In the field of fuzzy regression (more precisely: regression in a fuzzy environment), there are two main approaches: the approach based on the least sum of distances (including two general methods: least sum of squares and least sum of deviations) and the probabilistic approach (the approach of the least total ambiguity under some constraints). In addition to these two main approaches, numerous heuristic methods have been proposed in the field of fuzzy regression. Some of these methods are based on a combination of the two approaches above. Some heuristic methods are based on specific computational algorithms. Others use fuzzy inference systems.
Some methods are also based on clustering. The use of artificial neural networks, evolutionary algorithms, or nonparametric methods are other approaches used. In this article, while referring to the history and foundations of two classical approaches to fuzzy regression (the least sum of distances approach and the probabilistic approach), some heuristic methods in fuzzy regression are introduced and briefly reviewed. Also, ten criteria for evaluating fuzzy regression models are proposed, according to which different methods and models can be evaluated and compared.