Journal ArticleDOI
On weighted possibilistic mean and variance of fuzzy numbers
Robert Fullér,Péter Majlender +1 more
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TLDR
The notations of weighted interval-valued possibilistic mean value, variance and covariance of fuzzy numbers are introduced, which are consistent with the extension principle and it is shown that the weighted variance of linear combination of fuzzyNumbers can be computed in a similar manner as in probability theory.About:
This article is published in Fuzzy Sets and Systems.The article was published on 2003-06-16. It has received 251 citations till now. The article focuses on the topics: Fuzzy number & Weighted geometric mean.read more
Citations
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Possibility theory and statistical reasoning
TL;DR: An overview of numerical possibility theory is proposed, showing that some notions in statistics are naturally interpreted in the language of this theory and providing a natural definition of a subjective possibility distribution that sticks to the Bayesian framework of exchangeable bets.
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Fuzzy portfolio optimization under downside risk measures
TL;DR: Two fuzzy portfolio selection models where the objective is to minimize the downside risk constrained by a given expected return are presented where the rates of returns on securities are approximated as LR-fuzzy numbers of the same shape.
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The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers
TL;DR: This work investigates multiple attribute group decision-making problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown, and develops the triangular intuitionistic fuzzy weighted average (TIF-WA) operator.
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Parametric representation of fuzzy numbers and application to fuzzy calculus
TL;DR: The generality and the applicability of the proposed representation to a large class of problems are stressed, including the numerical solution of fuzzy differential equations, the fuzzy linear regression and the stochastic extensions of the fuzzy mathematics.
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Fuzzy process control: construction of control charts with fuzzy numbers
TL;DR: The construction of fuzzy control charts for a process with fuzzy outcomes derived from the subjective quality ratings provided by a group of experts, whose construction and out-of-control conditions are developed using possibility theory.
References
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Journal ArticleDOI
Elementary fuzzy calculus
Roy H. Goetschel,William Voxman +1 more
TL;DR: This paper shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in [4] to define differentiation and integration of fuzzy-valued functions in ways that parallel closely the corresponding definitions for real differentiation and Integration.
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On Possibilistic Mean Value and Variance of Fuzzy Numbers
Christer Carlsson,Robert Fullér +1 more
TL;DR: The interval-valued possibilistic mean value is defined and the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.
Journal ArticleDOI
The mean value of a fuzzy number
Didier Dubois,Henri Prade +1 more
TL;DR: Some light is shed on the debate between probability and possibility theory, and the problem of how to carry measure-theoretic notions into the field of possibility theory.
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The expected value of a fuzzy number
TL;DR: The expected interval is defined as the expectedvalue of an interval random set generated by the fuzzy number and the expected value of this number isdefined as the centre of the expected interval.
Journal ArticleDOI
On a canonical representation of fuzzy numbers
TL;DR: This paper proposes two parameters, value and ambiguity, for fuzzy number representation and uses them to obtain canonical representations and to deal with fuzzy numbers in decision-making problems.