HIGHER LEVEL FUZZY NUMBERS ARISING FROM FUZZY REGRESSION-MODELS

Consider a fuzzy random variable Y, with expectation θ{symbol} = B + βX, where B is an unknown fuzzy number and β an unknown real number. For N observations Yi, Xi there is a model Yi = B + βXi + Ei, i = 1, 2, ..., N, where Ei are fuzzy valued errors, independently and identically distributed in some sense. The aim is to obtain estimates of β, B. When all fuzzy numbers are triangular and the Ei are uniformly distributed, maximum likelihood estimators emerge naturally as a special form of higher level fuzzy number. Thus MLE can be interpreted as an estimation procedure which transforms randomness into higher levels of fuzziness. © 1990.