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Titlebook: Uncertainty in Knowledge-Based Systems; International Confer B. Bouchon,R. R. Yager Conference proceedings 1987 Springer-Verlag Berlin Heid

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978-3-540-18579-6Springer-Verlag Berlin Heidelberg 1987
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Uncertainty in Knowledge-Based Systems978-3-540-48020-4Series ISSN 0302-9743 Series E-ISSN 1611-3349
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0302-9743 Overview: 978-3-540-18579-6978-3-540-48020-4Series ISSN 0302-9743 Series E-ISSN 1611-3349
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Lecture Notes in Computer Sciencehttp://image.papertrans.cn/u/image/941145.jpg
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https://doi.org/10.1007/3-540-18579-8information processing; knowledge-based systems; uncertainty
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O-theory: A probabilistic alternative to fuzzy set theory,lism, which is extended to include a complete set of basic operations for handling uncertainties in a set-theoretic framework. The new operator theory, O-Theory, retains the probabilistic flavor of Dempster‘s original point-to-set mappings but includes the potential for defining a range of operators like those found in fuzzy set theory.
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Fuzzy preferences in decision-making,ransitivity inside the family of max-⋆ transitivities is stablished. On the other hand, a necessary and sufficient condition for the existence of a non empty set of unfuzzy nondominated alternatives is proved. Moreover, other alternative methods are proposed in order to solve some practical difficulties.
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Derivation of some results on monotone capacities by Mobius inversion,Monotone capacities are characterized by properties of their Möbius inverses. A necessary property of probabilities dominating a given capacity is given. It is shown to be also sufficient if and only if the capacity is monotone of infinite order. A characterization of dominating probabilities specific to capacities or order 2 is also proved.
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