Two Approaches to Inner Estimations of the Optimal Solution Set in Interval Linear Programming

The present paper aims to propose an alternative solution approach in obtaining the fuzzy optimal solution to a fuzzy linear programming problem with variables given as fuzzy numbers with minimum uncertainty. In this paper, the fuzzy linear programming problems with variables given as fuzzy numbers is transformed into equivalent interval linear programming problems with variables given as interval numbers. The solutions to these interval linear programming problems with variables given as interval numbers are then obtained with the help of linear programming technique. A set of six random numerical examples has been solved using the proposed approach.

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Construction Method of Constraint Matrices Corresponded by an Optimal Solution

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.513-517.1617 ◽

2014 ◽

Vol 513-517 ◽

pp. 1617-1620

Author(s):

Xiao Liu ◽

Wei Li ◽

Peng Zhen Liu

Keyword(s):

Linear Programming ◽

Programming Problem ◽

Linear Programming Problem ◽

Linear Equations ◽

Optimal Solution ◽

Construction Method ◽

Interval Linear Programming ◽

Interval Linear

Through deep analysis of the solvability, which is based on interval linear equations and inequalities systems, for a given optimal solution to interval linear programming problem, we propose the construction method of constraint matrices corresponded by the optimal solution in this paper.

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Piecewise-Linear Pathways to the Optimal Solution Set in Linear Programming

Journal of Optimization Theory and Applications ◽

10.1023/a:1022651331550 ◽

1997 ◽

Vol 93 (3) ◽

pp. 619-634 ◽

Cited By ~ 4

Author(s):

M. Ç. Pinar

Keyword(s):

Linear Programming ◽

Piecewise Linear ◽

Optimal Solution ◽

Solution Set ◽

Optimal Solution Set

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Learning from Data by Interval Linear Programming

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.439-440.710 ◽

2010 ◽

Vol 439-440 ◽

pp. 710-714

Author(s):

Li Wei

Keyword(s):

Linear Programming ◽

Generalized Inverse ◽

Optimal Solution ◽

Explicit Representation ◽

Interval Linear Programming ◽

Regression Problem ◽

Constraint Matrix ◽

Learning From Data ◽

Interval Linear ◽

Regression Problems

The linear programming based method are popular methods for learning from empirical data (observations, samples, examples, records). In this paper, an interval linear programming based method for regression problems is proposed. The explicit representation of the general optimal solution of regression problem is obtained in terms of a generalized inverse of the constraint matrix. This explicit solution has obvious theoretical (and possibly computational) advantages over the well-known iterative methods of linear programming.

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