A stochastic technique to solve interval non-linear programming problems using GH-difference.

Purpose: A stochastic technique for solving interval non-linear problems using generalized Hukuhara (GH)-difference is proposed. The non-linear programming problem in interval form is transformed into an equivalent non-linear programming problem with real coefficients by associating a Gaussian random variable to the interval and the six-sigma rule. The conceptualized idea eliminates the decision maker's instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. To demonstrate a coherent understanding, numerical examples have been used. Design/methodology/approach: A stochastic approach has been used to develop a solution technique for solving interval nonlinear programming problems which arise in the modeling of scientific and engineering problems under uncertain environments. Findings: The proposed idea eliminates the decision maker's instinctive selection of weight functions and provides an alternative to the order relation method, max-min criteria-based methods and bi-level approaches for representing intervals as real numbers. This method provides specific results rather than in the interval form, which are more practical and implementable by the decision maker. Originality/value: This is to certify, that the research paper submitted is an outcome of original work. I have duly acknowledged all the sources from which the ideas and extracts have been taken. This article has not been submitted elsewhere for publication. [ABSTRACT FROM AUTHOR]