{
  "id": "1702.03521",
  "version": "v1",
  "published": "2017-02-12T13:07:44.000Z",
  "updated": "2017-02-12T13:07:44.000Z",
  "title": "$(L,M)$-fuzzy convex structures",
  "authors": [
    "Fu-Gui Shi",
    "Zhen-Yu Xiu"
  ],
  "comment": "22 pages",
  "categories": [
    "math.GN"
  ],
  "abstract": "In this paper, the notion of $(L,M)$-fuzzy convex structures is introduced. It is a generalization of $L$-convex structures and $M$-fuzzifying convex structures. In our definition of $(L,M)$-fuzzy convex structures, each $L$-fuzzy subset can be regarded as an $L$-convex set to some degree. The notion of convexity preserving functions is also generalized to lattice-valued case. Moreover, under the framework of $(L,M)$-fuzzy convex structures, the concepts of quotient structures, substructures and products are presented and their fundamental properties are discussed. Finally, we create a functor $\\omega$ from $\\mathbf{MYCS}$ to $\\mathbf{LMCS}$ and show that there exists an adjunction between $\\mathbf{MYCS}$ and $\\mathbf{LMCS}$, where $\\mathbf{MYCS}$ and $\\mathbf{LMCS}$ denote the category of $M$-fuzzifying convex structures, and the category of $(L,M)$-fuzzy convex structures, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-12T13:07:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fuzzy convex structures",
      "fuzzifying convex structures",
      "quotient structures",
      "fundamental properties",
      "fuzzy subset"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}