Linear programming with rough interval coefficients

Authors:
Ali Hamzehee;Mohammad Ali Yaghoobi;Mashaalah Mashinchi
Affiliations:
Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran;Department of Mathematics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran;Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran
Venue:
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Year:
2014

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Abstract

In this paper, a linear programming LP problem is considered where some or all of its coefficients in the objective function and/or constraints are rough intervals. In order to solve this problem, we will construct two LP problems with interval coefficients. One of these problems is an LP where all of its coefficients are upper approximations of rough intervals and the other is an LP where all of its coefficients are lower approximations of rough intervals. Via these two LPs, two newly solutions completely and rather satisfactory are defined. Some examples are given to demonstrate the results.