﻿ 一种模糊多属性决策选优算法 An Algorithm to Select Satisfying Alternative for Fuzzy Multiple Attribute Decision Making Problem

Operations Research and Fuzziology
Vol.07 No.01(2017), Article ID:19807,9 pages
10.12677/ORF.2017.71003

An Algorithm to Select Satisfying Alternative for Fuzzy Multiple Attribute Decision Making Problem

Yingying Jiang

School of Mathematics, Yunnan Normal University, Kunming Yunnan

Received: Feb. 7th, 2017; accepted: Feb. 21st, 2017; published: Feb. 24th, 2017

ABSTRACT

In this paper, the decision programming with L-R fuzzy number changed into common decision programming by sorting rule. A multi-attribute decision algorithm is presented to help decision- maker find the best alternative from alternatives set based on nonlinear utility function and outranking relation.

Keywords:Sorting Rule, L-R Fuzzy Number, Nonlinear Utility Function

1. 引言

2. 备用知识

2.1. 偏好于效用函数

(对于完全明确的偏好，若为两个决策方案，为一效用函数，则有优于或无差异于 [8] (劣于或无差异于)。)

2.2. 隶属度

2.3. L-R模糊数

(1)

(2)

(3)在区间单调递减，则称为模糊数的基准函数。

L-R模糊数运算法则：

(1)

(2)

2.4. 不同类型属性指标值归一化

(1) 收益类模糊指标值的归一化

(2) 成本类模糊指标值的归一化

3. 问题描述与算法

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

。将其加入到规划(7)，(8)的约束中，然后用新的替换规划(7)，(8)约束中的；否则保留

4. 算例

(9)

。则优于，则把从中删除，生成约束条件

(10)

5. 结论

An Algorithm to Select Satisfying Alternative for Fuzzy Multiple Attribute Decision Making Problem[J]. 运筹与模糊学, 2017, 07(01): 22-30. http://dx.doi.org/10.12677/ORF.2017.71003

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