Abstract
Multiobjective programming, known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives. This paper aims to provide a new multiobjective programming named uncertain multiobjective programming that is a type of multiobjective programming involving uncertain variables. Some mathematical properties are also explored. Besides, uncertain goal programming is introduced as a compromise method for solving the uncertain multiobjective programming models. Both the uncertain multiobjective programming model and the uncertain goal programming model are transformed to crisp programming models with the help of the operational law of uncertain variables via inverse uncertainty distributions.
Highlights
Multiobjective programming was introduced by Neumann and Morgenstern [19] to optimize two or more conflicting objectives subject to certain constraints
As a compromise method for solving multiobjective programming, goal programming was proposed by Charnes and Cooper [2]
Since the constraint functions gj are strictly increasing with respect to ξ1, ξ2, · · ·, ξsj and strictly decreasing with respect to ξsj+1, ξsj+2, · · ·, ξn, for j = 1, 2, · · ·, m, respectively, it follows from the operational law of uncertain variables that the inverse uncertainty distributions of the uncertain variables gj(x, ξ ) are
Summary
Multiobjective programming was introduced by Neumann and Morgenstern [19] to optimize two or more conflicting objectives subject to certain constraints. In order to describe an uncertain variable in practice, the concept of uncertainty distribution was defined by Liu [8] as the following function, (x) = M {ξ ≤ x} , ∀x ∈ . (Liu [13]) Let ξ be an uncertain variable with regular uncertainty distribution .
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