Issue:From 0,1-based logic to interval logic

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Title of paper: From [0,1]-based logic to interval logic Author(s): Hung Nguyen Department of Mathematical Sciences, New Mexico State University, Las Cruces, NM 88003, USA hunguyen@nmsu.edu Vladik Kreinovich Department of Computer Science, University of Texas at El Paso, El Paso, TX vladik@cs.utep.edu Presented at: 6th ICIFS, Varna, 13—14 Sept 2002 Published in: Conference proceedings, "Notes on IFS", Volume 8 (2002) Number 3, pages 75—94 Download:  PDF (  Kb, File info) Abstract: Since early 1960s, we have a complete description of all possible [0,1]-based logical operations, namely of "and"-operations (t-norms) and of "or"-operations (t-conorms). In some real-life situations, intervals provide a more adequate way of describing uncertainty, so we need to describe interval-based logical operations (intuitionistic fuzzy logic can be viewed as an equivalent form of interval-valued fuzzy logic). Usually, researchers followed a pragmatic path and simply derived these operations from the [0,1]-based ones. From the foundational viewpoint, it is desirable not to a priori restrict ourselves to such derivative operations but, instead, to get a description of all interval-based operations which satisfy reasonable properties. Such description is presented in this paper. It turns out that all such operations can be described as the result of applying interval computations to the corresponding [0,1]-based ones. References: Atanassov K. Intuitionistic Fuzzy Sets: Theory and Applications, Physica-Verlag, Heidelberg, 1999. W. Bandler and L. J. Kohout, "Unified theory of multi-valued logical operations in the light of the checklist paradigm", Proc. of IEEE Conference on Systems, Man, and Cybernetics, Halifax, Nova Scotia, Oct. 1984. D. Berleant and H. 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