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Interactive fuzzy programming for two-level linear fractional programming problems

FUZZY SETS AND SYSTEMS 2001年第1期119卷 31-40页

作者： Sakawa, M Nishizaki, I Hiroshima Univ Fac Engn Dept Ind & Syst Engn Higashihiroshima Hiroshima 7398527 Japan

This paper presents interactive fuzzy programming for two-level linear fractional programming problems with the essentially cooperative decision makers. Tn our interactive method, after determining the fuzzy goals of the decision makers at both levels, a satisfactory solution is efficiently derived by updating the satisfactory level of the decision maker at the upper level with considerations of overall satisfactory balance between both levels. In an interactive process, optimal solutions to the formulated programming problems are obtained by combined use of the bisection method and the phase one of linear programming and the variable transformation by Charnes and Cooper. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method. (C) 2001 Elsevier Science B.V. All rights reserved.

关键词： two-level linear fractional programming problem fuzzy programming fuzzy goals interactive methods

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Interactive fuzzy programming for decentralized two-level linear fractional programming (DTLLFP) problems

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OMEGA-INTERNATIONAL JOURNAL OF MANAGEMENT SCIENCE 2007年第4期35卷 432-450页

作者： Ahlatcioglu, Mehmet Tiryaki, Fatma Yildiz Tech Univ Fac Arts & Sci Dept Math Istanbul Turkey

This paper presents two new interactive fuzzy programming approaches for a decentralized two-level linear fractional programming (DTLLFP) problem with a single decision maker (DM0) at the upper level and multiple DMs (DMi, i = 1,..., k) at the lower level. In the first approach, DM0 specifies the minimal satisfactory level for own objective without considering the satisfactory levels of own decision variables and decreases it in favour of objectives at the lower level. Whereas, in the second approach, DM0 does not specify the minimal satisfactory level for own objective, but instead DM0 transfers the degree of satisfaction for not only own objective but also the own decision variables to the lower level. In both our approaches, with the help of analytic hierarchy process (AHP) method [Saaty TL. The analytical hierarchy process. New York: McGraw-Hill, 1980], DM0 assigns weights w(1), w(2),..., w(k) to objectives at the lower level. The most important idea to be emphasized is that equivalence is established such that the satisfactory levels of all objectives are proportional to their own weights. To obtain an overall satisfactory balance between both levels, by updating the satisfactory degree of the DM0 which is in the first approach or the tolerances of the DM0's decision variables which is in the second approach, transformed main problems are constructed corresponding to DTLLFP. Maximizing the least degree of equivalent satisfaction among all DMs, they efficiently find a satisfactory or compromise solution from a Pareto optimal set for DTLLFP problem. If the DM0 is not satisfied with this solution, a strongly efficient satisfactory solution can be reached by interacting with him or her. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed methods. (c) 2005 Elsevier Ltd. All rights reserved.

关键词： multiple level programming two-level linear fractional programming problem fuzzy programming fuzzy goals interactive methods AHP

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