### Abstract

This paper proposes an extended approach to construct an appropriate membership function as objectively as possible. It is important to set an appropriate membership function to obtain a reasonable optimal solution for real-world decision making. The main academic contribution of our proposed approach is to integrate a general continuous and nonlinear function minimizing the subjectivity into an interval estimation by a heuristic method under a given probability density function based on real-world data. Our approach is an extend approach of Civanlar and Trussell's study. One of two main steps of our proposed approach is to set membership values which a decision maker confidently judges whether an element is included in the given set or not. Another is to obtain other values objectively by solving Civanlar and Trussell's mathematical programming problem with a nonlinear membership function. In this paper, the given membership function is approximately transformed into a piecewise linear membership function, and the appropriate values of parameters in the piecewise linear membership function are determined.

Original language | English |
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Title of host publication | IMECS 2016 - International Multiconference of Engineers and Computer Scientists 2016 |

Publisher | Newswood Limited |

Pages | 862-866 |

Number of pages | 5 |

Volume | 2 |

ISBN (Electronic) | 9789881404763 |

Publication status | Published - 2016 |

Event | International Multiconference of Engineers and Computer Scientists 2016, IMECS 2016 - Tsimshatsui, Kowloon, Hong Kong Duration: 2016 Mar 16 → 2016 Mar 18 |

### Other

Other | International Multiconference of Engineers and Computer Scientists 2016, IMECS 2016 |
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Country | Hong Kong |

City | Tsimshatsui, Kowloon |

Period | 16/3/16 → 16/3/18 |

### Fingerprint

### Keywords

- Interactive approach
- Mathematical programming
- Membership function
- Piecewise linear function

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

### Cite this

*IMECS 2016 - International Multiconference of Engineers and Computer Scientists 2016*(Vol. 2, pp. 862-866). Newswood Limited.

**Construction of an appropriate membership function based on size of fuzzy set and mathematical programming.** / Hasuike, Takashi; Katagiri, Hideki.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*IMECS 2016 - International Multiconference of Engineers and Computer Scientists 2016.*vol. 2, Newswood Limited, pp. 862-866, International Multiconference of Engineers and Computer Scientists 2016, IMECS 2016, Tsimshatsui, Kowloon, Hong Kong, 16/3/16.

}

TY - GEN

T1 - Construction of an appropriate membership function based on size of fuzzy set and mathematical programming

AU - Hasuike, Takashi

AU - Katagiri, Hideki

PY - 2016

Y1 - 2016

N2 - This paper proposes an extended approach to construct an appropriate membership function as objectively as possible. It is important to set an appropriate membership function to obtain a reasonable optimal solution for real-world decision making. The main academic contribution of our proposed approach is to integrate a general continuous and nonlinear function minimizing the subjectivity into an interval estimation by a heuristic method under a given probability density function based on real-world data. Our approach is an extend approach of Civanlar and Trussell's study. One of two main steps of our proposed approach is to set membership values which a decision maker confidently judges whether an element is included in the given set or not. Another is to obtain other values objectively by solving Civanlar and Trussell's mathematical programming problem with a nonlinear membership function. In this paper, the given membership function is approximately transformed into a piecewise linear membership function, and the appropriate values of parameters in the piecewise linear membership function are determined.

AB - This paper proposes an extended approach to construct an appropriate membership function as objectively as possible. It is important to set an appropriate membership function to obtain a reasonable optimal solution for real-world decision making. The main academic contribution of our proposed approach is to integrate a general continuous and nonlinear function minimizing the subjectivity into an interval estimation by a heuristic method under a given probability density function based on real-world data. Our approach is an extend approach of Civanlar and Trussell's study. One of two main steps of our proposed approach is to set membership values which a decision maker confidently judges whether an element is included in the given set or not. Another is to obtain other values objectively by solving Civanlar and Trussell's mathematical programming problem with a nonlinear membership function. In this paper, the given membership function is approximately transformed into a piecewise linear membership function, and the appropriate values of parameters in the piecewise linear membership function are determined.

KW - Interactive approach

KW - Mathematical programming

KW - Membership function

KW - Piecewise linear function

UR - http://www.scopus.com/inward/record.url?scp=84978698964&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84978698964&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84978698964

VL - 2

SP - 862

EP - 866

BT - IMECS 2016 - International Multiconference of Engineers and Computer Scientists 2016

PB - Newswood Limited

ER -