计数的辩证法与模糊数学
Dialectics of Counting and the Mathematics of Vagueness
摘要：
本文从形式和非形式两个角度引入了粗糙自然数系统的新概念。这些被用来改善大多数粗糙集理论的措施，在一般粗糙集合论（\textsf{RST}）和表示粗糙语义。该理论的基础也依赖于公理化的方法粒度的所有类型的一般\textsf{RST}最近开发的作者。后一种理论在本文中进行了扩展。它还表明，经典的\textsf{RST}的代数语义可以从开发的辩证计数程序。模糊集合论也被证明是代表在纯粒理论方面的一般观点，解决污染问题，弥漫在这篇研究论文。所有这一切构成了一个完全不同的方法数学的模糊现象，并建议新的方向，更现实的扩展数学基础的模糊性从基础和应用的观点。代数对应的概念\emph{rough naturals}也进行了研究和变种的特点是在倒数第二节。
英文摘要：
New concepts of rough natural number systems are introduced in this research paper from both formal and less formal perspectives. These are used to improve most rough set-theoretical measures in general Rough Set theory (\textsf{RST}) and to represent rough semantics. The foundations of the theory also rely upon the axiomatic approach to granularity for all types of general \textsf{RST} recently developed by the present author. The latter theory is expanded upon in this paper. It is also shown that algebraic semantics of classical \textsf{RST} can be obtained from the developed dialectical counting procedures. Fuzzy set theory is also shown to be representable in purely granule-theoretic terms in the general perspective of solving the contamination problem that pervades this research paper. All this constitutes a radically different approach to the mathematics of vague phenomena and suggests new directions for a more realistic extension of the foundations of mathematics of vagueness from both foundational and application points of view. Algebras corresponding to a concept of \emph{rough naturals} are also studied and variants are characterised in the penultimate section.
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