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- W2007281617 abstract "In the usual set theory, the power set of a set X is lattice isomorphicto 2x. The theory of fuzzy sets, or fuzzy set theory, involves generalizing the lattice 2 = {0, 1} to a more general, usually non-Boolean, lattice. A ‘point’ in this lattice need not have Boolean properties. Thus proper generalizations must be based on notions which are defined without explicitly using points. In the light of this we give equivalent definitions of function, relation and quotient set involving the members of a power set but not specifically the singletons. A number of authors [1,2,5] have worked with generalizations of functions and quotient sets which are not strictly point free. It emerges that these are special cases of the ones we produce." @default.
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- W2007281617 date "1980-01-01" @default.
- W2007281617 modified "2023-10-18" @default.
- W2007281617 title "Functions, equivalence relations, quotient spaces and subsets in fuzzy set theory" @default.
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- W2007281617 doi "https://doi.org/10.1016/0165-0114(80)90006-8" @default.
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