Warianty tytułu
Application of Fuzzy Relation "Less Than" in Fuzzy Probability Space
Języki publikacji
Abstrakty
W niniejszej pracy przedstawione zostaną tezy zaprezentowane przez autora w trakcie ICM-82 [4]. Ze względu na ograniczoną objętość artykułu pominięte zostaną tutaj wszystkie dowody twierdzeń. Znaleźć je będzie można w [6]. (fragment tekstu)
A class of fuzzy probability spaces, in the sense given by E.P. Klement is investigated in this paper. This class is distinguished by the fuzzy relation "less than" defined here. This relation enables to express two additional conditions for the fuzzy probability spaces in the real line. These conditions are sufficient for explicit definition of probability distribution on the Borel field by means of its cumulative distribution function. The fuzzy probability measure derived in this way satisfies the usual identity for the opposite event. Utilizing the notion of fuzzy random variable, the results obtained Eire then extended to the case of any family of elementary events. (original abstract)
Słowa kluczowe
Rocznik
Strony
158-168
Opis fizyczny
Twórcy
autor
Bibliografia
- P.R. Halmos. Measure theory (D. Van Nostrand, New York 1950).
- E.P. Klement, R. Lowen, W. Schwychla. Fuzzy probability measures, Fuzzy Sets and Systems 5 (1981) 21-30.
- S.A. Orlovsky. Decision making with a fuzzy preference relation, Fuzzy Sets and Systems 1 (1978) 155-167.
- K. Piasecki. Application of fuzzy relation "less than" in theory of probability, ICM-82 Short Communications vol. VIII 1983 57.
- K. Piasecki. Probability arrangement as a fuzzy relation "less than", Proceedings Polish Symposium on Interval and Fuzzy Mathematics Poznań'83 1985 187-192.
- K. Piasecki. Probability space defined by means of fuzzy relation "less than", Fuzzy Sets and Systems 19 1986, 273-289.
- C.R. Rao. Linear statistical inference and its applications (John Wiley and Sons, New York 1965).
- St. Wierzchoń. Application of fuzzy decision - making theory to coping with ill-defined problems, Fuzzy Sets and Systems 7 (1982) 1-18.
- L.A. Zadeh. Probability measures of fuzzy events. J. Math. Anal. Appl. (1968) 421-427.
Typ dokumentu
Bibliografia
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