1. neutrosophic set A generalisation of the intuitionistic set, classical set, fuzzy set, paraconsistent set, dialetheist set, paradoxist set, tautological set based on Neutrosophy. An element xT, I, F belongs to the set in the following way: it is t true in the set, i indeterminate in the set, and f false, where t, i, and f are real numbers taken from the sets T, I, and F with no restriction on T, I, F, nor on their sum n=t+i+f. The neutrosophic set generalises: - the intuitionistic set, which supports incomplete set theories for 0 and i=0, 0<=t,i,f<=100; - the fuzzy set for n=100 and i=0, and 0<=t,i,f<=100; - the classical set for n=100 and i=0, with t,f either 0 or 100; - the paraconsistent set for n>100 and i=0, with both t,f<100; - the dialetheist set, which says that the intersection of some disjoint sets is not empty for t=f=100 and i=0; some paradoxist sets can be denoted this way. Home http://www. gallup. unm. edu/~smarandache/NeutSet. txt. ["Neutrosophy / Neutrosophic Probability, Set, and Logic", Florentin Smarandache, American Research Press, 1998].
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