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## Numerical Comparison Function for Weibull Distribution Probability Values with PossibilityValues for Fuzzy Logic

الناشر \ المحرر \ الكاتب (Author / Editor / Publisher)

بشرى حسين عليوي الواوي

Citation Information

بشرى,حسين,عليوي,الواوي ,Numerical Comparison Function for Weibull Distribution Probability Values with PossibilityValues for Fuzzy Logic , Time 5/28/2011 8:32:02 AM : كلية التربية للعلوم الصرفة

وصف الابستركت (Abstract)

The relationship between possibility and probability

الوصف الكامل (Full Abstract)

Numerical Comparison Function for Weibull Distribution Probability Values with PossibilityValues for Fuzzy Logic
Bushra Hussien Aliwi      Kawther Fawzi Hamza
Education Collage (Ibn Hayan) _ Department of Mathematics
University of Babylon, Iraq 2010

Introduction:

The relationship between possibility and probability is cleared through the rang of functions values for each one of them, which is equivalent to be in the closed interval [0, 1], and it has some variation in values.

The goal of this research is to find the type of relation and to decrease the variations in values through finding a combination between several probability distributions and membership function in fuzzy logic to be either continuous or discrete .

In this paper the weibull distribution has been exploited with a continuous membership function, Gaussian membership and applied failure rate function with that distribution.

Someone asks, why we don’t use the statistic instead of fuzzy logic? More detailed difference between the concepts led us use one instead of the other.That is, the difference between the degree of membership in the set (of some member), and a probability of being in that set.

The point of difference is, the probability involves a crisp set theory (probability of it belongs to class or not), and don’t allow for an element to be a partial member in a class (or a set, as in fuzzy logic).

Probability is an indicator of frequency or likelihood that an element is in a class, while fuzzy set theory deals with the similarity of an element to a class[3] that is between elements in a class. Anyone who doesn’t know and haven t study fuzzy logic and fuzzy sets think ,that fuzziness is just a clever disguise for probability, which is never true .

Although  fuzzy logic is known latterly ,it has been communicated with many other sciences for its benefits in practical applications(applicable branches).Since 1991, fuzzy logic is used in technology as an industrial tool in reference[5]to be fuzzy control, but the theoretical side stay requisite .Probability theory and fuzzy set theory have been communicated since they were depend on same range to be in closed interval  ,also membership function(MF) that characterize the fuzzy set depend on some parameters(time_ verify parameters)and its values chosen from parameter space(real number).While probability distribution also depend on parameters describe the distribution and determine its values and shape ,which chosen from parameter space, many ways used to locate these parameter values.

Also the values of MF constraints[0,1] , while probability has a main condition. To shed light on such a relationship, a probability distribution used to compare the values that computed by Weibull distribution function with that values computed by Gaussian MF (both were continuous functions)on tables for values of dependent variable(s) applied for both functions and values for parameters that be in each function .

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