On Advanced Computing With Words Using the Generalized Extension Principle for Type-1 Fuzzy Sets

Rajati, Mohammad Reza; Mendel, Jerry M.

doi:10.1109/tfuzz.2013.2287028

Cited by 21 publications

(16 citation statements)

References 43 publications

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“…Pedrycz [39] introduced a concept of a granular representation of numeric membership functions of fuzzy sets, which offers a synthetic and qualitative view at fuzzy sets and their ensuing processing. Rajati and Mendel [40] proposed and demonstrated an effective methodology for implementing the generalized extension principle to solve Advanced Computing with Words problems using ordinary fuzzy sets.…”

Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

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Fuzzy sets have a great progress in every scientific research area. It found many application areas in both theoretical and practical studies from engineering area to arts and humanities, from computer science to health sciences, and from life sciences to physical sciences. In this paper, a comprehensive literature review on the fuzzy set theory is realized. In the recent years, ordinary fuzzy sets have been extended to new types and these extensions have been used in many areas such as energy, medicine, material, economics and pharmacology sciences. This literature review also analyzes the chronological development of these extensions. In the last section of the paper, we present our interpretations on the future of fuzzy sets.

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Section: Co-published By Atlantis Press and Taylor And Francismentioning

confidence: 99%

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Kahraman¹,

Öztayşi²,

Onar³

2016

IJCIS

View full text Add to dashboard Cite

show abstract

“…Equation (12.2) is a complicated (functional) optimization problem that is difficult to solve. To the best of our knowledge, [87] offers the only published effective methodology to carry out the calculations related to this optimization problem.…”

Section: Computing Solutions To Acww Problemsmentioning

confidence: 99%

“…Based on the above discussions the following framework is provided for solving an ACWW problem [87]:…”

Section: A General Guide For Formulation Of Acww Problemsmentioning

confidence: 99%

“…8. Carry out the calculations related to the GEP according to the algorithms that were presented in [87] to derive the membership function of the fuzzy constraint yielded by the GEP. 9.…”

Section: A General Guide For Formulation Of Acww Problemsmentioning

confidence: 99%

“…The ranges of the parameters of those distributions are also part of the World Knowledge that has to be available. A comprehensive approach to solving problems involving the GEP is in [87].…”

Section: Tall Swedes Problem (Ahs)mentioning

confidence: 99%

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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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Type-2 Fuzzy Sets Including Word Models

Mendel

2024

Explainable Uncertain Rule-Based Fuzzy Systems

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On Advanced Computing With Words Using the Generalized Extension Principle for Type-1 Fuzzy Sets

Cited by 21 publications

References 43 publications

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

A Comprehensive Literature Review of 50 Years of Fuzzy Set Theory

Advanced Computing with Words: Status and Challenges

Type-2 Fuzzy Sets Including Word Models

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