"bounded lattice" meaning in English

{
  "forms": [
    {
      "form": "bounded lattices",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "bounded lattice (plural bounded lattices)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "derived": [
        {
          "word": "lower bounded lattice"
        },
        {
          "word": "upper bounded lattice"
        }
      ],
      "examples": [
        {
          "text": "2004, Anna Maria Radzikowska, Etienne Kerre, On L-Fuzzy Rough Sets, Leszek Rutkowski, Jörg Siekmann, Ryszard Tadeusiewicz, Lotfi A. Zadeh (editors), Artificial Intelligence and Soft Computing — ICAISC 2004: 7th International Conference, Proceedings, Springer, LNAI 3070, page 526,\nA residuated lattice is an extension of a bounded lattice by a monoid operation and its residuum, which are abstract counterparts of a triangular norm and a fuzzy residual implication, respectively."
        },
        {
          "text": "2006, Bart Van Gasse, Chris Cornelis, Glad Deschrijver, Etienne Kerre, Triangle Lattices: Towards an Axiomatization of Interval-Valued Residuated Lattices, Salavatore Greco, Yukata Hata, Shoji Hirano, Masahiro Inuiguchi, Sadaaki Miyamoto, Hung Son Nguyen, Roman Słowiński (editors), Rough Sets and Current Trends in Computing: 5th International Conference, Proceedings, Springer, LNAI 4259, page 117,\nIndeed, in the scope of these logics, formulas can be assigned not only 0 and 1 as truth values, but also elements of [0,1], or, more generally, of a bounded lattice ℒ."
        },
        {
          "ref": "2018, Gül Deniz Çayli, Funda Karaçal, “Some Remarks on Idempotent Nullnorms on Bounded Lattices”, in Vicenç Torra, Radko Mesiar, Bernard De Baets, editors, Aggregation Functions in Theory and in Practice, Springer,, page 32",
          "text": "In this paper, we study idempotent nullnorms on bounded lattices. We prove that there is no idempotent nullnorm on a distributive bounded lattice L different from the proposal in [13].",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any lattice (type of partially ordered set) that has both a greatest and a least element."
      ],
      "id": "en-bounded_lattice-en-noun-KOd-QTkc",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "lattice",
          "lattice"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ],
        [
          "greatest",
          "greatest"
        ],
        [
          "least",
          "least"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebra, order theory) Any lattice (type of partially ordered set) that has both a greatest and a least element."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "order-theory",
        "sciences"
      ]
    }
  ],
  "word": "bounded lattice"
}

{
  "derived": [
    {
      "word": "lower bounded lattice"
    },
    {
      "word": "upper bounded lattice"
    }
  ],
  "forms": [
    {
      "form": "bounded lattices",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "bounded lattice (plural bounded lattices)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Algebra"
      ],
      "examples": [
        {
          "text": "2004, Anna Maria Radzikowska, Etienne Kerre, On L-Fuzzy Rough Sets, Leszek Rutkowski, Jörg Siekmann, Ryszard Tadeusiewicz, Lotfi A. Zadeh (editors), Artificial Intelligence and Soft Computing — ICAISC 2004: 7th International Conference, Proceedings, Springer, LNAI 3070, page 526,\nA residuated lattice is an extension of a bounded lattice by a monoid operation and its residuum, which are abstract counterparts of a triangular norm and a fuzzy residual implication, respectively."
        },
        {
          "text": "2006, Bart Van Gasse, Chris Cornelis, Glad Deschrijver, Etienne Kerre, Triangle Lattices: Towards an Axiomatization of Interval-Valued Residuated Lattices, Salavatore Greco, Yukata Hata, Shoji Hirano, Masahiro Inuiguchi, Sadaaki Miyamoto, Hung Son Nguyen, Roman Słowiński (editors), Rough Sets and Current Trends in Computing: 5th International Conference, Proceedings, Springer, LNAI 4259, page 117,\nIndeed, in the scope of these logics, formulas can be assigned not only 0 and 1 as truth values, but also elements of [0,1], or, more generally, of a bounded lattice ℒ."
        },
        {
          "ref": "2018, Gül Deniz Çayli, Funda Karaçal, “Some Remarks on Idempotent Nullnorms on Bounded Lattices”, in Vicenç Torra, Radko Mesiar, Bernard De Baets, editors, Aggregation Functions in Theory and in Practice, Springer,, page 32",
          "text": "In this paper, we study idempotent nullnorms on bounded lattices. We prove that there is no idempotent nullnorm on a distributive bounded lattice L different from the proposal in [13].",
          "type": "quotation"
        }
      ],
      "glosses": [
        "Any lattice (type of partially ordered set) that has both a greatest and a least element."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "lattice",
          "lattice"
        ],
        [
          "partially ordered set",
          "partially ordered set"
        ],
        [
          "greatest",
          "greatest"
        ],
        [
          "least",
          "least"
        ],
        [
          "element",
          "element"
        ]
      ],
      "raw_glosses": [
        "(algebra, order theory) Any lattice (type of partially ordered set) that has both a greatest and a least element."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "order-theory",
        "sciences"
      ]
    }
  ],
  "word": "bounded lattice"
}