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1 Journal of Artificial Intelligence and Soft Computing Research

1 2020

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Triangular fuzzy-rough set based fuzzification of fuzzy rule-based systems

Starczewski Janusz T., Goetzen Piotr, Napoli Christian

Journal of Artificial Intelligence and Soft Computing Research

2020

Vol. 10, No. 4

271--285

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 rulebased 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.