Fuzzy Relations, Fuzzy Graphs, and Fuzzy Arithmetic | ME 504, Study notes of Mechanical Engineering

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.- ~'..r'0~'7fY~f,f.'~~~Pf~:·if" ----~"---- -_.~- ---- Returning to our example, let us assume About-j'4 " is defined as Abollt-5' 4"; {0/5', 0/5' 1",0.4/5'2",0.8/5'3", 1 /5'4",0.8/5^1 5", OAI5'6"} (EO 4.6) Using the mux-Illin compositional rule of inference. we can compute the weight possibil ity distribution of a petite person about 5'4" tall:. nweight(90) = (0 AI) v (0 AI) v (0.4 AI) v (0.8 AI) v (I _1_ 0.8) v (0.8 A 0.6) v (0.4 _1_ 0)= 0.8· (EO 4.7) Similarly, we can compute the possibility degree for other weights. The final result is nweight = {0.8/9O, 0.8/95, 0.8/100,0.8/105,0.5/ 110, 004/115,0.1/120,0/125 } Mathematically, the composition of fuzzy relations can be defined using three basic operations: project;on, cylindrical extensioll, and ;llter.iectioll. We introduce the first two concepts before we give a formal definition of the composition of fuzzy relations. , _.i,;~~-~'~~~''','