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Ill-Known Set Approach to Disjunctive Variables: Calculations of Graded Ill-Known Intervals

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Advances on Computational Intelligence (IPMU 2012)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 297))

Abstract

In this paper, we represent the possible ranges of unknown variables as graded ill-known sets and investigate the extension principle for graded ill-known sets. Because graded ill-known sets can be seen as fuzzy sets in the power set, calculations of function values with graded ill-known sets are generally complex. We show that lower and upper approximations of function values with graded ill-known sets can be obtained by calculations of two kinds of fuzzy sets in the universe under certain assumptions which are frequently satisfied.

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Author information

Authors and Affiliations

  1. Graduate School of Engineering Science, Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka, 560-8531, Japan

    Masahiro Inuiguchi

Authors
  1. Masahiro Inuiguchi
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Editor information

Editors and Affiliations

  1. Faculty of Economics, University of Catania, Corso Italia, 55, 95129, Catania, Italy

    Salvatore Greco  & Benedetto Matarazzo  & 

  2. Université Pierre et Marie Curie - Paris6, CNRS UMR 7606, DAPA, LIP6 8, rue du Capitaine Scott, F-75015, Paris, France

    Bernadette Bouchon-Meunier

  3. Dip. Matematica e Informatica, Università di Perugia, 06123, Perugia, Italy

    Giulianella Coletti

  4. Department of Computer and Management Science, University of Trento, Via Inama 5, 38122, Trento, Italy

    Mario Fedrizzi

  5. Machine Intelligence Institute, IONA College, 10801, New Rochelle, NY, USA

    Ronald R. Yager

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© 2012 Springer-Verlag Berlin Heidelberg

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Inuiguchi, M. (2012). Ill-Known Set Approach to Disjunctive Variables: Calculations of Graded Ill-Known Intervals. In: Greco, S., Bouchon-Meunier, B., Coletti, G., Fedrizzi, M., Matarazzo, B., Yager, R.R. (eds) Advances on Computational Intelligence. IPMU 2012. Communications in Computer and Information Science, vol 297. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31709-5_65

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  • DOI: https://doi.org/10.1007/978-3-642-31709-5_65

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-31708-8

  • Online ISBN: 978-3-642-31709-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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