Abstract
In information services fuzzy concepts are frequently encountered because a customer or client asks a question about something which could be interpreted in many different ways, or, a document is transmitted of a type or meaning which cannot be easily allocated to a known type or category, or to a known procedure. It might take considerable inquiry to “place” the information, or establish in what framework it should be understood. The fuzzy set theory can be used in a wide range of domains in which information is incomplete or imprecise, such as bioinformatics. In applications statistical models are used to estimate data uncertainty. But their models are describing variability and not the imprecision of individual measurement results. Therefore other models are necessary to quantify the imprecision and uncertainty. In case of fuzzy data compare Bandemer [1], Klir and Yuan [8], and Viertl [14]. In 1987 Dubois and Prade defined an interval valued expectation of fuzzy numbers, viewing them as random sets. Carlsson and Fuller defined an interval valued mean value of fuzzy numbers [3]. Fuller and Majlender (2000) defined a mean and variance of fuzzy numbers for weighted possibilistic distribution [5]. They also introduced the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers. Rahim and Rasoul use the trapezoidal fuzzy number with η polynomial function and they calculated a median value of a fuzzy number for probabilistic distribution [10], [11], [12]. In this paper we redefine the types of curve-triangular and curve-trapezoidal fuzzy numbers and calculate their mean, variance, covariance, correlation coefficient, and median for weighted possibilistic distribution and compare to simple fuzzy number[3], [13], [14].
Published Version
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