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Conductive transformation under complicatedbasic-element correlative network
TANG Long , YANG Chunyan
Research Institute of Extenics and Innovation Methods, Guangdong University of Technology, Guangzhou 510006, China
Abstract: Complex systems are characterized by various relationships, among which correlations and conductive transformations should be considered while processing contradictory problems. Using the basic-element theory, this study investigates irregular basic-element correlative relationship-based conductive transformation theories by taking the complex system as a background. A basic-element correlative matrix and basic-element correlative function are proposed. We also establish conductive reasoning rules and conductive effect models for complicated basic-element correlative networks. We then employ supply and marketing activities for commercial productions to verify the validity of the proposed theories. These concepts can provide a theoretical basis and operable approaches for processing contradictory problems in complex systems and pave the way for generating a strategy for solving complex problems with the assistance of computers.
Key words: complex system     Extenics     basic-element     correlative network     conductive transformation     contradictory problem     correlative matrix     correlative function

1 基元相关矩阵和基元相关函数 1.1 基元相关矩阵

ρij=1；否则ρij=0。若ρji>=ρij=1，则表示基元BiBj关于评价特征c互为相关，记作

 图 1 6个基元的相关关系 Fig. 1 Correlations of the six basic-elements

(ρij)kl=1;否则(ρij)kl=0。

1.2 基元相关函数

2 复杂基元相关网下的传导推理规则

ji时，Qj(0)=0，Qj(1)=1，Tiφj=(Bj,Bj′)表示由不同对象之间的相关性引起的传导变换；当 j=i时，Qj(0)=1，Qj(1)=2，φj(2)=(Bj ′,Bj″)表示由相同对象关于不同评价特征的相关性引起的自身传导变换，故φ(2)j称为二阶变换。

ji，表示由不同对象之间的相关性引起的传导变换；若j=i，表示由相同对象关于不同评价特征的相关性引起的自身传导变换。

3 复杂基元相关网下传导效应的计算模型

4 案例分析

(c11)M1(c13)M1

(c12)M1(c13)M1

(c11)M1(c14)M1

(c12)M1(c14)M1

(c14)M1(c15)M1

(c13)M1(c21)M2

(c15)M1(c21)M2

(c22)M2(c21)M2

(c21)M2(c31)M3

(c31)M3(c32)M3

(c14)M1(c32)M3

(c15)M1(c32)M3

(c32)M3(c33)M3

U0(T1)=(1,1),(1,2)。根据传导推理规则2有：U1(T1)=(1,3),(1,4)；则根据传导推理规则1，T1一次传导变换集合为

5 结论

1)作为矛盾问题处理过程中传导推理的重要依据，已有传导变换理论应从基元相关链和相关环的情况推广至任意基元相关网的情况；

2)本文针对复杂基元相关网，提出了基元相关矩阵和基元相关函数的概念，为基元相关性的形式化表述提供了工具；

3)在此基础上，进一步给出了复杂基元相关网下传导变换对象的判定规则及其传导效应的计算模型；

4)以某企业的产品供销活动为例，通过构建产品供销系统的传导机制对所建立理论进行解读，验证了其有效性。

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DOI: 10.11992/tis.201507054

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#### 文章信息

TANG Long, YANG Chunyan

Conductive transformation under complicatedbasic-element correlative network

CAAI Transactions on Intelligent Systems, 2016, 11(01): 104-110.
DOI: 10.11992/tis.201507054