### Abstract

This paper considers two general 0-1 random fuzzy programming problems based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problems are not well defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goal for the objective function, 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, each 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 |
---|---|

Journal | IAENG International Journal of Applied Mathematics |

Volume | 39 |

Issue number | 2 |

Publication status | Published - 2009 May |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*IAENG International Journal of Applied Mathematics*,

*39*(2).

**Efficient strict solution methods for 0-1 random fuzzy programming problems based on the necessity measure.** / Hasuike, Takashi; Katagiri, Hideki; Ishii, Hiroaki.

Research output: Contribution to journal › Article

*IAENG International Journal of Applied Mathematics*, vol. 39, no. 2.

}

TY - JOUR

T1 - Efficient strict solution methods for 0-1 random fuzzy programming problems based on the necessity measure

AU - Hasuike, Takashi

AU - Katagiri, Hideki

AU - Ishii, Hiroaki

PY - 2009/5

Y1 - 2009/5

N2 - This paper considers two general 0-1 random fuzzy programming problems based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problems are not well defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goal for the objective function, 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, each 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 two general 0-1 random fuzzy programming problems based on the degree of necessity which include some previous 0-1 stochastic and fuzzy programming problems. The proposal problems are not well defined due to including randomness and fuzziness. Therefore, by introducing chance constraint and fuzzy goal for the objective function, 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, each 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 - Random fuzzy variables

KW - Relaxation problem

UR - http://www.scopus.com/inward/record.url?scp=67650246039&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650246039&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67650246039

VL - 39

JO - IAENG International Journal of Applied Mathematics

JF - IAENG International Journal of Applied Mathematics

SN - 1992-9978

IS - 2

ER -