Trapezoidal approximation based on middle of maxima and middle of support
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CitationHajjari, T. (2009). Trapezoidal approximation based on middle of maxima and middle of support. Maltepe Üniversitesi. s. 370.
In many fuzzy logic applications, the calculations strongly depend on the fuzzy number membership functions. Less regular membership functions lead to calculations that are more complicated. A natural need is to approximate fuzzy numbers with the simpler shapes which are easy to handle and have natural interpretations. Since one can easily propose many other approximation methods, a natural question arises: how to construct a good approximation operator? Defuzzification methods have been widely studied for some years and were applied to fuzzy expert system. The major idea behind these methods was to obtain a typical value from a given fuzzy set according to some specified characters. In other words, each defuzzification method provides a correspondence from the set of all fuzzy sets into the set of real numbers. Obviously, in defuzzification methods that replace a fuzzy set by a single number, we generally loose too much important information. The aforementioned explanation shows that the trapezoidal approximation of a fuzzy number is meaningful topic. Since trapezoidal approximation could be also performed in many ways, there are a number of criteria such as translation invariance, scale invariance, identity which the approximation operator should or just can possess. In this paper, we introduce a trapezoidal approximation of an arbitrary fuzzy number, which preserves its the middle of maxima and middle of support. The operator is called trapezoidal approximation based on middle of maxima and middle of support. In case that the middle of maxima and middle of support are identical the trapezoidal approximation is symmetric. We then discuss properties of the approximation strategy including translation invariance, scale invariance and identity. The advantage is that the presented method is simpler than other methods computationally. The method is illustrated by some numerical examples.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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