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Interval Additive Generators of Interval T-Norms
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On interval fuzzy S-implications
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Interval valued QL-implications
WoLLIC'07 Proceedings of the 14th international conference on Logic, language, information and computation
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Interval valued fuzzy coimplication
WoLLIC'10 Proceedings of the 17th international conference on Logic, language, information and computation
Robustness of interval-valued fuzzy inference
Information Sciences: an International Journal
Generation of interval-valued fuzzy implications from Kα operators
WILF'11 Proceedings of the 9th international conference on Fuzzy logic and applications
Interval representations, Łukasiewicz implicators and Smets-Magrez axioms
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Interval-valued fuzzy coimplications and related dual interval-valued conjugate functions
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An interval is a continuum of real numbers, defined by its end-points. Interval analysis, proposed by R. Moore in the 50's, concerns the discovery of interval functions to produce bounds on the accuracy of numerical results that are guaranteed to be sharp and correct. The last criterion, correctness, is the main one since it establishes that the result of an interval computation must always contains the value of the related real function.Correctness rests on the ``Fundamental Theorem of Interval Arithmetic''. This theorem, induced us to define interval representations, which captures the fact that interval analysis works like a kind of language to express computations with real numbers, this is implicitly formulated at [HJE01] p. 1045, lemma 2.Until now the idea of intervals as representation of real numbers was not explicitly defined and its relation with some aspects of interval analysis was not explored. Here we show some of these relations in terms of the topological aspects of intervals (Scott and Moore topologies). The paper also defines what we call the canonical interval representation of a real function, which is the obvious best ``mathematical'' (not necessarily computable) interval representation of a real function **. The idea is to show some properties of correct interval algorithms giving a relationship with some other kind of functions, such as extensions and inclusion monotonic functions; and to show how this ideal object preserves the continuity of real functions into Scott and Moore topologies.