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An ABS-FRE algorithm for solving systems of fuzzy relation equations
Zun-Quan Xia,Fang-Fang Guo 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.-
The general scheme of an algorithm, called an ABS-FRE al-gorithm, for solving systems of fuzzy relation equations (systems of FRE)via the ABS algorithms is presented. As special cases, two particular algo-rithms for obtaining the greatest and minimal solutions of systems of FREare described. Several new operations used in this scheme are given, forinstance, operators∨and ∧, called quasi-inverses of operators∨and ∧,respectively, etc.
Zun-Quan Xia,Fang-Fang Guo 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.-
In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.
Xia, Zun-Quan,Guo, Fang-Fang 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.16 No.1
In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.
AN ABS-FRE ALGORITHM FOR SOLVING SYSTEMS OF FUZZY RELATION EQUATIONS
Xia, Zun-Quan,Guo, Fang-Fang 한국전산응용수학회 2004 Journal of applied mathematics & informatics Vol.15 No.1
The general scheme of an algorithm, called an ABS-FRE algorithm, for solving systems of fuzzy relation equations (systems of FRE) via the ABS algorithms is presented. As special cases, two particular algorithms for obtaining the greatest and minimal solutions of systems of FRE are described. Several new operations used in this scheme are given, for instance, operators $\veebar$ and $\underline{\wedge}$ called quasi-inverses of operators $\vee$ and $\wedge$, respectively, etc.
A Stackelberg model for server-proxies-userssystems
Hai-Shan Han,Zun-Quan Xia 한국전산응용수학회 2005 Journal of applied mathematics & informatics Vol.17 No.1-2
A Server-Proxies-Users communication system is studied by using Stackelberg strategy theory of game. A new model, in which the server, proxies and users are not equal is established, and that is a threelevel programming. The solution existence of the model is proved.
RELATION BETWEEN DEMYANOV DIFFERENCE ANDMINKOWSKI DIFFERENCE OF CONVEX COMPACTSUBSETS IN R2
CHUN-LING SONG,ZUN-QUAN XIA,LI-WEI ZHANG,SHU-YANG LI 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets in R2 being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.
RELATION BETWEEN DEMYANOV DIFFERENCE AND MINKOWSKI DIFFERENCE OF CONVEX COMPACT SUBSETS IN $R^2$
Song, Chun-Ling,Xia, Zun-Quan,Zhang, Li-Wei,Li, Shu-Yang 한국전산응용수학회 2007 Journal of applied mathematics & informatics Vol.23 No.1
A necessary and sufficient condition for Demyanov difference and Minkowski difference of compact convex subsets in $R^2$ being equal is given in this paper. Several examples are computed by Matlab to test our result. The necessary and sufficient condition makes us to compute Clarke subdifferential by quasidifferential for a special of Lipschitz functions.
Ge, Ren-Dong,Xia, Zun-Quan,Qiang, Guo 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.22 No.1
A modified BFGS algorithm for solving the unconstrained optimization, whose Hessian matrix at the minimum point of the convex function is of rank defects, is presented in this paper. The main idea of the algorithm is first to add a modified term to the convex function for obtain an equivalent model, then simply the model to get the modified BFGS algorithm. The superlinear convergence property of the algorithm is proved in this paper. To compared with the Tensor algorithms presented by R. B. Schnabel (seing [4],[5]), this method is more efficient for solving singular unconstrained optimization in computing amount and complication.