2009
DOI: 10.1016/j.cam.2008.03.045
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The possibilistic moments of fuzzy numbers and their applications

Abstract: a b s t r a c tThis paper, introduces the nearest weighted interval and point approximations of a fuzzy number, and then suggests weighted possibilistic moments about these points of fuzzy numbers. The possibilistic moments play an important role in fuzzy sets and systems, specifically in physics, mathematics and statistics. We provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory; some of their applications are mentioned.

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Cited by 60 publications
(15 citation statements)
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“…The following conclusion is shown in Saeidifar and Pasha (2009) [16]. The semi-variance of the return is expressed as…”
Section: =1mentioning
confidence: 94%
“…The following conclusion is shown in Saeidifar and Pasha (2009) [16]. The semi-variance of the return is expressed as…”
Section: =1mentioning
confidence: 94%
“…Ã Note that the results proved in Propositions 2 and 3 are only established between the crisp possibilistic expected values of LR-type fuzzy numbers (in the sense of Dubois and Prade) and the credibility expected values of LR-type fuzzy variables. That is, when non-unit constant weights are considered for different c-cuts of the membership function of a fuzzy number, these equivalencies may disappear (see, for instance, Fullér & Majlender, 2003;Saedifar & Pasha, 2009); this may also be the case if fuzzy variables other than LR-type are used for quantifying uncertainty.…”
Section: Credibility Expected Values and Possibilistic Momentsmentioning
confidence: 95%
“…Liu and Liu [52] propose a definition of expected value of a fuzzy variable based on the possibilistic notion of credibility measure. Saeidifar and Pasha [53] define possibilistic moments of fuzzy numbers. Georgescu [54] proposes risk aversion by possibility theory and find out the risk premium by defining a new notion of possibilistic variance.…”
Section: Possibilistic Moments and Possibilistic Risk Aversionmentioning
confidence: 99%