Mehdi Shams; Gholamreza Hesamian
Abstract
In this paper, the Wilcoxon ranked-sum test is generalized to the fuzzy environment based on a sample of fuzzy random variables. In the proposed approach, first by remembering the concept of induced fuzzy random variable from a family of distributions with fuzzy parameter, the fuzzy median of the population ...
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In this paper, the Wilcoxon ranked-sum test is generalized to the fuzzy environment based on a sample of fuzzy random variables. In the proposed approach, first by remembering the concept of induced fuzzy random variable from a family of distributions with fuzzy parameter, the fuzzy median of the population and the fuzzy median of a sample of fuzzy random variables are generalized to the fuzzy environment. The large sample property of a sequence of fuzzy sample mean is then investigated based on a popular fuzzy distance. Then a new method for testing fuzzy hypotheses for fuzzy median of a population is extended based on a criterion of belonging of a fuzzy set to the conventional critical region. For this purpose, the fuzzy Wilcoxon test statistic is first defined based on the fuzzy observations. Finally, at a given level of exact significance, a fuzzy test is proposed to test the fuzzy hypotheses of fuzzy median. The proposed method is finally illustrated with a practical example. The proposed approach is compared with other existing methods and the differences are examined.
Location Modeling
Sepideh Taghikhani; Fahimeh Baroughi; Behrooz Alizadeh
Abstract
In this paper, the -product and t-state uncapacitated facility location problem is investigated. To be more precise, it is assume that each customer can request different products in a -state network. First, the mathematical formulation for the -product and t-state uncapacitated facility location ...
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In this paper, the -product and t-state uncapacitated facility location problem is investigated. To be more precise, it is assume that each customer can request different products in a -state network. First, the mathematical formulation for the -product and t-state uncapacitated facility location problem with certain costs is proposed. Also, it is shown that this paoblem is NP-hard. Since in most real-world problems the input of data are often ambiguous and uncertain, we study the -product and -state uncapacitated facility location problem in which the facility set-up costs and customer service costs are fuzzy random variables. Using three criteria, probability-possibility, probability-necessity and probability-credibility, the -product and -state uncapacitated facility location problem is formulated as a quadratic programming. Finally, a practical example is given to illustrate the efficiency of the proposed approaches.
stochastic/Probabilistic/fuzzy/dynamic modeling
Hossein Jafari; Mohammad Javad Ebadi
Abstract
The Cramer-Rao lower bound is obtained by using integration by parts and the Cauchy-Schwarz inequality. The integration by parts formulas of Malliavin calculus plays a role in this study. The point estimation problem is very crucial and has a wide range of applications. When we deal with some concepts ...
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The Cramer-Rao lower bound is obtained by using integration by parts and the Cauchy-Schwarz inequality. The integration by parts formulas of Malliavin calculus plays a role in this study. The point estimation problem is very crucial and has a wide range of applications. When we deal with some concepts such as random variables, the parameters of interest and estimates may be observed as imprecise. Therefore, the theory of fuzzy sets is important in formulating such situations. Using the fuzzy set theory, we define a fuzzy-valued random variable and fuzzy stochastic process. We use the Malliavin derivative and Skorohod integral to study the asymptotic properties of the statistical model for fuzzy random variables. We show how to use the conditional expectations of certain expressions to derive Cramer-Rao lower bounds for Fuzzy valued Random Variables that they do not require the explicit expression of the likelihood function. As an example, we consider a fuzzy random sample of size n induced by independent standard normally distributed random variables with fuzzy parameter.