基于概率语言术语集评价的三支决策方法研究

doi:10.13232/j.cnki.jnju.2020.04.008

南京大学学报(自然科学版) ›› 2020, Vol. 56 ›› Issue (4): 505–514.doi: 10.13232/j.cnki.jnju.2020.04.008

基于概率语言术语集评价的三支决策方法研究

顾萍萍¹,周献中^1,²()

^1.南京大学工程管理学院，南京，210093
^2.南京大学智能装备新技术研究中心，南京，210093

收稿日期:2020-06-24 出版日期:2020-07-30 发布日期:2020-08-06
通讯作者: 周献中 E-mail:zhouxz@nju.edu.cn
基金资助:
国家自然科学基金(61876079)

Approaches to three⁃way decisions based on the evaluation of probabilistic linguistic terms sets

Pingping Gu¹,Xianzhong Zhou^1,²()

^1.School of Management and Engineering，Nanjing University，Nanjing，210093，China
^2.Research Center for Novel Technology of Intelligent Equipment，Nanjing University，Nanjing，210093，China

Received:2020-06-24 Online:2020-07-30 Published:2020-08-06
Contact: Xianzhong Zhou E-mail:zhouxz@nju.edu.cn

摘要/Abstract

摘要：

概率阈值的确定一直是三支决策研究的重点，尤其是在复杂模糊环境下.引入概率语言术语集评价损失函数，提出基于概率语言术评价的三支决策阈值确定以及规则的获取方法.首先依据概率语言术语集的内涵和性质，构建三支决策问题中的概率语言术语集损失函数矩阵；再借助决策粗糙集等价模型，构建等价模型 $α - m o d e l$ 和 $β - m o d e l$ 并找出其最优解，进而确定相应的概率阈值；还提出一种具有概率语言术评价的三支决策方法．

关键词: 三支决策, 阈值概率, 概率语言术语集, 等价模型

Abstract:

The method of determining probability thresholds of three?way decisions (3WDs) has always been the key of research，especially in the current environment with a large number of data and uncertainties. In the light of these problems，the loss function with Probabilistic Linguistic Terms Sets (PLTSs) is introduced in the paper，and we also propose a PLTS evaluation?based approach to achieve the thresholds and 3WDs. According to the definition and characters of PLTSs，the PLTSs loss function matrix is constructed firstly. Then，using the equivalent model of Decision?theoretic Rough Sets (DTRSs)，we construct the equivalent model (i.e.，the $α o p t - m o d e l$ and the $β o p t - m o d e l$ ) and try to find the optimal solution to determine the thresholds. Based on that，we propose a novel three?way decision approach under PLTSs evaluations. Finally，the validity of the method is verified by an example.

Key words: three?way decisions, probability thresholds, Probabilistic Linguistic Terms Sets, equivalent model

中图分类号:

C934

顾萍萍,周献中. 基于概率语言术语集评价的三支决策方法研究[J]. 南京大学学报(自然科学版), 2020, 56(4): 505–514.

Pingping Gu,Xianzhong Zhou. Approaches to three⁃way decisions based on the evaluation of probabilistic linguistic terms sets[J]. Journal of Nanjing University(Natural Sciences), 2020, 56(4): 505–514.

图/表 4

表1

决策代价损失函数"

	$C (P)$	$? C (N)$
$a P$	$λ P P = λ a P C$	$λ P N = λ a P ? C$
$a B$	$λ B P = λ a B C$	$λ B N = λ a B ? C$
$a N$	$λ N P = λ a N C$	$λ N N = λ a N ? C$

表1

表2

具有多对象的概率语言术语集损失函数矩阵"

	$λ P P$	$λ P N$	$λ B P$	$λ B N$	$λ N P$	$λ N N$
$o 1$	$λ P P 1 = L P P 1 (P)$	$λ P N 1 = L P N 1 (P)$	$λ B P 1 = L B P 1 (P)$	$λ B N 1 = L B N 1 (P)$	$λ N P 1 = L N P 1 (P)$	$λ N N 1 = L N N 1 (P)$
$o 2$	$λ P P 2 = L P P 2 (P)$	$λ P N 2 = L P N 2 (P)$	$λ B P 2 = L B P 2 (P)$	$λ B N 2 = L B N 2 (P)$	$λ N P 2 = L N P 2 (P)$	$λ N N 2 = L N N 2 (P)$
…	…	…	…	…	…	…
$o i$	$λ P P i = L i P P (P)$	$λ P N i = L i P N (P)$	$λ B P i = L i B P (P)$	$λ B N i = L B N i (P)$	$λ N P i = L N P i (P)$	$λ N N i = L N N i (P)$
…	…	…	…	…	…	…
$o m$	$λ P P m = L P P m (P)$	$λ P N m = L P N m (P)$	$λ B P m = L m B P (P)$	$λ B N m = L B N m (P)$	$λ N P m = L N P m (P)$	$λ N N m = L N N m (P)$

表2

表3

三家企业的概率语言术损失函数矩阵"

	$o 1$	$o 2$	$o 3$
$λ P P$	$s 1 (0.40), s 2 (0.45), s 3 (0.15)$	$s 1 (0.80), s 2 (0.10), s 3 (0.10)$	$s 1 (0.15), s 2 (0.25), s 3 (0.60)$
$λ P N$	$s 1 (0.25), s 2 (0.25), s 3 (0.50)$	$s 1 (0.05), s 2 (0.20), s 3 (0.75)$	$s 1 (0.70), s 2 (0.15), s 3 (0.15)$
$λ B P$	$s 1 (0.30), s 2 (0.55), s 3 (0.15)$	$s 1 (0.70), s 2 (0.10), s 3 (0.15)$	$s 1 (0.15), s 2 (0.20), s 3 (0.65)$
$λ B N$	$s 1 (0.25), s 2 (0.35), s 3 (0.40)$	$s 1 (0.10), s 2 (0.25), s 3 (0.65)$	$s 1 (0.75), s 2 (0.15), s 3 (0.10)$
$λ N P$	$s 1 (0.25), s 2 (0.50), s 3 (0.25)$	$s 1 (0.65), s 2 (0.10), s 3 (0.25)$	$s 1 (0.15), s 2 (0.15), s 3 (0.70)$
$λ N N$	$s 1 (0.35), s 2 (0.25), s 3 (0.40)$	$s 1 (0.10), s 2 (0.35), s 3 (0.55)$	$s 1 (0.80), s 2 (0.15), s 3 (0.05)$

表3

表4

采用提出方法获得的三家企业三支决策概率阈值及三支决策规则"

$O$	$o 1$	$o 2$	$o 3$
$P r C o i$	0.7035	0.6535	0.3545
$α ? i o p t$	0.5	0.75	0.6667
$β ? i o p t$	0.4	0.2857	0.6667
决策模式	三支决策	三支决策	二支决策
决策规则	$P O S C$	$B N D C$	$N E G C$

表4

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基于概率语言术语集评价的三支决策方法研究

Approaches to three⁃way decisions based on the evaluation of probabilistic linguistic terms sets

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