Parameter Estimation by ANFIS in Cases Where Outputs are Non-Symmetric Fuzzy Numbers
Türkan Erbay Dalkiliç, Ayşen Apaydin

Abstract
Regression analysis is an area of statistics that deals with the investigation of the dependence of a variable upon one or more variables. Recently, much research has studied fuzzy estimation. There are some approaches existing in the literature for the estimation of the fuzzy regression model. Two of them are frequently used in parameter estimation, one of which is proposed by Tanaka et al [21] and known as linear programming approach and the other is fuzzy least square approach [17]. The fuzzy inference system forms a useful computing framework based on the concepts of fuzzy set theory, fuzzy reasoning, and fuzzy if-then rules. The fuzzy inference system is a powerful function approximator. There are several different types of fuzzy inference systems developed for function approximation. The Adaptive-Network Based Fuzzy Inference System (ANFIS) is a neural network architecture that can solve any function approximation problem. In this study we will use the ANFIS for parameter estimation and propose an algorithm, in cases where outputs are non-symmetric fuzzy numbers. In this algorithm the error measure is defined as the difference between the estimated outputs which are obtained by adaptive networks and the target outputs. In order to obtain the difference between two fuzzy numbers, some fuzzy ranking methods must be used to define the operator {-}. There are many fuzzy ranking methods for the measuring of the difference between the two fuzzy numbers in literature. In this work, the method of Chang and Lee [2], which is based on the concept of overall existence, will be used.

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