Notions of core, support, and inversion of a soft set have been defined and studied. Soft approximations are soft sets developed through core and support and are used for granulating the soft space. Membership structure of a soft set has been probed in and many interesting properties are presented. We present a new conjecture to solve an optimum choice problem. Our Example 31 presents a case wh...

We study the properties and relations of fuzzy pseudo-filters of pseudo-BCK algebras. After we discuss the equivalent conditions of fuzzy normal pseudo-filter of pseudo-BCK algebra (pP), we propose fuzzy implicative pseudo-filter and its relation with fuzzy Boolean filter of (bounded) pseudo-BCK algebras (pP). Then two open problems: “In pseudo-BCK algebra or bounded pseudo-BCK algebra, Is the ...

The notions of int-soft filters, int-soft G-filters, regular int-soft filters, and MV-int-soft filters in residuated lattices are introduced, and their relations, properties, and characterizations are investigated. Conditions for an int-soft filter to be an int-soft G-filter, a regular int-soft filter, or an MV-int-soft filter are provided. The extension property for an int-soft G-filter is dis...

We present a data structure for three-dimensional fields C continuous in the modelling space. Regular grids storing the field values discretely are combined with a triquadratic approximation filter to define volume objects. This association of a grid and an approximation/interpolation filter allows the field to be defined by a C continuous real function and the surface to be directly visualised...

We present a data structure for three-dimensional fields C continuous in the modelling space. Regular grids storing the field values discretely are combined with a triquadratic approximation filter to define volume objects. This association of a grid and an approximation/interpolation filter allows the field to be defined by a C continuous real function and the surface to be directly visualised...

Boolean matching is a fundamental problem in FPGA synthesis, but existing Boolean matchers are not scalable to complex PLBs (programmable logic blocks) and large circuits. This paper proposes a filter-based Boolean matching method, F-BM, which accelerates Boolean matching using lookup tables implemented by Bloom filters storing precalculated matching results. To show the effectiveness of the pr...

Double Boolean algebras are algebras (D,u,t, , ,⊥,>) of type (2, 2, 1, 1, 0, 0). They have been introduced to capture the equational theory of the algebra of protoconcepts. A filter (resp. an ideal) of a double Boolean algebra D is an upper set F (resp. down set I) closed under u (resp. t). A filter F is called primary if F 6= ∅ and for all x ∈ D we have x ∈ F or x ∈ F . In this note we prove t...

The aim of this paper is to introduce the notions of interval valued (∈,∈ ∨q)-fuzzy Boolean (implicative, positive implicative and fantastic) filters in BL-algebras and to investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, the relations among these generalized fuzzy filters are discussed. It is proved that an interval valued (∈,∈...

Existing research has shown that naive users find it difficult to correctly express queries using the standard Boolean connectives AND, OR, and NOT. We conducted an empirical study examining the query production performance of naive users on four different systems: One of these systems was non-procedural textual (Boolean connectives); another was procedural textual (If-Then-Else), another non-p...