二元关系传递性泛系研究新探
A New Pansystems Research About Binary Relation’s Transitivity
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摘要: 本文基于泛系数学研究和一般事物机理分析的需要,讨论了二元关系对多元关系的传递性,引进一种被叫作“g-传递性”的广义传递概念,考察了它的基本性质,g-传递性不但是普通传递性、拟传递性、半序、拟半序等泛序概念的推广,还包容闭性、凸性、拓扑、对偶性等基本概念为其特例,从而表明这一概念的普适性。Abstract: Beca use of the great needs for both the rcsoarch of pansystems mathematics and the analysis of general things' mechanism,this paper discusses the binary relations transitivity confincd to multirelation.The so-called "g-transitivity"-a completoly new concept about transitivity-is introduced and its basic properties are investigated.The study sfiows that it is not only g-transitivity a generalization of traditional transitivity,quasi-transitivity,semorder,quasi-order and other panorder,but also includes many basic concepts such as closeness,convexity,topology,duality as its special cases.
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Key words:
- pansystems theory /
- relation /
- panorder /
- order /
- transitivity /
- quasi-transitivity /
- g-transitivity
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[1] 吴学谋,《遇近转化论与数学中的泛系概念》,湖南科学技术出版社(1984). [2] 吴学谋,《从泛系观看世界》,中国人民大学出版社(1990). [3] 吴学谋,《泛系理论与数学方法》,江苏教育出版社(1990). [4] 吴守志、吴学谋,Generalized fundamental equation in pansystems network analysis,Kybernetes,15(1986). [5] 吴守志,Fuzzy传递性的泛系研究,模糊数学,(1)(1984). [6] 吴守志、陈北方,Quasi-transitivity and the problem of social choice,科学探索,(2)(1984). [7] Avriel,M,,Nonlinear Programming-Analgsis and Methods,Prentics-Hall Inc,(1976). -
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