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Fuzzy Data Processing Beyond Min t-Norm

  • Andrzej Pownuk
  • Vladik Kreinovich
  • Songsak Sriboonchitta
Chapter
Part of the Studies in Systems, Decision and Control book series (SSDC, volume 125)

Abstract

Usual algorithms for fuzzy data processing—based on the usual form of Zadeh’s extension principle—implicitly assume that we use the \(\min \) “and”-operation (t-norm). It is known, however, that in many practical situations, other t-norms more adequately describe human reasoning. It is therefore desirable to extend the usual algorithms to situations when we use t-norms different from \(\min \). Such an extension is provided in this chapter.

Notes

Acknowledgements

This work was supported in part by the National Science Foundation grants HRD-0734825 and HRD-1242122 (Cyber-ShARE Center of Excellence) and DUE-0926721, and by an award “UTEP and Prudential Actuarial Science Academy and Pipeline Initiative” from Prudential Foundation. We also acknowledge the partial support of the Center of Excellence in Econometrics, Faculty of Economics, Chiang Mai University, Thailand.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Andrzej Pownuk
    • 1
  • Vladik Kreinovich
    • 1
  • Songsak Sriboonchitta
    • 2
  1. 1.Computational Science ProgramUniversity of TexasEl PasoUSA
  2. 2.Faculty of EconomicsChiang Mai UniversityChiang MaiThailand

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