• Korean Journal of Mathematics
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• v.23 no.1
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• pp.29-36
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• 2015

A signed digraph S is the digraph D by assigning signs 1 or -1 to each arc of D. The base of S is the minimum number k such that there is a pair walks which have the same initial and terminal point with length k, but different signs. In this paper we show that for $n{\geq}5$ the upper bound of the base of a primitive non-powerful signed tournament Sn, which is the signed digraph by assigning 1 or -1 to each arc of a primitive tournament $T_n$, is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

• East Asian mathematical journal
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• v.28 no.5
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• pp.579-585
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• 2012

Let D be a finite digraph with the vertex set V(D) and arc set A(D). A two-valued function $f:V(D){\rightarrow}\{-1,\;1\}$ defined on the vertices of a digraph D is called a signed 2-independence function if $f(N^-[v]){\leq}1$ for every $v$ in D. The weight of a signed 2-independence function is $f(V(D))=\sum\limits_{v{\in}V(D)}\;f(v)$. The maximum weight of a signed 2-independence function of D is the signed 2-independence number ${\alpha}_s{^2}(D)$ of D. Recently, Volkmann [3] began to investigate this parameter in digraphs and presented some upper bounds on ${\alpha}_{s}^{2}(D)$ for general digraph D. In this paper, we improve upper bounds on ${\alpha}_s{^2}(D)$ given by Volkmann [3].

• Korean Journal of Mathematics
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• v.21 no.1
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• pp.55-62
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• 2013

The base $l(S)$ of a signed digraph S is the maximum number $k$ such that for any vertices $u$, $v$ of S, there is a pair of walks of length $k$ from $u$ to $v$ with different signs. A graph can be regarded as a digraph if we consider its edges as two-sided arcs. A signed cyclic graph $\tilde{C_n}$ is a signed digraph obtained from the cycle $C_n$ by giving signs to all arcs. In this paper, we compute the base of a signed cyclic graph $\tilde{C_n}$ when $\tilde{C_n}$ is neither symmetric nor antisymmetric. Combining with previous results, the base of all signed cyclic graphs are obtained.

• Korean Journal of Mathematics
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• v.22 no.3
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• pp.491-500
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• 2014

The base of a signed digraph S is the minimum number k such that for any vertices u, v of S, there is a pair of walks of length k from u to v with different signs. Let K be a signed complete graph of order n, which is a signed digraph obtained by assigning +1 or -1 to each arc of the n-th order complete graph $K_n$ considered as a digraph. In this paper we show that for $n{\geq}3$ the base of a primitive non-powerful signed complete graph K of order n is 2, 3 or 4.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.2
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• pp.159-167
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• 2003

This study suggests the hybrid fault diagnosis method of signed digraph (SDG) and partial least squares (PLS). SDG offers a simple and graphical representation for the causal relationships between process variables. The proposed method is based on SDG to utilize the advantage that the model building needs less information than other methods and can be performed automatically. PLS model is built on local cause-effect relationships of each variable in SDG. In addition to the current values of cause variables, the past values of cause and effect variables are inputted to PLS model to represent the Process armies. The measured value and predicted one by dynamic PLS are compared to diagnose the fault. The diagnosis example of CSTR shows the proposed method improves diagnosis resolution and facilitates diagnosis of masked multiple-fault.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.389-394
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• 1989

본 연구에서는 화학공정의 자동화와 관련된 실시간 나프타 분해로 이상진단 시스템의 한 부분을 구성하고 있는 지식기반의 구현을 위하여 공정변수 상호간의 관계를 나타낸 signed directed graph(SDG)를 기반으로 이상에서 파급되는 증상들을 순서대로 나타내는 fault-consequence digraph(FCD)를 지식모델로 사용했고, 이를 사고사례를 이용하여 검토해본 결과 초기에 정확한 이상원인 후보를 찾아내므로써 이상진단 전문가 시스템의 지식모델로 적합함을 알 수 있었다.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.283-286
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• 1996

This study suggests a new methodology for the fault diagnosis based on the signed digraph in developing the fault diagnosis system of a boiler plant. The suggested methodology uses the new model, fault-effect tree. The SDG has the advantage, which is simple and graphical to represent the causal relationship between process variables, and therefore is easy to understand. However, it cannot handle the broken path cases arisen from data uncertainty as it assumes consistent path. The FET is based on the SDG to utilize the advantages of the SDG, and also covers the above problem. The proposed FET model is constructed by clustering of measured variables, decomposing knowledge base and searching the fault propagation path from the possible faults. The search is performed automatically. The fault diagnosis system for a boiler plant, ENDS was constructed using the expert system shell G2 and the advantages of the presented method were confirmed through case studies.

• 제어로봇시스템학회:학술대회논문집
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• 2004.08a
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• pp.110-115
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• 2004

The hybrid fault diagnosis method based on a combination of the signed digraph (SDG) and the partial least-squares (PLS) has the advantage of improving the diagnosis resolution, accuracy and reliability, compared to those of previous qualitative methods, and of enhancing the ability to diagnose multiple fault. In this study, the method is applied for the multiple fault diagnosis of the Tennessee Eastman challenge process, which is a realistic industrial process for evaluating process contol and monitoring methods. The process is decomposed using the local qualitative relationships of each measured variable. Dynamic PLS (DPLS) model is built to estimate each measured variable, which is then compared with the estimated value in order to diagnose the fault. Through case studies of 15 single faults and 44 double faults, the proposed method demonstrated a good diagnosis capability compared with previous statistical methods.

• Journal of the Korean Institute of Intelligent Systems
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• v.8 no.6
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• pp.70-77
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• 1998

Although many methods of knowledge acquisition has been developed in the exper systems field, such a need form causal knowledge acquisition hs not been stressed relatively. In this respect, this paper is aimed at suggesting a causal knowledge acquisition process, and then investigate the causal knowledge-based inference process. A vehicle for causal knowledge acquisition is FCM (Fuzzy Cognitive Map), a fuzzy signed digraph with causal relationships between concept variables found in a specific application domain. Although FCM has a plenty of generic properties for causal knowledge acquisition, it needs some theoretical improvement for acquiring a more refined causal knowledge. In this sense, we refine fuzzy implications of FCM by proposing fuzzy causal relationship and fuzzy partially causal relationship. To test the validity of our proposed approach, we prototyped a causal knowledge-driven inference engine named CAKES and then experimented with some illustrative examples.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.461-467
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• 1998

Although many methods of knowledge acquisition has been developed in the expert systems field, such a need for causal knowledge acquisition has not been stressed relatively. In this respect, this paper is aimed at suggesting a causal knowledge acquisition process, and then investigate the causal knowledge-based inference process. A vehicle for causal knowledge acquisition is FCM (Fuzzy Cognitive Map), a fuzzy signed digraph with causal relationships between concept variables found in a specific application domain. Although FCM has a plenty of generic properties for causal knowledge acquisition, it needs some theoretical improvement for acquiring a more refined causal knowledge. In this sense, we refine fuzzy implications of FCM by proposing fuzzy implications of FCM by proposing fuzzy causal relationship and fuzzy partially causal relationship. To test the validity of our proposed approcach, we prototyped a causal knowledge-driven inference engine named CAKES and then experime ted with some illustrative examples.