Download e-book for kindle: Aspects of Vagueness by Jiři Bečvář (auth.), Heinz J. Skala, S. Termini, E. Trillas

By Jiři Bečvář (auth.), Heinz J. Skala, S. Termini, E. Trillas (eds.)

ISBN-10: 9400963092

ISBN-13: 9789400963092

ISBN-10: 9400963114

ISBN-13: 9789400963115

The moment international convention on arithmetic on the carrier of guy used to be held on the Universidad Politecnica de Las Palmas, Canary Islands, Spain, June 28 to July three, 1982. the 1st quantity of the court cases of the convention, entitled "Functional Equations-Theory and purposes" has seemed within the Reidel sequence "Mathematics and Its Applications". The papers during this quantity include the invited lectures introduced on the convention, part 7: Non-Classical Logics and Modelling, in addition to a few chosen papers which provide an creation to the philosophy, technique and to the lite­ rature of the vast and interesting box of vagueness, imprecision and uncertainty. The contributed papers seemed within the quantity of photo-offset preprints allotted on the convention. it really is our desire that the papers current a great pattern with recognize to the history, the formalism and perform of this sector of study so far as we are aware of it this present day. because the topic "Vagueness" touches many facets of human considering, the contributions were made up of a extensive spectrum starting from philo~ophy via natural arithmetic to likelihood concept and mathematical economics, hence the cautious reader may still locate a few new insights right here. In end, the editors are looking to thank all authors who've contributed to this quantity; the publishers of "Commenta­ tiones Mathematicae Universitatis Carolinae" for permission to reprint the paper "Fuzziness and Fuzzy Equality", Commentationes Mathematicae Universitatis Carolinae 23 (1982), 249-267, and D. Reidel for pleasant cooperation.

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Then the mapp~ng

J. J. J. )))). ) ) . 1. E L} for all (J E I(L). J. J. J. I. ) are indistinguishable with respect to (J. 6) m m m I(L) where u is the canonical probability measure associated with m m. Now we calculate these entropies for several special plausibility measures (Hohle [9]). 1 Proposition. Let m be a probability measure on P(~) , the power set of ~ . ln(m({n})), S2(p(~))=O. m In particular the entropy of discernibleness coincides with S han non's entropy. Proof. 1)- follows from E (P(~)) m = J ~ e m I>

Aspects of Vagueness. 51- 74. © 1984 by D. Reidel Publishing Company. KATZ 52 point of view the scope of this paper is much broader, and the handling of error and approximation much subtler, than what we have in [1982a]. 2. AXIOMATIC THEORIES We are concerned here with formal theories in the behavioral sciences, and according to the influential work of Coombs [1964] the two basic predicates of such theories should be those of proximity and qominance, since virtually any type of behavioral data can be reduced to these two predicates.

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Aspects of Vagueness by Jiři Bečvář (auth.), Heinz J. Skala, S. Termini, E. Trillas (eds.)

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