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ABBASI MOLAI, A., KHORRAM, E. (2008). LINEAR PROGRAMMING PROBLEM WITH INTERVAL COEFFICIENTS AND AN INTERPRETATION FOR ITS CONSTRAINTS. Iranian Journal of Science and Technology (Sciences), 32(4), 369-390. doi: 10.22099/ijsts.2008.2295
A. ABBASI MOLAI; E. KHORRAM. "LINEAR PROGRAMMING PROBLEM WITH INTERVAL COEFFICIENTS AND AN INTERPRETATION FOR ITS CONSTRAINTS". Iranian Journal of Science and Technology (Sciences), 32, 4, 2008, 369-390. doi: 10.22099/ijsts.2008.2295
ABBASI MOLAI, A., KHORRAM, E. (2008). 'LINEAR PROGRAMMING PROBLEM WITH INTERVAL COEFFICIENTS AND AN INTERPRETATION FOR ITS CONSTRAINTS', Iranian Journal of Science and Technology (Sciences), 32(4), pp. 369-390. doi: 10.22099/ijsts.2008.2295
ABBASI MOLAI, A., KHORRAM, E. LINEAR PROGRAMMING PROBLEM WITH INTERVAL COEFFICIENTS AND AN INTERPRETATION FOR ITS CONSTRAINTS. Iranian Journal of Science and Technology (Sciences), 2008; 32(4): 369-390. doi: 10.22099/ijsts.2008.2295

LINEAR PROGRAMMING PROBLEM WITH INTERVAL COEFFICIENTS AND AN INTERPRETATION FOR ITS CONSTRAINTS

Article 3, Volume 32, Issue 4, Autumn 2008, Page 369-390  XML PDF (220 K)
Document Type: Regular Paper
DOI: 10.22099/ijsts.2008.2295
Authors
A. ABBASI MOLAI ; E. KHORRAM
Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Hafez Avenue, Tehran, I. R. of Iran
Abstract
In this paper, we introduce a Satisfaction Function (SF) to compare interval values on the basis of
Tseng and Klein’s idea. The SF estimates the degree to which arithmetic comparisons between two interval
values are satisfied. Then, we define two other functions called Lower and Upper SF based on the SF. We
apply these functions in order to present a new interpretation of inequality constraints with interval
coefficients in an interval linear programming problem. This problem is as an extension of the classical linear programming problem to an inexact environment. On the basis of definitions of the SF, the lower and upper SF and their properties, we reduce the inequality constraints with interval coefficients in their satisfactory crisp equivalent forms and define a satisfactory solution to the problem. Finally, a numerical example is given and its results are compared with other approaches
Keywords
Interval number; inequality relation; equality relation; satisfaction function; interval linear programming
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