I am a PhD student in the School of Mathematics and Statistics at the University of Sydney, under the supervision of Prof. Nalini Joshi. My research is on discrete nonlinear integrable systems.
I completed my masters degree on discrete mathematics, and my thesis was titled “Demonic operators on fuzzy relations with illustration Mathematica”. For this thesis I was supervised by Dr Fairouz Tchier at King Saud University, Saudi Arabia.
Different versions of "composition" have been suggested which differ in their results, and also in their mathematical properties. The max-min composition has become the best known and the most frequently used. However, often the so-called max-product or max-average compositions lead to results that are more appealing.
In the following images, figures (1) and (2) represent fuzzy relations R and S. While figures (3), (4) and (5) represent the max-min composition, max-product composition and max-average composition two fuzzy relations R and S, respectively.
(3) The max-min composition of fuzzy relations R and S
(4) The max-product composition of fuzzy relations R and S
(5) The max-av composition of fuzzy relations R and S
Huda Alrashdi and Fairouz Tchier (2010) Demonic fuzzy operators Recent Advances in Neural Networks, Fuzzy Systems & Evolutionary Computing June: 149-156