Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....

In this paper, we introduce new definitions of L-fuzzy neighborhood systems, L-fuzzy interior operators and L-fuzzy closure operators. Three characterizations of the category L-FTOP of L-fuzzy topological spaces and their L-fuzzy continuous mappings are presented by means of the category L-FNS of L-fuzzy neighborhood spaces and their continuous mappings, the category L-FIS of L-fuzzy interior s...

A neural fuzzy system learning with linguistic teaching signals is proposed in this paper. This system is able to process and learn numerical information as well as linguistic information. It can be used either as an adaptive fuzzy expert system or as an adaptive fuzzy controller. At first, we propose a fivelayered neural network for the connectionist realization of a fuzzy inference system. Th...

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...

This paper studies connectedness of Goetschel–Voxman fuzzy matroids (briefly, G–V fuzzy matroids), an analog of connectedness of crisp finite matroids. Based on the results of fuzzy circuits given by Goetschel and Voxman, the transitivity theorem concerning fuzzy circuits of G–V fuzzy matroids is established, and thus the useful notion of refined G–V fuzzy matroid is introduced. The connectedne...