Estimation of a Fuzzy Regression Model Using Fuzzy Distances


Regression analysis could be a powerful statistical tool that has many applications in several areas. The problem of regression analysis under a fuzzy environment has been treated within the literature from totally different points of view and considering a selection of input/output knowledge (crisp or fuzzy). But, we tend to understand that, normally, most analysis papers have a conflict between the solution of the fuzzy regression drawback using crisp distances (minimizing a real error function) and also the interpretation of fuzzy information as chance distributions. The most aim of this paper is to develop a strategy to resolve this downside introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers. The new approach permits us to obtain linear and nonlinear models that reach very cheap fuzzy error; the estimation process, generally, can be thought-about easier to use in observe, and it is not restricted to triangular fuzzy numbers. Numerical examples are provided to illustrate the usefulness and applicability of these results, and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory.

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