Journal ArticleDOI
The mean value of a fuzzy number
Didier Dubois,Henri Prade +1 more
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TLDR
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.About:
This article is published in Fuzzy Sets and Systems.The article was published on 1987-12-01. It has received 717 citations till now. The article focuses on the topics: Fuzzy number & Fuzzy measure theory.read more
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Expected value of fuzzy variable and fuzzy expected value models
Baoding Liu,Yian-Kui Liu +1 more
TL;DR: A novel concept of expected values of fuzzy variables is presented, which is essentially a type of Choquet integral and coincides with that of random variables, and is designed to calculate the expected value of general fuzzy variable.
Book
Theory and practice of uncertain programming
TL;DR: This book provides a self-contained, comprehensive and up-to-date presentation of uncertain programming theory, including numerous modeling ideas, hybrid intelligent algorithms, and applications in system reliability design, project scheduling problem, vehicle routing problem, facility location problem, and machine scheduling problem.
Journal ArticleDOI
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
Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem
TL;DR: Some fuzzy linear programming methods and techniques from a practical point of view are reviewed and some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed.
Journal ArticleDOI
Ranking and defuzzification methods based on area compensation
Philippe Fortemps,Marc Roubens +1 more
TL;DR: It has been proved that this method produces more than a fuzzy interval order: it induces a ranking of fuzzy numbers, and extensions to non-normal fuzzy numbers and fuzzy quantities are proposed.
References
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Book
A mathematical theory of evidence
TL;DR: This book develops an alternative to the additive set functions and the rule of conditioning of the Bayesian theory: set functions that need only be what Choquet called "monotone of order of infinity." and Dempster's rule for combining such set functions.
Journal ArticleDOI
Fuzzy sets as a basis for a theory of possibility
TL;DR: The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable.
Book
Probability theory
TL;DR: These notes cover the basic definitions of discrete probability theory, and then present some results including Bayes' rule, inclusion-exclusion formula, Chebyshev's inequality, and the weak law of large numbers.
Book
Fuzzy Sets and Systems: Theory and Applications
Didier Dubois,Henri Prade +1 more
TL;DR: This book effectively constitutes a detailed annotated bibliography in quasitextbook style of the some thousand contributions deemed by Messrs. Dubois and Prade to belong to the area of fuzzy set theory and its applications or interactions in a wide spectrum of scientific disciplines.