Generalized bipolar product and sum View Full Text


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Article Info

DATE

2015-04-23

AUTHORS

Salvatore Greco, Radko Mesiar, Fabio Rindone

ABSTRACT

Aggregation functions on [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,1]$$\end{document} with annihilator 0 can be seen as a generalized product on [0,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[0,1]$$\end{document}. We study the generalized product on the bipolar scale [-1,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]$$\end{document}, stressing the axiomatic point of view ( compare also Greco et al. in IPMU 2014, CCIS 444, Springer International Publishing, New York, 2014). Based on newly introduced bipolar properties, such as the bipolar monotonicity, bipolar unit element, bipolar idempotent element, several kinds of generalized bipolar product are introduced and studied. A special stress is put on bipolar semicopulas, bipolar quasi-copulas and bipolar copulas. Inspired by the truncated sum on [-1,1]\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$[-1,1]$$\end{document} we introduce also the class of generalized bipolar sums, which differ from uninorms due to the non-associativity. More... »

PAGES

21-31

References to SciGraph publications

  • 2000. Triangular Norms in NONE
  • 1998. Metamathematics of Fuzzy Logic in NONE
  • 2009. Generalized Measure Theory in NONE
  • 2013-08-02. The bipolar Choquet integral representation in THEORY AND DECISION
  • 2014. Generalized Product in INFORMATION PROCESSING AND MANAGEMENT OF UNCERTAINTY IN KNOWLEDGE-BASED SYSTEMS
  • 2010-12-25. Bipolar aggregation using the Uninorms in FUZZY OPTIMIZATION AND DECISION MAKING
  • 1992-10. Advances in prospect theory: Cumulative representation of uncertainty in JOURNAL OF RISK AND UNCERTAINTY
  • 2012. The Bipolar Universal Integral in ADVANCES IN COMPUTATIONAL INTELLIGENCE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s10700-015-9217-5

    DOI

    http://dx.doi.org/10.1007/s10700-015-9217-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1028138807


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