![]() Regularity of generalized derivations in BCI-algebras, Communications of the Korean Mathematical Society, 2016, 31(2): 229–235. On left (θ, ϕ)-derivations in BCI-algebras, Journal of the Egyptian Mathematical Society, 2014, 22: 157–161. On Symmetric Left Bi-Derivations in BCI-Algebras, International Journal of Mathematics and Mathematical Sciences, 2013, 2013: Article ID 238490. ![]() G Muhiuddin, A M Al-roqi, Y B Jun, et al. On t-derivations of BCI-algebras, Abstract and Applied Analysis, 2012, 1–12. An overview on the 2-tuple linguistic model for computing with words in decision making: extensions, applications and challenges, Information Sciences, 2012, 207: 1–18. Study on the properties of A-subset, Journal of Intelligent & Fuzzy Systems, 2017, 33(6): 3939–3947. ![]() ILI-ideals and prime LI-ideals in lattice implication algebras, Information Sciences, 2003, 155: 157–175. Interval-valued intuitionistic (T, S)-fuzzy filters theory on residuated lattices, International Journal of Machine Learning and Cybernetics, 2014, 5: 683–696. A note on derivations on basic algebras, Soft Computing, 2015, 19(7): 1765–1771. Derivations on universally complete f-algebras, Indagationes Mathematicae, 2015, 26: 1–18. On derivations of BCI-algebras, Information Sciences, 2004, 159: 167–176. Fuzzy positive implicative and fuzzy associative filters of lattice implication algebras, Fuzzy Sets and Systems, 2001, 121(2): 353–357. On symmetric bi-derivations of BCI-algebras, Applied Mathematical Sciences, 2011, (57–60)(5): 2957–2966. On derivations and their fixed point sets in residuated lattices, Fuzzy Sets and Systems, 2016, 303: 97–113. (⊖, ⊕)-Derivations and (⊖, ⊙)-Derivations on Mv-algebras, Iranian Journal of Mathematical Sciences and Informatics, 2013, 8(1): 75–90. On derivations of lattices, Pure Mathematics and Applications, 2001, 12(4): 365–382. Generalizations of Derivations in BCI-Algebras, Applied Mathematics & Information Sciences, 2015, 9(1): 89–94. A linguistic multi-criteria decision making approach based on logical reasoning, Information Sciences, 2014, 258: 266–276. ![]() S W Chen, J Liu, H Wang, Y Xu, J C Augusto. 2-Local derivations on matrix algebras over-commutative regular algebras, Linear Algebra and its Applications, 2013, 439: 1294–1311. On semigroup ideals and n-derivations in near-rings, Journal of Taibah University for Science, 2005, 9: 126–132. Derivations of MV-Algebras, International Journal of Mathematics and Mathematical Sciences, 2010, 10: 932–937. And we will prove the properties of lattices. Together we will learn how to identify extremal elements such as maximal, minimal, upper, and lower bounds, as well as how to find the least upper bound (LUB) and greatest lower bound (GLB) for various posets, and how to determine whether a partial ordering is a lattice. Boolean Lattice – a complemented distributive lattice, such as the power set with the subset relation.Īdditionally, lattice structures have a striking resemblance to propositional logic laws because a lattice consists of two binary operations, join and meet. ![]() Distributive Lattice – if for all elements in the poset the distributive property holds.Namely, the complement of 1 is 0, and the complement of 0 is 1. Complemented Lattice – a bounded lattice in which every element is complemented.Bounded Lattice – if the lattice has a least and greatest element, denoted 0 and 1 respectively.Complete Lattice – all subsets of a poset have a join and meet, such as the divisibility relation for the natural numbers or the power set with the subset relation.Moreover, several types of lattices are worth noting: Exampleįor example, let A =, we can’t identify which one of these vertices is the least upper bound (LUB) - therefore, this poset is not a lattice. Now, if you recall, a relation R is called a partial ordering, or poset, if it is reflexive, antisymmetric, and transitive, and the maximal and minimal elements in a poset are quickly found in a Hasse diagram as they are the highest and lowest elements respectively. In other words, it is a structure with two binary operations:īut to fully understand lattices and their structure, we need to take a step back and make sure we understand the extremal elements of a poset because they are critical in understanding lattices. Jenn, Founder Calcworkshop ®, 15+ Years Experience (Licensed & Certified Teacher) Definitionįormally, a lattice is a poset, a partially ordered set, in which every pair of elements has both a least upper bound and a greatest lower bound. ![]()
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