Year: 1995
Type: article
Abstract: The collection of fuzzy subsets of a set X forms a complete lattice that extends the complete lattice đ«(X) of crisp subsets of X. In this paper, we interpret this extension as a special case of the fuzzification of an arbitrary complete lattice A. We show how to construct a complete lattice F(A, L) the Lâfuzzificatio of A, where L is the valuation lattice that extends A while preserving all suprema and infima. The fuzzy objects in F(A, L) may be interpreted as the supâpreserving maps from A to the dual of L. In particular, each complete lattice coincides with its 2âfuzzification, where 2 is the twoelement lattice. Some familiar fuzzifications (fuzzy subgroups, fuzzy subalgebras, fuzzy topologies, etc.) are special cases of our construction. Finally, we show that the binary relations on a set X may be seen as the fuzzy subsets of X with respect to the valuation lattice đ«(X).
Author: Arturo A. L. Sangalli
Institution: Champlain Regional College
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,240
OpenAlex ID: W2102043716