in this paper, our purpose is twofold. firstly, the tensor andresiduum operations on $l-$nested systems are introduced under thecondition of complete residuated lattice. then we show that$l-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. thus the new representation theorem of$l-$subsets on complete re...

Abstract Extending the belongs to (∈) relation and quasi-coincidence with(q) relation between fuzzy points and a fuzzy subsets, the concept of (α, β)-fuzzy filters and (α, β)-fuzzy filters of lattice implication algebras are introduced, where α, β ∈ {∈h , qδ, ∈h ∨qδ, ∈h ∧qδ}, α, β ∈ {∈h, qδ, ∈h ∨ qδ, ∈h ∧ qδ} but α ∈h ∧qδ, α ∈h ∧ qδ, respectively, and some related properties are investigated. S...

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

We present two masked priming lexical decision experiments in which we examined whether a nonword prime word would activate associative/semantic information from its corresponding addition neighbor (e.g., lght-dark via the addition neighbor light), producing associative/semantic priming. The rationale was the following: If a nonword prime with a missing letter produced a semantic/associative pr...

This paper reports the results of feature reduction in the analysis of a population based dataset for which there were no specific target variables. All attributes were assessed as potential targets in models derived from the full dataset and from subsets of it. The feature selection methods used were of the filter and wrapper types as well as clustering techniques. The predictive accuracy and ...

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated to Legendre multiresolution analysis is ...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion , 2. topology, and 3. powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary m...