### 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. In order to address regression problems in the presence of such hybrid uncertain data, fuzzy random variables are introduced in this study to serve as an integral component of regression models. A new class of fuzzy regression models that is based on fuzzy random data is built, and is called the confidence-interval-based fuzzy random regression model (CI-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 inputoutput data. The CI-FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a nonlinear programming problem that 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 nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming. Therefore, we resort to some heuristics. Finally, an illustrative example is provided.

Original language | English |
---|---|

Article number | 5173567 |

Pages (from-to) | 1273-1283 |

Number of pages | 11 |

Journal | IEEE Transactions on Fuzzy Systems |

Volume | 17 |

Issue number | 6 |

DOIs | |

Publication status | Published - 2009 Dec |

### Fingerprint

### Keywords

- Confidence interval
- Expected value
- Fuzzy random variable
- Fuzzy regression model
- Variance

### ASJC Scopus subject areas

- Control and Systems Engineering
- Artificial Intelligence
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*IEEE Transactions on Fuzzy Systems*,

*17*(6), 1273-1283. [5173567]. https://doi.org/10.1109/TFUZZ.2009.2028331

**Building confidence-interval-based fuzzy random regression models.** / Watada, Junzo; Wang, Shuming; Pedrycz, Witold.

Research output: Contribution to journal › Article

*IEEE Transactions on Fuzzy Systems*, vol. 17, no. 6, 5173567, pp. 1273-1283. https://doi.org/10.1109/TFUZZ.2009.2028331

}

TY - JOUR

T1 - Building confidence-interval-based fuzzy random regression models

AU - Watada, Junzo

AU - Wang, Shuming

AU - Pedrycz, Witold

PY - 2009/12

Y1 - 2009/12

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. In order to address regression problems in the presence of such hybrid uncertain data, fuzzy random variables are introduced in this study to serve as an integral component of regression models. A new class of fuzzy regression models that is based on fuzzy random data is built, and is called the confidence-interval-based fuzzy random regression model (CI-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 inputoutput data. The CI-FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a nonlinear programming problem that 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 nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear 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. In order to address regression problems in the presence of such hybrid uncertain data, fuzzy random variables are introduced in this study to serve as an integral component of regression models. A new class of fuzzy regression models that is based on fuzzy random data is built, and is called the confidence-interval-based fuzzy random regression model (CI-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 inputoutput data. The CI-FRRM is established based on the σ-confidence intervals. The proposed regression model gives rise to a nonlinear programming problem that 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 nonlinearity of this optimization makes it difficult to exploit the techniques of linear programming or classical nonlinear programming. Therefore, we resort to some heuristics. Finally, an illustrative example is provided.

KW - Confidence interval

KW - Expected value

KW - Fuzzy random variable

KW - Fuzzy regression model

KW - Variance

UR - http://www.scopus.com/inward/record.url?scp=72649105250&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=72649105250&partnerID=8YFLogxK

U2 - 10.1109/TFUZZ.2009.2028331

DO - 10.1109/TFUZZ.2009.2028331

M3 - Article

AN - SCOPUS:72649105250

VL - 17

SP - 1273

EP - 1283

JO - IEEE Transactions on Fuzzy Systems

JF - IEEE Transactions on Fuzzy Systems

SN - 1063-6706

IS - 6

M1 - 5173567

ER -