Abstract: Number of Disciplines and Theories changed their status from status of Natural Science discipline to Mathematics. The Theory of Probability is the classical example of that kind. The main privilege of the new, Math, status is the conception of Math truth, which distinguish Math from other theories. Some disciplines, used in Applications, pretended to be Math, not being such. It’s entirely true for Fuzzy Subsets Theory with its pretension to be Math and to be exclusive tools in uncertainty handling. Fundamental pretensions of classical Fuzzy subset theory including pretension to be math is discussed as well as the some gaps of the theory are discussed in the article. Statistical interpretation of membership functions is proposed. It is proved, that such the interpretation take place for practically all supporters with minimal constraint on it. Namely, a supporter must be the space with a measure. The interpretation proposed makes it clear the modifying of the classical fuzzy object to correct the gaps. It becomes possible to say about observations of fuzzy subset within the conception of modification and to extend Likelihood method on the new area. Fuzzy likelihood equation adduced as example of new possibilities within approach proposed. One more interpretation for the Fuzzy subset theory is proposed to discuss: multiset theory one.

Keywords: f Uncertainty, Plural model of uncertainty, Fuzzy subsets Theory, statistical interpretation of the membership function, modification of Fuzzy subsets, Fuzzy likelihood equation, Multiset theory.

ACM Classification Keywords: G.2.m. Discrete mathematics: miscellaneous,G.2.1 Combinatorics. G.3 Probability and statistics, G.1.6. Numerical analysis I.5.1.Pattern Recognition: Models Fuzzy sets; H.1.m. Models and Principles: miscellaneous:

Link:

FUZZY SETS AS A MEAN FOR UNCERTAINTY HANDLING: MATH, APPLIED MATH, HEURISTICS

Volodymyr Donchenko

http://foibg.com/ijita/vol18/ijita18-4-p01.pdf