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Towards A More Adequate Defuzzification Of Interval-Valued Fuzzy Sets, Vladik Kreinovich, Van Nam Huynh, Yoshiteru Nakamori
Towards A More Adequate Defuzzification Of Interval-Valued Fuzzy Sets, Vladik Kreinovich, Van Nam Huynh, Yoshiteru Nakamori
Departmental Technical Reports (CS)
It is known that interval-valued fuzzy sets [m(x)] provide a more adequate description of expert uncertainty than the more traditional "type-1" (number-valued) fuzzy techniques. Specifically, an interval-valued fuzzy set can be viewed as a class of possible fuzzy sets m(x) from [m(x)]. In this case, as a result of defuzzification, it is natural to return the range [u] of all possible values u(m) that can be obtained by defuzzifying membership functions m(x) from this class. In practice, it is reasonable to restrict ourselves only to fuzzy numbers m(x), i.e., to "unimodal" fuzzy sets. Under this restriction, in general, we get …
Towards A More Adequate Use Of Interval-Valued Fuzzy Techniques In Intelligent Control: A Fuzzy Analogue Of Unimodality, Van Nam Huynh, Vladik Kreinovich
Towards A More Adequate Use Of Interval-Valued Fuzzy Techniques In Intelligent Control: A Fuzzy Analogue Of Unimodality, Van Nam Huynh, Vladik Kreinovich
Departmental Technical Reports (CS)
It is known that interval-valued fuzzy sets provide a more adequate description of expert uncertainty than the more traditional "type-1" (number-valued) fuzzy techniques. In the current approaches for using interval-valued fuzzy techniques, it is usually assumed that all fuzzy sets m(x) from the interval [l(x),u(x)] are possible. In this paper, we show that it is reasonable to restrict ourselves only to fuzzy numbers m(x), i.e., "unimodal" fuzzy sets. We also describe feasible algorithms for implementing thus modified intelligent control.
Why Intervals? Why Fuzzy Numbers? Towards A New Justification, Vladik Kreinovich
Why Intervals? Why Fuzzy Numbers? Towards A New Justification, Vladik Kreinovich
Departmental Technical Reports (CS)
The purpose of this paper is to present a new characterization of the set of all intervals (and of the corresponding set of fuzzy numbers). This characterization is based on several natural properties useful in mathematical modeling; the main of these properties is the necessity to be able to combine (fuse) several pieces of knowledge.