Construction of Normal Fuzzy Numbers Using the ...

Two independent laws of measure theoretically defined randomness, one in the interval [α, β] and the other in the interval [β, γ]，are necessary and sufficient to define a normal fuzzy number [α, β, γ], the membership function of which is the distribution function with reference to the law of randomness defined in [α, β] and is the complementary distribution function with reference to the law of randomness defined in [β, γ]. Thus to construct a normal fuzzy number [α, β, γ], we need to define two probability measures, one in [α, β] and the other in [β, γ].