### Abstract

This paper proposes a new approach of constructing an appropriate membership function to integrate a specific given probability density function, particularly Gaussian function, and fuzzy Shannon entropy extending the information theory based on the human cognitive behavior and subjectivity. The proposed approach is formulated as a more general mathematical programming problem than previous approaches due to using a general Gaussian-based function and the fuzzy Shannon entropy. The optimal condition of parameters is obtained by performing deterministic equivalent transformations to the initial problem. Furthermore, in order to show the appropriate membership function using the proposed approach, some probability density functions are provided as numerical examples.

Original language | English |
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Pages (from-to) | 809-813 |

Number of pages | 5 |

Journal | ICIC Express Letters |

Volume | 8 |

Issue number | 3 |

Publication status | Published - 2014 Feb 4 |

Externally published | Yes |

### Keywords

- Constructing membership function
- Fuzzy entropy
- Mathematical programming
- S-curve function

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)

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## Cite this

*ICIC Express Letters*,

*8*(3), 809-813.