Ideals and Filters on a Lattice in Neutrosophic Setting

Abstract

The notionsofidealsandfiltershavestudiedinmanyalgebraic(crisp)fuzzystructuresandusedto study theirvariousproperties,representationsandcharacterizations.Inadditiontotheirtheoretical roles, theyhaveusedinsomeareasofappliedmathematics.Inarecentpaper,Arockiaraniand AntonyCrispinSweetyhavegeneralizedandstudiedthesenotionswithrespecttotheconceptof neutrosophic setsintroducedbySmarandachetorepresentimprecise,incompleteandinconsistent information. Inthisarticle,weaimtodeepenthestudyoftheseimportantnotionsonagivenlattice in theneutrosophicsetting.Weshowtheirvariouspropertiesandcharacterizations,inparticular, we payattentiontotheircharacterizationsbasedonofthelatticeminandmaxoperations.In addition, westudythenotionofprimesingle-valuedneutrosophicideal(respectively,filter)as interesting kindandwediscusssomeitsset-operations,complementandassociatesets