Yong-ho YonŞule Ayar ÖzbalÖzbal, Şule AyarYon, Yong Ho2025-10-06202414327643, 143374791432-76431433-747910.1007/s00500-023-09624-52-s2.0-85198065852https://www.scopus.com/inward/record.uri?eid=2-s2.0-85198065852&doi=10.1007%2Fs00500-023-09624-5&partnerID=40&md5=88fed931c4b825b178d703852a60dd86https://gcris.yasar.edu.tr/handle/123456789/8187https://doi.org/10.1007/s00500-023-09624-5In this paper first we consider an algebra that has a binary operation and a join of arbitrary nonempty subset. A lattice implication algebra is a lattice with a binary operation which has a join and a meet of finite nonempty subsets. In this work the notion of join-complete implication algebras L is defined as a join-complete lattice with a binary operation and some properties of this algebra L are searched. Moreover we prove that the interval [a 1] in L is a lattice implication algebra and show that L satisfies the completely distributive law when it has the smallest element 0. Finally we state the concept of filter and multipliers of L and provide finite and infinite examples of them. In addition we research some properties of these concepts in detail. © 2024 Elsevier B.V. All rights reserved.Englishinfo:eu-repo/semantics/openAccessFilter, Join-complete Implication Algebra, Lattice Implication Algebra, Multiplier, Fuzzy Filters, Binary Operations, Complete Lattices, Distributive Laws, Filter, Implication Algebra, Join-complete Implication Algebra, Lattice Implication Algebra, Multiplier, Nonempty Subsets, Property, AlgebraFuzzy filters, Binary operations, Complete lattices, Distributive laws, Filter, Implication algebra, Join-complete implication algebra, Lattice implication algebra, Multiplier, Nonempty subsets, Property, AlgebraFilterLattice Implication AlgebraJoin-Complete Implication AlgebraMultiplierArticle