs is fuzzy, they are better able to model uncertainty than FSs [12].…”

Section: Introductionmentioning

confidence: 99%

Examples of Aggregation Operators on Membership Degrees of Type-2 Fuzzy Sets

Cubillo

Hernández

Torres-Blanc

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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Z. Takáč in [16] introduced the aggregation operators on any subalgebra of M (set of all fuzzy membership degrees of the type-2 fuzzy sets, that is, the functions from [0,1] to [0,1]). Furthermore, he applied the Zadeh's extension principle (see [24]) to obtain in [16,17] a set of aggregation operators on L* (the strongly normal and convex functions of M). In this paper, we introduce the aggregation operators on any partially ordered and bounded set (poset). This will allow us to suitably provide aggregation operators on M. In this sense, firstly we define a set of operators on M, more general than those given by Z. Takáč, studying some of their properties. Secondly, we focus on some operators obtained through a very different way, proving that they are aggregation operators on L (set of normal and convex functions of M), and on M.

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Section: Introductionmentioning

confidence: 99%

Examples of Aggregation Operators on Membership Degrees of Type-2 Fuzzy Sets

Cubillo

Hernández

Torres-Blanc

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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“…In [17,[31][32][33], it turns out that an interval type 2 fuzzy set is the same as an IVFS if we take a = 1. Handbook of Granular Computing…”

Section: Relation To Other Extensionsmentioning

confidence: 99%

A Survey of Interval‐Valued Fuzzy Sets

Bustince

Montero

Pagola

et al. 2008

Handbook of Granular Computing

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“…comes in many guises and is independent of the kind of fuzzy logic (FL) or any kind of methodology one uses to handle it [2]. Uncertainty involved in any real life problem-solving situation, due to information deficiency of various forms.…”

Section: Modeling Uncertainty Using Fuzzy Logicmentioning

confidence: 99%

Color Image Segmentation using Type-2 Fuzzy Sets

Maity¹,

Sil²

2009

IJCEE

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Abstract--Domain knowledge of real life problems are often uncertain, imprecise and inexact, therefore create difficulty in decision making while solving by conventional approaches.Among various methods of handling uncertainties, fuzzy logic has been most intensively studied almost over four decades. Fuzzy logic (FL) explores human reasoning power using linguistic terms, which are modeled as type-1 fuzzy sets and represented by membership functions (MF). However, the MF of type-1 fuzzy set is crisp and cannot tackle all kind of uncertainties. Introducing type-2 fuzzy sets, an extension of type-1 simplifies the problem where the MF is itself fuzzy with three dimension representations. Moreover, a type-2 fuzzy set maps elements of a crisp domain to type-1 fuzzy numbers bounded in the range [0, 1]. Research on type-2 fuzzy sets is still in its infancy and very recently has been applied on emerging areas that need development of more efficient and robust systems. The aim of the review paper is to describe type-2 fuzzy systems for managing uncertainties, presenting the frontier research areas where type-2 fuzzy logic has been applied and proposes algorithm on application of type-2 fuzzy sets in color image segmentation.

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Type-2 fuzzy sets made simple

Cited by 2,263 publications

References 35 publications

Examples of Aggregation Operators on Membership Degrees of Type-2 Fuzzy Sets

Examples of Aggregation Operators on Membership Degrees of Type-2 Fuzzy Sets

A Survey of Interval‐Valued Fuzzy Sets

Color Image Segmentation using Type-2 Fuzzy Sets

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