Abstract
AbstractIn this paper, the researcher proposed a method to cardinal, median value, variance and covariance of exponential fuzzy numbers with shape function . The covariance used in this method is obtained from the exponential trapezoidal fuzzy number, first by finding mathematical expectation and then calculating the variance of each exponential fuzzy numbers by E(A), E2(A) and then finding the possibilistic covariance between fuzzy numbers A and B. We are going to utilize Dubois and another researcher dominance possibility and necessity indices, within a exponential fuzzy numbers with shape function and its applications, in the case of measure of possibilistic correlation between fuzzy numbers A and B by their ranking possibility of their interaction compared to their possibilistic fuzzy number. Finally, we proposed a new method for ranking exponential fuzzy numbers with possibilistic variance between fuzzy numbers A and B. This approach helps avoiding any approximation that may exist due to incorrect compa...
Highlights
Comparison of fuzzy numbers is considered one of the most important topics in fuzzy logic theory
The covariance used in this method is obtained from the exponential trapezoidal fuzzy number, first by finding mathematical expectation and calculating the variance of each exponential fuzzy numbers by E(A), E2(A) and finding the possibilistic covariance between fuzzy numbers A and B
This method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques and the proposed approach is very simple and easy to apply in the real life problems
Summary
Comparison of fuzzy numbers is considered one of the most important topics in fuzzy logic theory. In 1987 Dubois and Prade [11] defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. In 2015 Rezvani defined a ranking fuzzy numbers for variance as values are calculated by finding expected values using the probability density function corresponding to the membership functions of the given fuzzy number and provides the correct ordering of exponential trapezoidal fuzzy numbers [24]. Rezvani ([16]-[24]) evaluated the system of ranking fuzzy numbers This ranking used in these field was based on formulating a possibility function, whether in the case of trapezoidal fuzzy numbers.The researcher proposed a method to cardinal, median value, variance and covariance of exponential fuzzy numbers with shape function. The results of the proposed approach are compared with different existing approaches
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