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Soft Computing Based Optimization and Decision Models pp 223–229Cite as

Gradual Numbers and Fuzzy Solutions to Fuzzy Optimization Problems

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Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 360))

Abstract

This short paper indicates that early examples of fuzzy elements in a fuzzy set, that is, entities that assign elements to membership values, in contrast with fuzzy sets that assign membership values to elements, can be found in papers by Verdegay in the early 1980, following a line of thought opened by Orlovsky. They are so-called fuzzy solutions to fuzzy optimization problems. The notion of fuzzy element, and more specifically gradual number sheds some light on the ambiguous notion of fuzzy number often viewed as generalizing a number while it generalizes intervals. The notion of fuzzy solution is in fact a parameterized solution, in the style of parametric programming. These considerations show the pioneering contributions of Verdegay to the development of fuzzy optimization.

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Authors and Affiliations

  1. CNRS-IRIT, Université Paul, Sabatier 118, Route de Narbonne, 31062, Toulouse, Cedex 9, France

    Didier Dubois & Henri Prade

Authors
  1. Didier Dubois
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  2. Henri Prade
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Correspondence to Didier Dubois .

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Editors and Affiliations

  1. Department of Computer Science and A.I. Higher Technical School of Information Technology and Telecommunications Engineering, University of Granada, Granada, Spain

    David A. Pelta

  2. Department of Computer Science and A.I. Higher Technical School of Information Technology and Telecommunications Engineering, University of Granada , Granada, Spain

    Carlos Cruz Corona

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Dubois, D., Prade, H. (2018). Gradual Numbers and Fuzzy Solutions to Fuzzy Optimization Problems. In: Pelta, D., Cruz Corona, C. (eds) Soft Computing Based Optimization and Decision Models. Studies in Fuzziness and Soft Computing, vol 360. Springer, Cham. https://doi.org/10.1007/978-3-319-64286-4_13

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  • DOI: https://doi.org/10.1007/978-3-319-64286-4_13

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-64285-7

  • Online ISBN: 978-3-319-64286-4

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