Triangular Fuzzy-Rough Set Based Fuzzification of Fuzzy Rule-Based Systems

Janusz T. Starczewski 1 , Piotr Goetzen 2  and Christian Napoli 3
  • 1 Department of Computational Intelligence, Czestochowa University of Technology, 42-200, Częstochowa, Poland
  • 2 Information Technology Institute, University of Social Sciences, Clark University, , 90-113, Łódz
  • 3 Department of Computer, Control and Management Engineering, Sapienza University of Rome, Roma, Italy

Abstract

In real-world approximation problems, precise input data are economically expensive. Therefore, fuzzy methods devoted to uncertain data are in the focus of current research. Consequently, a method based on fuzzy-rough sets for fuzzification of inputs in a rule-based fuzzy system is discussed in this paper. A triangular membership function is applied to describe the nature of imprecision in data. Firstly, triangular fuzzy partitions are introduced to approximate common antecedent fuzzy rule sets. As a consequence of the proposed method, we obtain a structure of a general (non-interval) type-2 fuzzy logic system in which secondary membership functions are cropped triangular. Then, the possibility of applying so-called regular triangular norms is discussed. Finally, an experimental system constructed on precise data, which is then transformed and verified for uncertain data, is provided to demonstrate its basic properties.

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