Interactive Fuzzy Decision Making for Multilevel Multiobjective Programming Problems using Generalized Λ-Extreme Points and Its Application to Environmental Systems

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  • 一般化Λ極点を用いた多重レベル多目的計画問題に対する対話型ファジィ意思決定と環境問題への適用
  • イッパンカ ラムダ キョクテン オ モチイタ タジュウ レベル タモクテキ ケイカク モンダイ ニ タイスル タイワガタ ファジィ イシ ケッテイ ト カンキョウ モンダイ エノ テキヨウ

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Abstract

In this paper, we focus on multilevel multiobjective programming problems (MLMOPs) where multiple decision makers in a hierarchical organization have their own multiple objective functions. For MLMOPs, we propose an interactive fuzzy decision making method to obtain a satisfactory solution which reflects not only the hierarchical relationships between multiple decision makers, but also their own preferences for their objective functions from among the generalized Λ-extreme point set. The concept of generalized Λ-extreme points is defined by using the Λ-extreme points of each decision maker, which is an extended concept of Pareto optimal solutions in multiob jective programming problems. In the proposed method, after the decision makers specify the decision powers and reference membership values for their membership functions, the corresponding generalized Λ-extreme point is obtained on the basis of the hyperplane method. In order to show the efficiency of the proposed method, an illustrative numerical example and an industrial pollution control problem in Japan are demonstrated along with the computer outputs.

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