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Fuzzy Logic in Its 50th Year pp 87–107Cite as

Some Comments on Ordinary Reasoning with Fuzzy Sets

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 341))

Abstract

The main goal of Computing with Words is essentially a calculation allowing to automate a part of the reasoning done thanks to the natural language. Fuzzy Logic is the main tool to perform this calculation because it is be able to represent the most common kind of predicates in natural language, graded predicates, in terms of functions, and to calculate with them. However there is still not an adequate framework to perform this task, commonly referred to as commonsense reasoning. This chapter proposes a general framework to model a part of this type of reasoning. The fundamental fact of this framework is its ability to adequately represent noncontradiction, the minimum condition for considering a reasoning as valid. Initially, the characteristics of the commonsense reasoning are analyzed, and a model for the crisp case is shown. After that the more general case in which graded predicates are taken under consideration is studied.

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Notes

  1. 1.

    If the negation is strong, if μ is contradictory with ρ is equivalent to ρ is contradictory with μ because \(0\, < \,r\, < \,\left( {\mu \,{ \preccurlyeq }\,\rho^{\prime}} \right)\, \le \,\left( {\rho^{\prime\prime}\,{ \preccurlyeq }\,\mu^{\prime}} \right) = \left( { \rho \,{ \preccurlyeq }\,\mu^{\prime}} \right)\).

  2. 2.

    If P is clear from the context we use ρ instead of ρ P for the résumé of P.

  3. 3.

    Note that in a framework of a graded ordering relation, first condition is a strong one but necessary to avoid self-contradiction.

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Acknowledgments

This author acknowledges the support of the Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under grant TIN2014-56633-C3-1-R.

Author information

Authors and Affiliations

  1. Oviedo (Asturias), Spain

    Enric Trillas

  2. University of León, León, Spain

    Adolfo R. de Soto

Authors
  1. Enric Trillas
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  2. Adolfo R. de Soto
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Correspondence to Enric Trillas .

Editor information

Editors and Affiliations

  1. Department of Industrial Engineering, Istanbul Technical University, Istanbul, Turkey

    Cengiz Kahraman

  2. School of Industrial Engineering, Eindhoven University of Technology, Eindhoven, The Netherlands

    Uzay Kaymak

  3. Department of Computer Engineering, Middle East Technical University (M, Ankara, Turkey

    Adnan Yazici

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Trillas, E., de Soto, A.R. (2016). Some Comments on Ordinary Reasoning with Fuzzy Sets. In: Kahraman, C., Kaymak, U., Yazici, A. (eds) Fuzzy Logic in Its 50th Year. Studies in Fuzziness and Soft Computing, vol 341. Springer, Cham. https://doi.org/10.1007/978-3-319-31093-0_4

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  • DOI: https://doi.org/10.1007/978-3-319-31093-0_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-31091-6

  • Online ISBN: 978-3-319-31093-0

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