a theorem was recently introduced to establish a relationship betweengoal programming and fuzzy programming for vectormaximum problems.in this short note it is shown that the relationship does not exist underall circumstances. the necessary correction is proposed.

bilevel linear programming  is a decision making problem with a two-level decentralized organization. the textquotedblleft leadertextquotedblright~ is in the upper level and the textquotedblleft followertextquotedblright, in the lower. making a decision at one level affects that at the other one. in this paper, bilevel linear programming  with inexact parameters has been studied and a method is...

Fuzzy linear symmetrical bi-level programming is the most extensive problem in multi-level programming. A new method based on tolerance degree has been introduced in this paper. The method mainly concerns the modeling of complicated Supply Chain with bi-level Stackelberg structure. We analyze the reason lead to uncertainties in supply chain, summarize methods of dealing with uncertainties, and ...

In this paper, we integrate goal programming (GP), Taylor Series, Kuhn-Tucker conditions and Penalty Function approaches to solve linear fractional bi-level programming (LFBLP)problems. As we know, the Taylor Series is having the property of transforming fractional functions to a polynomial. In the present article by Taylor Series we obtain polynomial objective functions which are equivalent to...

This paper proposes a fuzzy goal programming based on Taylor series for solving decentralized bilevel multiobjective fractional programming (DBLMOFP) problem. In the proposed approach, all of the membership functions are associated with the fuzzy goals of each objective at the both levels and also the fractional membership functions are converted to linear functions using the Taylor series appr...

This paper presents a fuzzy approach for solving the bi-level integer linear fractional programming problem (BILFPP). At the first phase of the solution algorithm and to avoid the complexity of non convexity of this problem, we begin by finding the convex hull of its original set of constraints using the cutting-plane algorithm, and then the Charnes & Cooper transformation is used to convert th...