### Abstract

This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.

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

Title of host publication | AIP Conference Proceedings |

Pages | 69-82 |

Number of pages | 14 |

Volume | 1174 |

DOIs | |

Publication status | Published - 2009 |

Externally published | Yes |

Event | International MultiConference of Engineers and Computer Scientists, IMECS 2009 - Hong Kong, China Duration: 2009 Mar 18 → 2009 Mar 20 |

### Other

Other | International MultiConference of Engineers and Computer Scientists, IMECS 2009 |
---|---|

Country | China |

City | Hong Kong |

Period | 09/3/18 → 09/3/20 |

### Fingerprint

### Keywords

- 0-1 programming problem
- Degree of necessity
- Maximm approach
- Random fuzzy variables
- Relaxation problem

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*AIP Conference Proceedings*(Vol. 1174, pp. 69-82) https://doi.org/10.1063/1.3256262

**A maximin approach for the bi-criteria 0-1 random fuzzy programming problem based on the necessity measure.** / Hasuike, Takashi; Katagiri, Hideki; Ishii, Hiroaki.

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

*AIP Conference Proceedings.*vol. 1174, pp. 69-82, International MultiConference of Engineers and Computer Scientists, IMECS 2009, Hong Kong, China, 09/3/18. https://doi.org/10.1063/1.3256262

}

TY - GEN

T1 - A maximin approach for the bi-criteria 0-1 random fuzzy programming problem based on the necessity measure

AU - Hasuike, Takashi

AU - Katagiri, Hideki

AU - Ishii, Hiroaki

PY - 2009

Y1 - 2009

N2 - This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.

AB - This paper considers a bi-criteria general 0-1 random fuzzy programming problem based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problem is not well-defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goals for objectives, and considering the maximization of the aspiration level for total profit and the degree of necessity that the objective function's value satisfies the fuzzy goal, the main problem is transformed into a deterministic equivalent problem. Furthermore, by using the assumption that each random variable is distributed according to a normal distribution, the problem is equivalently transformed into a basic 0-1 programming problem, and the efficient strict solution method to find an optimal solution is constructed.

KW - 0-1 programming problem

KW - Degree of necessity

KW - Maximm approach

KW - Random fuzzy variables

KW - Relaxation problem

UR - http://www.scopus.com/inward/record.url?scp=70450225530&partnerID=8YFLogxK

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U2 - 10.1063/1.3256262

DO - 10.1063/1.3256262

M3 - Conference contribution

AN - SCOPUS:70450225530

SN - 9780735407138

VL - 1174

SP - 69

EP - 82

BT - AIP Conference Proceedings

ER -