### Abstract

This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

Original language | English |
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Title of host publication | Procedia Computer Science |

Publisher | Elsevier |

Pages | 994-1003 |

Number of pages | 10 |

Volume | 60 |

Edition | 1 |

DOIs | |

Publication status | Published - 2015 |

Event | 19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015 - , Singapore Duration: 2015 Sep 7 → 2015 Sep 9 |

### Other

Other | 19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015 |
---|---|

Country | Singapore |

Period | 15/9/7 → 15/9/9 |

### Fingerprint

### Keywords

- Fuzzy entropy
- Mathematical programming
- Membership function
- Smoothing function

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Procedia Computer Science*(1 ed., Vol. 60, pp. 994-1003). Elsevier. https://doi.org/10.1016/j.procs.2015.08.140

**A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory.** / Hasuike, Takashi; Katagiri, Hideki; Tsubaki, Hiroe.

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

*Procedia Computer Science.*1 edn, vol. 60, Elsevier, pp. 994-1003, 19th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2015, Singapore, 15/9/7. https://doi.org/10.1016/j.procs.2015.08.140

}

TY - GEN

T1 - A constructing algorithm for appropriate piecewise linear membership function based on statistics and information theory

AU - Hasuike, Takashi

AU - Katagiri, Hideki

AU - Tsubaki, Hiroe

PY - 2015

Y1 - 2015

N2 - This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

AB - This paper proposes a constructing algorithm for an appropriate membership function to integrate the fuzzy Shannon entropy with a piecewise linear function into subjective intervals estimation by the heuristic method based on the human cognitive behavior and subjectivity under a given probability density function. It is important to set a membership function appropriately in real-world decision making. The main parts of our proposed approach are to give membership values a decision maker confidently set, and to obtain the others by solving a nonlinear mathematical programming problem objectively. It is difficult to solve the initial mathematical programming problem efficiently using previous constructing approaches. In this paper, introducing some natural assumptions in the real-world and performing deterministic equivalent transformations to the initial problem using nonlinear programming, an efficient algorithm to obtain the optimal condition of each appropriate membership value is developed.

KW - Fuzzy entropy

KW - Mathematical programming

KW - Membership function

KW - Smoothing function

UR - http://www.scopus.com/inward/record.url?scp=84941083827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84941083827&partnerID=8YFLogxK

U2 - 10.1016/j.procs.2015.08.140

DO - 10.1016/j.procs.2015.08.140

M3 - Conference contribution

AN - SCOPUS:84941083827

VL - 60

SP - 994

EP - 1003

BT - Procedia Computer Science

PB - Elsevier

ER -