Center of circles intersection, a new defuzzification method for fuzzy numbers

• Published in: Bulletin of the Polish Academy of Sciences. Technical sciences 2020-04, Vol.68 (2), p.185-190
• Main Authors: Zarzycki, H, Dobrosielski, W T, Apiecionek, Ł, Vince, T
• Format: Article
• Language: English
• Subjects: Center of gravity; Circles (geometry); defuzzification; Fuzzy control; fuzzy logic; Fuzzy sets; Intersections; ordered fuzzy numbers
• ISSN: 0239-7528; 2300-1917
• DOI: 10.24425/bpasts.2020.131850

The article introduces a new proposal of a defuzzification method, which can be implemented in fuzzy controllers. The first chapter refers to the origin of fuzzy sets. Next, a modern development based on this theory is presented in the form of ordered fuzzy numbers (OFN). The most important characteristics of ordered fuzzy numbers are also presented. In the following chapter, details about the defuzzification process are given as part of the fuzzy controller model. Then a new method of defuzzification is presented. The method is named center of circles intersection (CCI). The authors compare this method with a similar geometric solution: triangular expanding (TE) and geometric mean (GM). Also, the results are compared with other methods such as center of gravity (COG), first of maxima (FOM) and last of maxima (LOM). The analysis shows that the proposed solution works correctly and provides results for traditional fuzzy numbers as well as directed fuzzy numbers. The last chapter contains a summary, in which more detailed conclusions are provided and further directions of research are indicated.