Abstract
Because of the great needs both for the research of pansystem mathematics and for the analysis of general things’ mechanism, this paper discusses the binary relation’s transitivity confined to multirelation. The so-called “g-transitivity” a completely new concept about transitivity—is introduced and its basic properties are investigated. The study shows that it is not only g-transitivity a generalization of traditional transitivity, quasi-transitivity, semi-order, quasi-order and other panorder, but also includes many important concepts such as closenss, convexity, topology, duality as its special cases.
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References
Wu Xue-mou,Approximation-Transforming Theory and Pansystems Concepts in Mathematics, Press of Hu’nan Science and Technology (1984). (in Chinese)
Wu Xue-mou,The Pansystems View of the World, Press of Chinese People University (1990). (in Chinese)
Wu Xue-mou,Pansystems and Mathematical Methods, Press of Jiangsu Education (1990). (in Chinese)
Wu Shou-zhi and Wu Xue-mou, Generalized fundamental equation in pansystems network analysis,Kybernetes, 15, (1986).
Wu Shou-zhi, Pansystems investigation of fuzzy transitivity,Fuzzy Mathematics, 1 (1984). (in Chinese)
Wu Shou-zhi and Chen Bei-fang, Quasi-transitivity and the problem of social choice,Science Exploration, 2 (1984).
Avriel, M.Nonlinear Programming — Analysis and Methods, Prentice-Hall Inc. (1976).
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Shou-zhi, W. A new pansystems research about binary relation’s transitivity. Appl Math Mech 15, 1081–1085 (1994). https://doi.org/10.1007/BF02455399
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DOI: https://doi.org/10.1007/BF02455399