# Formulation of fuzzy random regression model

Junzo Watada, Shuming Wang, Witold Pedrycz

研究成果: Chapter

### 抄録

In real-world regression analysis, statistical data may be linguistically imprecise or vague. Given the co-existence of stochastic and fuzzy uncertainty, real data cannot be characterized by using only the formalism of random variables. To address regression problems in presence of such hybrid uncertain data, fuzzy random variables are introduced in this study, and serve as an integral component of regression models. A new class of fuzzy regression models based on fuzzy random data is built, and is called the fuzzy random regression model (FRRM). First, a general fuzzy regression model for fuzzy random data is introduced. Then, using expectations and variances of fuzzy random variables, σ-confidence intervals are constructed for fuzzy random input-output data. The FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a non-linear programming problem which consists of fuzzy numbers or interval numbers. Since sign-changes in the fuzzy coefficients modify the entire programming structure of the solution process, the inherent dynamic non-linearity of this optimization makes it hard to exploit the techniques of linear programming or classical non-linear programming. Therefore, we resort to some heuristics. Finally, an illustrative example is provided.

元の言語 English Studies in Computational Intelligence 1-20 20 372 https://doi.org/10.1007/978-3-642-11739-8_1 Published - 2011

### 出版物シリーズ

名前 Studies in Computational Intelligence 372 1860949X

### Fingerprint

Random variables
Nonlinear programming
Regression analysis
Linear programming

### ASJC Scopus subject areas

• Artificial Intelligence

### これを引用

Watada, J., Wang, S., & Pedrycz, W. (2011). Formulation of fuzzy random regression model. ： Studies in Computational Intelligence (巻 372, pp. 1-20). (Studies in Computational Intelligence; 巻数 372). https://doi.org/10.1007/978-3-642-11739-8_1

Formulation of fuzzy random regression model. / Watada, Junzo; Wang, Shuming; Pedrycz, Witold.

Studies in Computational Intelligence. 巻 372 2011. p. 1-20 (Studies in Computational Intelligence; 巻 372).

研究成果: Chapter

Watada, J, Wang, S & Pedrycz, W 2011, Formulation of fuzzy random regression model. ： Studies in Computational Intelligence. 巻. 372, Studies in Computational Intelligence, 巻. 372, pp. 1-20. https://doi.org/10.1007/978-3-642-11739-8_1
Watada J, Wang S, Pedrycz W. Formulation of fuzzy random regression model. ： Studies in Computational Intelligence. 巻 372. 2011. p. 1-20. (Studies in Computational Intelligence). https://doi.org/10.1007/978-3-642-11739-8_1
Watada, Junzo ; Wang, Shuming ; Pedrycz, Witold. / Formulation of fuzzy random regression model. Studies in Computational Intelligence. 巻 372 2011. pp. 1-20 (Studies in Computational Intelligence).
title = "Formulation of fuzzy random regression model",
abstract = "In real-world regression analysis, statistical data may be linguistically imprecise or vague. Given the co-existence of stochastic and fuzzy uncertainty, real data cannot be characterized by using only the formalism of random variables. To address regression problems in presence of such hybrid uncertain data, fuzzy random variables are introduced in this study, and serve as an integral component of regression models. A new class of fuzzy regression models based on fuzzy random data is built, and is called the fuzzy random regression model (FRRM). First, a general fuzzy regression model for fuzzy random data is introduced. Then, using expectations and variances of fuzzy random variables, σ-confidence intervals are constructed for fuzzy random input-output data. The FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a non-linear programming problem which consists of fuzzy numbers or interval numbers. Since sign-changes in the fuzzy coefficients modify the entire programming structure of the solution process, the inherent dynamic non-linearity of this optimization makes it hard to exploit the techniques of linear programming or classical non-linear programming. Therefore, we resort to some heuristics. Finally, an illustrative example is provided.",
keywords = "confidence interval, expected value, Fuzzy random regression model, fuzzy random variable, Fuzzy regression model, variance",
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