Trapezoidal fuzzy data in possibility linear regression analysis
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CitationRazzaghnia, T. (2009). Trapezoidal fuzzy data in possibility linear regression analysis. Maltepe Üniversitesi. s. 368.
Fuzzy linear regression was proposed by Tanaka et al.  in 1982. Many different fuzzy regression approaches have been proposed by different researchers since then , and also this subject has drawn much attention from more and more people concerned.and more people concerned. A fuzzy number A˜ is a convex normalized fuzzy subset of the real line R with an upper semi-continuous membership function of bounded support. Definition: A symmetric fuzzy numberA˜, denoted by A˜ = (α, c)L is defined as A˜ = L((x − α)/c),c > 0,Where α and c are the center and spread of A˜ and L(x) is a shape function of fuzzy numbers. A fuzzy regression analysis results in the following regression model:Y ˆ˜ = A˜0Xi0 + A˜1Xi1 + . . . + A˜pXip = AX˜ i i = 1, 2, . . . , n. In this paper, we aim to extended the constraints of Tanaka’s  model. Applied coefficients of the fuzzy regression by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidal one. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models is presented and a numerical example is given in order to compare the proposed models with previous one. Error values shows advantage of the presented models with respect to constraints of Tanaka’s model. For the possibility distribution with asymmetric trapezoidal fuzzy numbers, we prove the following theorem.
SourceInternational Conference of Mathematical Sciences
- Makale Koleksiyonu 
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