A Survey of Interval‐Valued Fuzzy Sets

Bustince, Humberto; Montero, Javier; Pagola, Miguel; Barrenechea, Edurne

doi:10.1002/9780470724163.ch22

Cited by 47 publications

(24 citation statements)

References 105 publications

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“…Other information measures (interval-valued entropy, interval-valued similarity, etc.) [15], [21], [27], [79], [111], [120], [134] should also be given by an interval. However, most of the works proposing measures, produce scalar measurements instead of interval ones.…”

Section: -Measures Yielding Intervals From the Definition Ofmentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

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407

159

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Section: -Measures Yielding Intervals From the Definition Ofmentioning

confidence: 99%

A Historical Account of Types of Fuzzy Sets and Their Relationships

Bustince

Barrenechea

Pagola

et al. 2016

IEEE Trans. Fuzzy Syst.

Self Cite

407

159

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show abstract

“…As was mentioned earlier, the process of assigning fuzzy sets to words is called precisiation (of meaning) [140,146]. Mendel in [66] argues that a correct first order model for a word is an Interval Type-2 Fuzzy Set [9,67,135], since words mean different things to different people. 4 In other words, a fuzzy set model for a word should represent both the intra-uncertainty and the inter-uncertainty associated with that word.…”

Section: Modeling Of Wordsmentioning

confidence: 98%

Advanced Computing with Words: Status and Challenges

Mendel

Rajati

2015

Towards the Future of Fuzzy Logic

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In this chapter, we focus on the status of Advanced Computing with Words (ACWW) and the challenges that it may encounter in the future. First, we elaborate on the notion of Computing with Words (CWW) and its various subareas. Then we present some non-engineering ACWW problems and connect them to more realistic engineering problems, after which we provide a roadmap for solving ACWW problems, and show how the Generalized Extension Principle (GEP) can be used to formulate their solutions. We also propose a syllogistic approach to solving ACWW problems that also uses the Extension Principle but in a different way. Finally, we discuss present and future challenges to ACWW, i.e. we explain what challenges ACWW encounters given the current trend of data abundance and widespread use of Internet for dealing with questions posed in natural languages. Introduction: Computing with Words and Advanced Computing with WordsComputing with Words (CWW or CW) [11,29,34,66,69,70,75,91,104,109,142,144,147,154] was probably conceived as the main area of application of fuzzy logic [132] when the field was originated. It is a methodology of computation whose objects are words rather than numbers, although those words are linked to numbers and classical calculations that can be carried out by computing machinery, via membership functions of fuzzy sets associated with words. To do that, a process called precisiation of meaning [152] is essential, which, in a nutshell, is determining membership functions of the fuzzy sets that model the words. Zadeh distinguishes two subareas for CWW:1. Basic Computing with Words (BCWW), which mainly deals with descriptions of complex systems in terms of fuzzy IF-THEN rules [134]. Soft constraints are generally possibilistic, i.e. they describe (physical) attributes like speed, temperature,

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“…One year later, GrattanGuinness ( [17]) established a definition of an interval-valued membership function. In that decade interval-valued fuzzy sets appeared in the literature in various guises and it was not until the 1980s, with the work of Gorzalczany and Turksen ( [11], [13]- [16], [7], [30]- [32], [33]), that the importance of these sets, as well as their name, was definitely established.…”

Section: Interval-valued Fuzzy Setsmentioning

confidence: 99%

Interval Type-2 Fuzzy Sets are Generalization of Interval-Valued Fuzzy Sets: Toward a Wider View on Their Relationship

Sola

Fernández

Hagras

et al. 2015

IEEE Trans. Fuzzy Syst.

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143

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Abstract-In this paper, we will present a wider view on the relationship between interval-valued fuzzy sets and interval type-2 fuzzy sets where we will show that interval-valued fuzzy sets are a particular case of the interval type-2 fuzzy sets. For this reason, both concepts should be treated in a different way. In addition, the view presented in this paper will allow a more general perspective of interval type-2 fuzzy sets which will allow representing concepts which could not be presented by intervalvalued fuzzy sets.Index Terms-Interval-valued fuzzy sets; Interval type-2 fuzzy sets; Type-2 fuzzy sets.

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A Survey of Interval‐Valued Fuzzy Sets

Cited by 47 publications

References 105 publications

A Historical Account of Types of Fuzzy Sets and Their Relationships

A Historical Account of Types of Fuzzy Sets and Their Relationships

Advanced Computing with Words: Status and Challenges

Interval Type-2 Fuzzy Sets are Generalization of Interval-Valued Fuzzy Sets: Toward a Wider View on Their Relationship

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