# A fuzzy logistic regression model based on the least squares estimation

## Abstract

To construct the relationship between fuzzy inputs and fuzzy output described by linguistic variable, we develop a fuzzy logistic regression model, which can be applied for various problems, such as clinical research, risk investment and decision making. In this regard, we introduce the integral calculation of distance of cut sets and a fuzzy adjustment term which could prevent a large fuzzy error for a fuzzy output caused by the output degenerating into crisp number when the independent variables are crisp numbers. The parameters of the fuzzy logistic regression model are derived by means of the least squares method. We adopt three criteria involving mean square error, Kim and Bishu criterion and capability index and also perform two ways of prediction including the in-sample forecast as well as the one-leave-out cross validation. The comparisons with five existing methods show that our proposed method has satisfactory performance and the results are illustrated in some case studies.

- Authors:

- University of Shanghai for Science and Technology (China)

- Publication Date:

- OSTI Identifier:
- 22769269

- Resource Type:
- Journal Article

- Journal Name:
- Computational and Applied Mathematics

- Additional Journal Information:
- Journal Volume: 37; Journal Issue: 3; Other Information: Copyright (c) 2018 SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0101-8205

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; COMPARATIVE EVALUATIONS; DECISION MAKING; FUZZY LOGIC; LEAST SQUARE FIT

### Citation Formats

```
Gao, Yifan, and Lu, Qiujun.
```*A fuzzy logistic regression model based on the least squares estimation*. United States: N. p., 2018.
Web. doi:10.1007/S40314-017-0531-0.

```
Gao, Yifan, & Lu, Qiujun.
```*A fuzzy logistic regression model based on the least squares estimation*. United States. doi:10.1007/S40314-017-0531-0.

```
Gao, Yifan, and Lu, Qiujun. Sun .
"A fuzzy logistic regression model based on the least squares estimation". United States. doi:10.1007/S40314-017-0531-0.
```

```
@article{osti_22769269,
```

title = {A fuzzy logistic regression model based on the least squares estimation},

author = {Gao, Yifan and Lu, Qiujun},

abstractNote = {To construct the relationship between fuzzy inputs and fuzzy output described by linguistic variable, we develop a fuzzy logistic regression model, which can be applied for various problems, such as clinical research, risk investment and decision making. In this regard, we introduce the integral calculation of distance of cut sets and a fuzzy adjustment term which could prevent a large fuzzy error for a fuzzy output caused by the output degenerating into crisp number when the independent variables are crisp numbers. The parameters of the fuzzy logistic regression model are derived by means of the least squares method. We adopt three criteria involving mean square error, Kim and Bishu criterion and capability index and also perform two ways of prediction including the in-sample forecast as well as the one-leave-out cross validation. The comparisons with five existing methods show that our proposed method has satisfactory performance and the results are illustrated in some case studies.},

doi = {10.1007/S40314-017-0531-0},

journal = {Computational and Applied Mathematics},

issn = {0101-8205},

number = 3,

volume = 37,

place = {United States},

year = {2018},

month = {7}

}