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2005•Logic Journal of IGPLRequires access

A Generalized Concept Lattice

Stanislav Krajči

Open publisher page 136 citations

Abstract

We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for so far known approaches: a classical crisp Ganter & Wille's [7] case, a fuzzy Pollandt [12] and Bělohlávek' [2] one and one-sided fuzzy concept lattice [5]. We define appropriate (symmetric) mappings and show that they form a Galois connection. In the end we show that these mappings generate a complete lattice.

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What this paper is about

We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for so far known approaches: a classical crisp Ganter & Wille's [7] case, a fuzzy Pollandt [12] and Bělohlávek' [2] one and one-sided fuzzy concept lattice [5]. We define appropriate (symmetric) mappings and show that they form a Galois connection. In the end we show that these mappings generate a complete lattice.

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OpenAlex reports 136 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We describe a new approach to fuzzify a concept lattice and we show that it is a generalization and common platform for so far known approaches: a classical crisp Ganter & Wille's [7] case, a fuzzy Pollandt [12] and Bělohlávek' [2] one and one-sided fuzzy concept lattice [5]. We define appropriate (symmetric) mappings and show that they form a Galois connection. In the end we show that these mappings generate a complete lattice.

Key concepts: Galois connection, Mathematics, Lattice (music), Fuzzy logic, Generalization, Complete lattice, Map of lattices, Discrete mathematics

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