Fuzzy Concept Lattice is Made by Proto-Fuzzy Concepts

Abstract-- An L-fuzzy context is a triple consisting of a set of objects, a set of attributes and an L-fuzzy binary relation between them. An l-cut is a classical context over the same sets with relation as a set of all object attribute pairs, which fuzzy relation assigns truth degree geater or equal than l. Proto-fuzzy concept is a triple made of a set of objects and a set of attributes, which form a concept in some cut of L-fuzzy context and a supremum of all degrees in which cuts this concept exists. Aim of the paper is to show the connection of the structure of proto-fuzzy concepts and fuzzy concept lattice constructed in the way of [1][5]. This connection can help to generate of all fuzzy concepts. Keywords-- formal concept analysis, fuzzy concept lattice, fuzzy Galois connection 1 Preliminaries Basic notions of Formal Concept Analysis(FCA) are formal context and formal concept. Definition 1 A formal context B, A, R consists of a set of objects B, a set of attributes A and a relat...

• Type: Journal
• Year: 2009
• Where: EUSFLAT
• Authors: Ondrej Kridlo, Stanislav Krajci
• Keywords: Concept Lattice, EUSFLAT 2009, Formal Concept, Fuzzy Logic, Ii Xi