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Fundamentals of a mathematical theory of fuzzy sets
Applications of Mathematics, Tome 27 (1982) no. 5, pp. 326-340

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Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
Fuzzy sets establish a mapping from the interval of values of a criterial function onto a system of subsets of a basic set. In the paper, a system of definitions and theorems is introduced, which is aimed at an adequate expression of this point of view. The criterial function, with an arbitrary interval of values, serves for expressing the really existing objective property, forming the basis for defining a fuzzy set.
DOI : 10.21136/AM.1982.103980
Classification : 03B52, 03E72, 94D05
Keywords: fuzzy sets; fuzzy relations; informational entropy; random variable 
Spal, Jindřich. Fundamentals of a mathematical theory of fuzzy sets. Applications of Mathematics, Tome 27 (1982) no. 5, pp. 326-340. doi: 10.21136/AM.1982.103980
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