1985
DOI: 10.1016/0165-0114(85)90093-4
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Probability of fuzzy events defined as denumerable additivity measure

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Cited by 80 publications
(34 citation statements)
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“…The proofs can be found in [38]. The monotonicity of fuzzy P-measure m implies that this measure transforms F into the interval [0,1].…”
Section: Basic Definitions and Factsmentioning
confidence: 99%
See 1 more Smart Citation
“…The proofs can be found in [38]. The monotonicity of fuzzy P-measure m implies that this measure transforms F into the interval [0,1].…”
Section: Basic Definitions and Factsmentioning
confidence: 99%
“…The above described triplet (Ω, F, m) is called in the terminology of Piasecki a fuzzy probability space [38]. The symbols ∪ ∞ n=1 f n = sup n f n and ∩ ∞ n=1 f n = inf n f n denote the fuzzy union and the fuzzy intersection of a sequence { f n } ∞ n=1 ⊂ F, respectively, in the sense of Zadeh [39].…”
Section: Basic Definitions and Factsmentioning
confidence: 99%
“…This would lead to an alternative interpretation of the inequality ¡xp < N°¡xp, namely, that P is 'weakly empty' with respect to N. In this sense, Piasecki (1985) established that a set P is w-empty if ¡xp < 1 -¡xp.…”
Section: Introductionmentioning
confidence: 99%
“…For this reason, various proposals were made to generalize the Kolmogorov-Sinai entropy concept. In [6], we generalized the Kolmogorov-Sinai entropy concept to the case of a fuzzy probability space [7]. This structure represents an alternative mathematical model of probability theory for the situations when the considered events are fuzzy events, i.e., events described unclearly, vaguely.…”
Section: Introductionmentioning
confidence: 99%