107,745 research outputs found

    An Interactive Fuzzy Satisficing Method for Fuzzy Random Multiobjective 0-1 Programming Problems through Probability Maximization Using Possibility

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    In this paper, we focus on multiobjective 0-1 programming problems under the situation where stochastic uncertainty and vagueness exist at the same time. We formulate them as fuzzy random multiobjective 0-1 programming problems where coefficients of objective functions are fuzzy random variables. For the formulated problem, we propose an interactive fuzzy satisficing method through probability maximization using of possibility

    A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation

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    Let XX be a fuzzy set--valued random variable (\frv{}), and \huku{X} the family of all fuzzy sets BB for which the Hukuhara difference X\HukuDiff B exists P\mathbb{P}--almost surely. In this paper, we prove that XX can be decomposed as X(\omega)=C\Mink Y(\omega) for P\mathbb{P}--almost every ω∈Ω\omega\in\Omega, CC is the unique deterministic fuzzy set that minimizes E[d2(X,B)2]\mathbb{E}[d_2(X,B)^2] as BB is varying in \huku{X}, and YY is a centered \frv{} (i.e. its generalized Steiner point is the origin). This decomposition allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink \indicator{\xi(\omega)} for some deterministic fuzzy convex set MM and some random element in \Banach). In particular, XX is an \frv{} translation if and only if the Aumann expectation EX\mathbb{E}X is equal to CC up to a translation. Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision; references, affiliation and acknowledgments added. Submitted versio

    Interactive Fuzzy Random Two-level Linear Programming through Fractile Criterion Optimization

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    This paper considers two-level linear programming problems involving fuzzy random variables. Having introduced level sets of fuzzy random variables and fuzzy goals of decision makers, following fractile criterion optimization, fuzzy random two-level programming problems are transformed into deterministic ones. Interactive fuzzy programming is presented for deriving a satisfactory solution efficiently with considerations of overall satisfactory balance

    A perspective on the extension of stochastic orderings to fuzzy random variables

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    International audienceIn this paper we study how to make joint extensions of stochastic orderings and interval orderings so as to extend methods for comparing random variables, from the point of view of their respective location or magnitude, to fuzzy random variables. The main idea is that the way fuzzy random variables are interpreted affects the choice of the comparison methods. We distinguish three views of fuzzy random variables, according to which various comparison methods seem to make sense. This paper offers an approach toward a systematic classification of combinations of stochastic and interval or fuzzy interval comparison methods

    FUZZY ROBUST ESTIMATES OF LOCATION AND SCALE PARAMETERS OF A FUZZY RANDOM VARIABLE

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    A random variable is a variable whose components are random values. To characterise a random variable, the arithmetic mean is widely used as an estimate of the location parameter, and variation as an estimate of the scale parameter. The disadvantage of the arithmetic mean is that it is sensitive to extreme values, outliers in the data. Due to that, to characterise random variables, robust estimates of the location and scale parameters are widely used: the median and median absolute deviation from the median. In real situations, the components of a random variable cannot always be estimated in a deterministic way. One way to model the initial data uncertainty is to use fuzzy estimates of the components of a random variable. Such variables are called fuzzy random variables. In this paper, we examine fuzzy robust estimates of location and scale parameters of a fuzzy random variable: fuzzy median and fuzzy median of the deviations of fuzzy component values from the fuzzy median.

    Chance-constrained programming with fuzzy stochastic coefficients

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    International audienceWe consider fuzzy stochastic programming problems with a crisp objective function and linear constraints whose coefficients are fuzzy random variables, in particular of type L-R. To solve this type of problems, we formulate deterministic counterparts of chance-constrained programming with fuzzy stochastic coefficients, by combining constraints on probability of satisfying constraints, as well as their possibility and necessity. We discuss the possible indices for comparing fuzzy quantities by putting together interval orders and statistical preference. We study the convexity of the set of feasible solutions under various assumptions. We also consider the case where fuzzy intervals are viewed as consonant random intervals. The particular cases of type L-R fuzzy Gaussian and discrete random variables are detailed
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