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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.

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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