We present some complexity results on checking necessary efficiency in interval multiobjective linear programming. Supposing that objective function coefficients perturb within prescribed intervals, a feasible point x is called necessarily efficient if it is efficient for all instances of interval data. We show that the problem of checking necessary efficiency is co-NP-complete even for the cas...

Determining the optimal solution (OS) set of interval linear fractional programming (ILFP) models is generally an NP-hard problem. Few methods have been proposed in this field which only able to obtain value objective function. Thus, there a need for appropriate method determine OS ILFP model. In paper, we introduce three algorithms ILFP. first and second algorithms, using definition strong wea...

In this paper, we consider the bilevel linear programming problem (BLPP) where all coefficients in are interval type-2 triangular fuzzy numbers (IT2TFNs). First, convert a BLPP with IT2TFN parameters to an BLPP. next step, solve BLPPs and obtain optimal solution as IT2TFN.

Abstract: Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. Supply chain planning problem...

  Bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. Three level programming results when second level is itself a bi-level programming. By extending this idea it is possible to define multi-level programs with any number of levels. Supply chain planning problems are co...

multiple objective programming (mop) problems have become famous among many researchers due to more practical and realistic implementations. there have been a lot of methods proposed especially during the past four decades. in this paper, we develop a new algorithm based on a new approach to solve mop problems by starting from a utopian point (which is usually infeasible) and moving towards the...

in this paper we nd solution of linear interval equation in dual form based on the generalizedprocedure of interval extension which is called interval extended zero method.moreover, proposed method has signicant advantage, is that it substantially decreasesthe excess width eect.

In the framework of interval uncertainty, a well-known classical problem in numerical analysis is considered, namely, to find “the best” interval solution for interval system of linear algebraic equations. This problem is known to be NP-hard and can be solved via multiple linear programming. In present paper, a simple approach is proposed for some particular models of interval uncertainty. This...