Solutions of fuzzy equations based on Kaucher arithmetic and AE-solution sets

Authors:
T. Rzeżuchowski;J. Wasowski
Affiliations:
Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland;Faculty of Mathematics and Information Science, Warsaw University of Technology, Pl. Politechniki 1, 00-661 Warsaw, Poland
Venue:
Fuzzy Sets and Systems
Year:
2008

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Abstract

We introduce and investigate two new types of fuzzy solutions to the equation f(a,x)=b where the parameters a and b are described in a fuzzy way. The solutions we propose are based on some known solutions to this type of equation with the parameters described by the interval data. We adapt to the fuzzy case so-called formal interval solutions (based on the Kaucher interval arithmetic) and AE-solution sets. In order to define fuzzy formal solutions we introduce a definition of fuzzy Kaucher arithmetic. We investigate the regularity of solutions in the case of linear dependence of f on a and discuss also the problem of interpretation and logical description of formal solutions.