The notions of (strong) intersection-soft filters in R 0 -algebras are introduced, and related properties are investigated. Characterizations of a (strong) intersection-soft filter are established, and a new intersection-soft filter from old one is constructed. A condition for an intersection-soft filter to be strong is given, and an extension property of a strong intersection-soft filter is es...

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCIalgebras are introduced, and related properties are investigated. Characterizations of doubleframed soft algebras are...

The notion of union-soft filters of a CI-algebra is introduced, and related properties are investigated. Characterization of a union-soft filter is discussed, and conditions for a soft set to be a union-soft filter are provided. New union-soft filter from old one is established. Mathematics Subject Classification: 06F35, 03G25, 06D72

The notion of extended filter of a filter associated to a subset of Rl-monoids is defined and related properties are investigated. Rachunek and Salounova proved that positive implicative filters and Boolean filters in Rl-monoids coincide with a condition in Rachunek and Salounova (Acta Univ Palacki Olomuc Fac rer nat Math 48(1):93–107, 2009). In this paper, we prove that positive implicative fi...

One of the powerful applications of Booiean expression is to allow users to extract relevant information from a database. Unfortunately, previous research has shown that users have difficulty specifying Boolean queries. In an attempt to overcome this limitation, a graphical Filter/Flow representation of Boolean queries was designed to provide users with an interface that visually conveys the me...

A reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of a given information system. The existing reduct approaches under soft set theory are still based on Boolean-valued information system. However, in the real applications, the data usually contain non-Boolean values. In this paper, an alternative approach for attribute...

The theory of Boolean algebras can be fruitfully applied to judgment aggregation: Assuming universality, systematicity and a sufficiently rich agenda, there is a correspondence between (i) non-trivial deductively closed judgment aggregators and (ii) Boolean algebra homomorphisms defined on the power-set algebra of the electorate. Furthermore, there is a correspondence between (i) consistent com...