New geometric inference techniques for type-2 fuzzy sets

Coupland, Simon; John, Robert

doi:10.1016/j.ijar.2008.03.001

Cited by 61 publications

(16 citation statements)

References 33 publications

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“…A grey number could be represented as a set of intervals with gaps in between. For example, g ± ∈ { [5,6], [10,12]} is a grey number where its underlying white number may get its value from [5,6] or [10,12], but we know for sure that it will not get its value within (6,10). This is clearly different from an interval [5,12] where (6, 10) is a valid part for candidate values.…”

Section: Generalised Grey Numbersmentioning

confidence: 98%

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Grey sets and greyness

Yang

John

2012

Information Sciences

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109

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This paper discusses the application of grey numbers for uncertainty representation. It highlights the difference between grey sets and interval-valued fuzzy sets, and investigates the degree of greyness for grey sets. It facilitates the representation of uncertainty not only for elements of a set, but also the set itself as a whole. Our results show that a grey set could be specified for interval-valued fuzzy sets or rough sets under special conditions. With the notion of grey sets and their associated degrees of greyness, various set operations between grey sets are discussed.

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Section: Generalised Grey Numbersmentioning

confidence: 98%

“…Type-2 fuzzy sets allow membership grades that are type-1 fuzzy sets. These are sometimes referred to as "fuzzy-fuzzy" [10,27]. This is a general extension to fuzzy sets, and interval-valued fuzzy sets can be considered as a special case of type-2 fuzzy sets.…”

Section: A Fuzzy Set With Interval Values As Its Membership Values Ismentioning

confidence: 99%

Grey sets and greyness

Yang

John

2012

Information Sciences

Self Cite

109

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“…Based on the fuzzy set, several additional and hybrid concepts such as theintervalvalued fuzzy set [69], the type-2 fuzzy set [69], the intuitionistic fuzzy set [2] were developed. Fuzzy sets play a tremendous role in signal processing [25], control theory [14], reasoning [7], decision making [23], medical diagnosis [31], geo-demographic analysis [33,37,41,42,65], dental segmentation [47,48,59], compression [43], recommender systems [34,36,38] and other fields [8,10,35,39,40,46,49,50,[56][57][58].…”

Section: Introductionmentioning

confidence: 99%

δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

2017

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Intuitionistic fuzzy set is capable of handling uncertainty with counterpart falsities which exist in nature. Proximity measure is a convenient way to demonstrate impractical significance of values of memberships in the intuitionistic fuzzy set. However, the related works of In this paper, we examine this problem and propose new notions of δ-equalities for the intuitionistic fuzzy set and δ-equalities for intuitionistic fuzzy relations. Two fuzzy sets are said to be δ-equal if they are equal to an extent of δ. The applications of δ-equalities are important to fuzzy statistics and fuzzy reasoning. Several characteristics of δ-equalities that were not discussed in the previous works are also investigated. We apply the δ-equalities to the application of medical diagnosis to investigate a patient's diseases from symptoms. The idea is using δ-equalities for intuitionistic fuzzy relations to find groups of intuitionistic fuzzified set with certain equality or similar degrees then combining them. Numerical examples are given to illustrate validity of the proposed algorithm. Further, we conduct experiments on real medical datasets to check the efficiency and applicability on real-world problems. The results obtained are also better in comparison with 10 existing diagnosis methods namely De et al. (Fuzzy Sets

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“…On the other hand, the high computational cost of the type-reduction process of an IT2-FLS is a major bottleneck [21], which may hinder its application in the real world. At present, scholars mainly utilize the K-M iterative type-reduction algorithm [22] and the Wu-Mendel uncertain boundary type-reduction algorithm [23] in the interval type-2 fuzzy controllers.…”

Section: Introductionmentioning

confidence: 99%

Interval Type-2 Fuzzy Model Based on Inverse Controller Design for the Outlet Temperature Control System of Ethylene Cracking Furnace

Zhao

Cao

et al. 2017

Information

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Multivariable coupling, nonlinear and large time delays exist in the coil outlet temperature (COT) control system of the ethylene cracking furnace, which make it hard to achieve accurate control over the COT of the furnace in actual production. To solve these problems, an inverse controller based on an interval type-2 fuzzy model control strategy is introduced. In this paper, the proposed control scheme is divided into two parts: one is the approach structure part of the interval type-2 fuzzy model (IT2-FM), which is utilized to approach the process output. The other is the interval type-2 fuzzy model inverse controller (IT2-FMIC) part, which is utilized to control the output process to achieve the target value. In addition, on the cyber-physical system platform, the actual industrial data are used to test and obtain the mathematical model of the COT control system of the ethylene cracking furnace. Finally, the proposed inverse controller based on the IT2-FM control scheme has been implemented on the COT control system of the ethylene cracking furnace, and the simulation results show that the proposed method is feasible.

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New geometric inference techniques for type-2 fuzzy sets

Cited by 61 publications

References 33 publications

Grey sets and greyness

Grey sets and greyness

δ-equality of intuitionistic fuzzy sets: a new proximity measure and applications in medical diagnosis

Interval Type-2 Fuzzy Model Based on Inverse Controller Design for the Outlet Temperature Control System of Ethylene Cracking Furnace

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