# Concept Equations

@article{Belohlvek2004ConceptE, title={Concept Equations}, author={Radim Belohl{\'a}vek}, journal={J. Log. Comput.}, year={2004}, volume={14}, pages={395-403} }

Studied in the paper are systems of equations which naturally arise in the formalization of the Port-Royal theory of concepts. The unknown quantity is a relation between objects and attributes. We study the case where the relation is fuzzy with truth values in a complete residuated lattice, covering therefore the special cases of complete Boolean algebras, Heyting algebras, MV-algebras etc. We answer the question of solvability, structure of solutions, and show how solvability of non-solvable…

## 8 Citations

### Multi-adjoint relation equations: Definition, properties and solutions using concept lattices

- Computer ScienceInf. Sci.
- 2013

### A general approach to fuzzy concepts

- ChemistryMath. Log. Q.
- 2004

A flexible way to build concepts within fuzzy logic and set theory that is general enough to capture some important particular cases, with their own independent interpretations, but also to allow the two universes to be equipped each with its own truth structure.

### Adjoint Triples and Residuated Aggregators

- Computer ScienceIPMU
- 2014

This paper presents the comparison of joint triples with other general operators considered in frameworks for fuzzy logic programming, formal concept analysis and fuzzy relation equations.

### Non-dual fuzzy connections

- Computer ScienceArch. Math. Log.
- 2004

Some kind of hardly describable ‘‘local preduality’’ still makes possible important parallel results and interesting new concepts besides antitone and isotone ones, that were classically reducible to the first, gain independency in fuzzy setting.

### Multi‐adjoint Relation Equations: A Decision Support System for Fuzzy Logic

- Computer ScienceInt. J. Intell. Syst.
- 2017

MARE is shown as a fundamental DSS in multi‐adjoint logic programming and two approximations of unsolvable equations will be obtained from a multiadjoint object‐oriented concept lattice theory.

### On Boolean factor analysis with formal concept as factors

- Computer Science
- 2006

Several results are proved, e.g. that each matrix is conceptfactorizable, that concept-factorizability is the best way to factorize binary matrices, describe sets of good factors, mandatory factors, etc.

### Optimal decompositions of matrices with entries from residuated lattices

- Mathematics, Computer ScienceJ. Log. Comput.
- 2012

It is shown that formal concepts of I, which play a central role in the Port-Royal approach to logic and which are the fixpoints of particular Galois connections associated to I, are optimal factors for decomposition of I in that they provide us with decompositions with the smallest number of factors.

### Akademie věd České republiky Teze doktorské disertačńı práce k źıskáńı vědeckého titulu“doktor věd” ve skupine věd “fyzikálně-matematické vědy” Concept lattices and attribute implications from data with fuzzy attributes komise pro obhajoby doktorských disertaćı v oboru “informati

- 2006

Akademie vědČeské republiky Teze doktorské disertační práce k získání vědeckého titulu " doktor věd " ve skupine věd " fyzikálně-matematické vědy " Concept lattices and attribute implications from…

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From the Publisher:
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