Date: 10 Jan 2012

Using Dempster-Shafer Structures to Provide Probabilistic Outputs in Fuzzy Systems Modeling

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Abstract

Our interest is in providing a capability to include probabilistic outputs in fuzzy systems modeling. To accomplish this we use Dempster-Shafer belief structures. We first discuss some basic ideas from the Dempster-Shafer theory of evidence. We then describe Mamdani’s paradigm for fuzzy systems modeling which provided the pioneering framework for the many applications of fuzzy logic control. We then show how to use the Dempster-Shafer belief structure to provide machinery for including randomness in the fuzzy systems modeling process. We show how to this can be used to include various types of uncertainties including additive noise in the fuzzy systems modeling process. We next describe the Takagi-Sugeno approach to fuzzy systems modeling. Finally we use the Dempster-Shafer belief structure to enable the inclusion of probabilistic aspects in the output of the Takagi-Sugeno model.