Axiomatisation of Discrete Fuzzy Integrals with Respect to Possibility and Necessity Measures

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• 关键词：Choquet integral ; Sugeno integral ; Possibility theory
• 刊名：Lecture Notes in Computer Science
• 出版年：2016
• 出版时间：2016
• 年：2016
• 卷：9880
• 期：1
• 页码：94-106
• 全文大小：215 KB
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  12.Marichal, J.-L.: An axiomatic approach of the discrete Choquet Integral as a tool to aggregate interacting criteria. IEEE Trans. Fuzzy Syst. 8, 800–807 (2000)MathSciNet CrossRef
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  16.Sugeno, M.: Theory of fuzzy integrals and its applications. Ph.D. thesis, Tokyo Institute of Technology (1974)
  17.Sugeno, M.: Fuzzy measures and fuzzy integrals: a survey. In: Gupta, M.M., et al. (eds.) Fuzzy Automata and Decision Processes, pp. 89–102. North-Holland (1977)
  
• 作者单位：D. Dubois (17)
  A. Rico (18)
  
  17. IRIT, Université Paul Sabatier, 31062, Toulouse Cedex 9, France
  18. ERIC, Université Claude Bernard Lyon 1, 69100, Villeurbanne, France
  
• 丛书名：Modeling Decisions for Artificial Intelligence
• ISBN：978-3-319-45656-0
• 刊物类别：Computer Science
• 刊物主题：Artificial Intelligence and Robotics
  Computer Communication Networks
  Software Engineering
  Data Encryption
  Database Management
  Computation by Abstract Devices
  Algorithm Analysis and Problem Complexity
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1611-3349
• 卷排序：9880

文摘

Necessity (resp. possibility) measures are very simple representations of epistemic uncertainty due to incomplete knowledge. In the present work, a characterization of discrete Choquet integrals with respect to a possibility or a necessity measure is proposed, understood as a criterion for decision under uncertainty. This kind of criterion has the merit of being very simple to define and compute. To get our characterization, it is shown that it is enough to respectively add an optimism or a pessimism axiom to the axioms of the Choquet integral with respect to a general capacity. This additional axiom enforces the maxitivity or the minitivity of the capacity and essentially assumes that the decision-maker preferences only reflect the plausibility ordering between states of nature. The obtained pessimistic (resp. optimistic) criterion is an average of the maximin (resp. maximax) criterion of Wald across cuts of a possibility distribution on the state space. The additional axiom can be also used in the axiomatic approach to Sugeno integral and generalized forms thereof. The possibility of axiomatising of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed.