{
  "id": "1408.1121",
  "version": "v1",
  "published": "2014-08-05T21:33:51.000Z",
  "updated": "2014-08-05T21:33:51.000Z",
  "title": "Dialectics of Counting and the Mathematics of Vagueness",
  "authors": [
    "A. Mani"
  ],
  "comment": "This paper includes my axiomatic approach to granules. arXiv admin note: substantial text overlap with arXiv:1102.2558",
  "journal": "Transactions on Rough Sets. Vol. XV. LNCS 7255. Pages: 122--180 (2012)",
  "categories": [
    "math.LO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-05T21:33:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "mathematics",
      "dialectics",
      "rough natural number systems",
      "research paper",
      "general rough set theory"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}