TY - CHAP

T1 - Formulation of fuzzy random regression model

AU - Watada, Junzo

AU - Wang, Shuming

AU - Pedrycz, Witold

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

KW - confidence interval

KW - expected value

KW - Fuzzy random regression model

KW - fuzzy random variable

KW - Fuzzy regression model

KW - variance

UR - http://www.scopus.com/inward/record.url?scp=80054727261&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054727261&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-11739-8_1

DO - 10.1007/978-3-642-11739-8_1

M3 - Chapter

AN - SCOPUS:80054727261

SN - 9783642117381

VL - 372

T3 - Studies in Computational Intelligence

SP - 1

EP - 20

BT - Studies in Computational Intelligence

ER -