Dictionary

bounded lattice en · NOUN

Meanings

1. Any lattice (type of partially ordered set) that has both a greatest and a least element.
   • 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, Indeed, 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.
   • 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]. 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:
   • 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, A 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.

Forms

Deriveds

upper bounded lattice · lower bounded lattice