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**Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming.**
*(English)*
Zbl 1044.90534

Summary: The modern trend in operations research methodology deserves modelling of all relevant vague or uncertain information involved in a real decision problem. Generally, vagueness is modelled by a fuzzy approach and uncertainty by a stochastic approach. In some cases, a decision maker may prefer using interval numbers as coefficients of an inexact relationship. As a coefficient an interval assumes an extent of tolerance or a region that the parameter can possibly take. However, its use in the optimization problems is not much attended as it merits.

This paper defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment. On the basis of a comparative study on ordering interval numbers, inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined. A numerical example is also given.

This paper defines an interval linear programming problem as an extension of the classical linear programming problem to an inexact environment. On the basis of a comparative study on ordering interval numbers, inequality constraints involving interval coefficients are reduced in their satisfactory crisp equivalent forms and a satisfactory solution of the problem is defined. A numerical example is also given.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C08 | Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) |

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\textit{A. Sengupta} et al., Fuzzy Sets Syst. 119, No. 1, 129--138 (2001; Zbl 1044.90534)

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### References:

[1] | Charnes, A.; Cooper, W.W., Chance-constrained programming, Manag. sci., 6, 73-79, (1959) · Zbl 0995.90600 |

[2] | Delgado, M.; Verdegay, J.L.; Vila, M.A., A general model for fuzzy linear programming, Fuzzy sets and systems, 29, 21-29, (1989) · Zbl 0662.90049 |

[3] | Ignizio, J.P., Linear programming in single and multiple objective systems, (1982), Prentice-Hall Englewood Cliffs, NJ · Zbl 0484.90068 |

[4] | Ishibuchi, H.; Tanaka, H., Multiobjective programming in optimization of the interval objective function, Eur. J. oper. res., 48, 219-225, (1990) · Zbl 0718.90079 |

[5] | Kall, P., Stochastic programming, Eur. J. oper. res., 10, 125-130, (1982) · Zbl 0483.90064 |

[6] | Luhandjula, M.K., Fuzzy optimization: an appraisal, Fuzzy sets and systems, 30, 257-282, (1989) · Zbl 0677.90088 |

[7] | Moore, R.E., Method and application of interval analysis, (1979), SIAM Philadelphia |

[8] | A. Sengupta, T.K. Pal, \(A\)-index for ordering interval numbers, Presented in Indian Science Congress 1997, Delhi University, January 3-8. |

[9] | Sengupta, J.K., Optimal decision under uncertainty, (1981), Springer New York |

[10] | Slowinski, R., A multicriteria fuzzy linear programming method for water supply systems development planning, Fuzzy sets and systems, 19, 217-237, (1986) · Zbl 0626.90085 |

[11] | Tong, S., Interval number and fuzzy number linear programming, Fuzzy sets and systems, 66, 301-306, (1994) |

[12] | Vajda, S., Probabilistic programming, (1972), Academic Press New York |

[13] | Zimmermann, H.J., Fuzzy set theory and its application, (1991), Kluwer Academic Pub. Boston · Zbl 0719.04002 |

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