Abstract
In this article, a methodology is developed to solve an interval and a fractional interval programming problem by converting into a non-interval form for second order cone constraints, with the objective function and constraints being interval valued functions. We investigate the parametric and non-parametric forms of the interval valued functions along with their convexity properties. Two approaches are developed to obtain efficient and properly efficient solutions. Furthermore, the efficient solutions or Pareto optimal solutions of fractional and non-fractional programming problems over R + n ⋃ { 0 } are also discussed. The main idea of the present article is to introduce a new concept for efficiency, called efficient space, caused by the lower and upper bounds of the respective intervals of the objective function which are shown in different figures. Finally, some numerical examples are worked through to illustrate the methodology and affirm the validity of the obtained results.
Highlights
We consider solving fractional interval programming problems with second order cone constraints with both the objective and constraints being interval valued functions
We investigate the efficient solution for interval fractional and non-fractional programming problems in Rn+ {0}
To compare the obtained results for the numerical examples, we use different diagrams and tables to show the advantages of the given Theorems 2 and 3 by showing that any solution of the problem ( P9) or ( P10) is an efficient solution of the problem ( P7)
Summary
We consider solving fractional interval programming problems with second order cone constraints with both the objective and constraints being interval valued functions. Nonlinear interval optimization problems have been studied in several directions by many researchers during the past few decades [1,2,3,4]. Most considered models used quadratic programming problems with interval parameters. A methodology applied to interval valued convex quadratic programming problems by Bhurjee and Panda [1] which categorized how a solution of a general optimization problem can exist. In the past few decades, fractional programming problems have attracted the interest of many researchers. These problems have applications in the real physical world such as finance, production planning, electronic, etc. Dinkelbach [7] considered the same objective
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
