Fuzzy linear regression analysis for fuzzy input-output data

Sakawa, Masatoshi; Yano, Hitoshi

doi:10.1016/0020-0255(92)90069-k

Cited by 39 publications

(29 citation statements)

References 5 publications

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“…In general, fuzzy regression methods are divided into two categories: the first one is based on linear programming (LP) approach and the second one is based on the fuzzy least squares (FLS) approach. The first class which minimizes the total vagueness of the estimated values for the output includes Tanaka et al's [46] method and its extensions [20,33,40,45,46]. The sec-ond class includes FLS methods to minimize the total square of errors in the estimated values [15,16,31,48].…”

Section: Fuzzy Regression Methodsmentioning

confidence: 99%

“…(3) and (4) = 0 (for a 1 < 0; see [16,31]). Sakawa and Yano [40], and Hojati et al [20] considered the following fuzzy regression model:…”

Section: Fuzzy Regression Methodsmentioning

confidence: 99%

“…Sakawa and Yano [40] formulated three types of problems for obtaining the FLR models with fuzzy input and fuzzy output using the three indices for equality between two fuzzy numbers as follows:…”

Section: Fuzzy Regression Methodsmentioning

confidence: 99%

“…In general, there are two main approaches in FR analysis: linear programmingbased methods and FLS-based methods. The first one is based on minimizing fuzziness as an optimal criterion [4][5][6]8,20,33,[36][37][38][40][41][42]45,47], whereas the second one is based on least squares (LS) of errors as a fitting criterion [3,9,15,16,[25][26][27]31,48].…”

Section: Introductionmentioning

confidence: 99%

“…Bardossy et al [6] introduced a general methodology for FR and applied to an actual hydrological case study including the imprecise relationship between soil electrical resistivity and hydraulic permeability. Sakawa and Yano [40] developed LP-based methods for solving formulated three types of problems for obtaining the FLR models, where both input and output data are fuzzy numbers. Sakawa and Yano [41] introduced three types of multiobjective programming (MOP) problems for obtaining FLR models with fuzzy input and fuzzy output data.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Fuzzy radial basis function network for fuzzy regression with fuzzy input and fuzzy output

Pehlivan

Apaydin

2016

Complex Intell. Syst.

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In this study, fuzzy regression (FR) models with fuzzy inputs and outputs are discussed. Some of the FR methods based on linear programming and fuzzy least squares in the literature are explained. Within this study, we propose a Fuzzy Radial Basis Function (FRBF) Network to obtain the estimations for FR model in the case that inputs and outputs are symmetric/nonsymmetric triangular fuzzy numbers. Proposed FRBF Network approach is a fuzzification of the inputs, outputs and weights of traditional RBF Network and it can be used as an alternative to FR methods. The FRBF Network approach is constructed on the basis of minimizing the square of the total difference between observed and estimated outputs. A simple training algorithm from the cost function of the FRBF Network through Backpropagation algorithm is developed in this study. The advantage of our proposed approach is its simplicity and easy computation as well as its performance. To compare the performance of the proposed method with those given in the literature, three numerical examples are presented.

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