New fuzzy logic-based arithmetic and visual representations for systems' modelling and optimization

Authors:
Walaa Ibrahim Mahmoud Gabr;Hassen Taher Dorrah
Affiliations:
Automatic Control and Systems Engineering Group, Dept. of Electric Power and Machines Engineering, Faculty of Engineering, Cairo University, Giza, Egypt;Automatic Control and Systems Engineering Group, Dept. of Electric Power and Machines Engineering, Faculty of Engineering, Cairo University, Giza, Egypt
Venue:
ROBIO '09 Proceedings of the 2008 IEEE International Conference on Robotics and Biomimetics
Year:
2009

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Abstract

This paper is directed towards developing two new fuzzy logic-based representations for systems modelling and optimization using the notion of the normalized fuzzy matrices. The first is the arithmetic type based on dual cell representation, expressed by replacing each parameter with a pair of parentheses, the first is the actual value and the second is corresponding fuzzy level, (Value, Fuzzy Level). The second is the visual type based on coloured cells representation expressed by replacing each parameter by its value and a coded (newly defined negative or positive colours based on the colour Hue circle) corresponding to its fuzzy level. For both cases, the theoretical foundations of the fuzzy logic algebra are presented for various cases of operations.