Abstract
This chapter provides a complete methodology for construction of uncertain fuzzy logic systems. The methodology comprises all techniques delivered by this book including: rough-fuzzy discretization of input domains (as well as imputation of missing inputs), possibilistic and fuzzy-rough fuzzification of inputs, fusion of multiple expert designs. Besides, this chapter answers the question whether it is worth to make use of fuzzy-valued fuzzy logic systems instead of ordinary crisp-valued fuzzy systems at the cost of the complexity. In response, two methods for the approximation of intervalvalued fuzzy systems by ordinary fuzzy logic systems are presented. In the first approximation the interval-valued fuzzy system is assumed to perform the extended minimum Cartesian product and conjunction reasoning, and to use uniform uncertainty of membership functions. In the latter approximation the interval system is assumed to perform the algebraic Cartesian product and employ lower membership functions proportional to their upper counterparts. The chapter is complemented by a comparative analysis of the interval and non-interval fuzzy systems and a brief discussion about generalization of this analysis to general fuzzy-valued fuzzy logic systems.
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Starczewski, J.T. (2013). Designing Uncertain Fuzzy Logic Systems. In: Advanced Concepts in Fuzzy Logic and Systems with Membership Uncertainty. Studies in Fuzziness and Soft Computing, vol 284. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29520-1_6
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DOI: https://doi.org/10.1007/978-3-642-29520-1_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29519-5
Online ISBN: 978-3-642-29520-1
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