##
**A fuzzy goal programming procedure for solving quadratic bilevel programming problems.**
*(English)*
Zbl 1038.68027

Summary: This article presents a fuzzy goal programming procedure for solving quadratic bilevel programming problems. In the proposed approach, the membership functions for the defined fuzzy objective goals of the Decision Makers (DM) at both the levels are developed first. Then, a quadratic programming model is formulated by using the notion of distance function minimizing the degree of regret to satisfaction of both DMs. At the first phase of the solution process, the quadratic programming model is transformed into an equivalent nonlinear goal programming model to maximize the membership value of each of the fuzzy objective goals on the extent possible on the basis of their priorities in the decision context. Then, at the second phase, the concept of linear approximation technique in goal programming is introduced for measuring the degree of satisfaction of the DMs at both the levels by arriving at a compromised decision regarding the optimality of two different sets of decision variables controlled separately by each of them. A numerical example is provided to illustrate the proposed approach.

### MSC:

68N19 | Other programming paradigms (object-oriented, sequential, concurrent, automatic, etc.) |

PDF
BibTeX
XML
Cite

\textit{B. B. Pal} and \textit{B. N. Moitra}, Int. J. Intell. Syst. 18, No. 5, 529--540 (2003; Zbl 1038.68027)

Full Text:
DOI

### References:

[1] | Candler, Comput Oper Res 9 pp 59– (1982) |

[2] | Bard, Comput Oper Res 9 pp 77– (1982) |

[3] | Bialas, IEEE Trans Automatic Control 27 pp 211– (1982) |

[4] | Bialas, Manag Sci 30 pp 1004– (1984) |

[5] | Burton, Omega 5 pp 457– (1977) |

[6] | Wen, Euro J Oper Res 62 pp 354– (1991) |

[7] | Zadeh, Inf Control 8 pp 338– (1965) |

[8] | Zimmermann, Fuzzy Sets Syst 1 pp 45– (1978) |

[9] | Dyson, J Oper Res Soc 31 pp 263– (1981) |

[10] | Fuzzy mathematical programming?methods and applications. Berlin: Springer; 1993. |

[11] | Fuzzy multiple objective decision making?methods and applications. Berlin: Springer; 1994. · Zbl 0810.90138 |

[12] | Zimmermann, Comput Oper Res 10 pp 291– (1983) |

[13] | Zimmermann, Inf Sci 36 pp 29– (1985) |

[14] | Fuzzy sets, decision making, and expert systems. Boston, MA: Kluwer Academic Publisher; 1987. |

[15] | Lai, Fuzzy Sets Syst 77 pp 321– (1996) |

[16] | Shih, Comput Oper Res 23 pp 73– (1996) |

[17] | Shih, Fuzzy Sets Syst 114 pp 71– (2000) |

[18] | Mohamed, Fuzzy Sets Syst 89 pp 215– (1997) |

[19] | A fuzzy goal programming approach for solving bilevel programming problems. In: editors. Advances in soft computing?AFSS 2002. Berlin: Springer; 2002, pp 91-98. |

[20] | Alemayehu, Opsearch 38 pp 508– (2001) |

[21] | Al-khayyal, Ann Oper Res 34 pp 125– (1992) |

[22] | Edmunds, IEEE Trans Syst Man Cybern 21 pp 83– (1991) |

[23] | Malhotra, Opsearch 37 pp 1– (2000) |

[24] | Thirwani, Intel J Manag Syst 14 pp 89– (1998) |

[25] | Vicente, J Optimiz Theory Appl 81 pp 379– (1994) |

[26] | Multipleobjective linear fractional programming?a fuzzy set theoretic approach. 1992; 52: 39-45. · Zbl 0786.90088 |

[27] | Hannan, Fuzzy Sets Syst 6 pp 235– (1981) |

[28] | Kao, Fuzzy Sets Syst 120 pp 435– (2001) |

[29] | Pal, Fuzzy Sets Syst. (2003) |

[30] | Yang, Fuzzy Sets Syst 41 pp 39– (1991) |

[31] | Goal programming and extensions. Lexington, MA: Lexington DC Heath; 1976. |

[32] | Yu, Manag Sci 19 pp 936– (1973) |

[33] | Griffith, Manag Sci 7 pp 379– (1961) |

[34] | Saber, Comput Oper Res 20 pp 275– (1993) |

[35] | Inuiguchi, Fuzzy Sets Syst 34 pp 15– (1990) |

[36] | Nakamura, Fuzzy Sets Syst 14 pp 211– (1984) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.