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**Fuzzy goal programming approach to multilevel programming problems.**
*(English)*
Zbl 1110.90084

Summary: The purpose of this paper is to propose a procedure for solving multilevel programming problems in a large hierarchical decentralized organization through linear fuzzy goal programming approach. Here, the tolerance membership functions for the fuzzily described objectives of all levels as well as the control vectors of the higher level decision makers are defined by determining individual optimal solution of each of the level decision makers. Since the objectives are potentially conflicting in nature, a possible relaxation of the higher level decision is considered for avoiding decision deadlock. Then fuzzy goal programming approach is used for achieving highest degree of each of the membership goals by minimizing negative deviational variables. Sensitivity analysis with variation of tolerance values on decision vectors is performed to present how the solution is sensitive to the change of tolerance values. The efficiency of our concept is ascertained by comparing results with other fuzzy programming approaches.

### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

### Keywords:

multilevel programming; fuzzy programming; fuzzy goal programming; membership function; tolerance values
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\textit{S. Pramanik} and \textit{T. K. Roy}, Eur. J. Oper. Res. 176, No. 2, 1151--1166 (2007; Zbl 1110.90084)

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