Concept-Forming Operators on Multilattices
نویسندگان
چکیده
Adjoint pairs or adjoint triples defined on lattices have proven to be a useful tool when working in fuzzy formal concept analysis. This paper shows that adjoint pairs and triples can play as well an important role within the framework of multilattices, especially in order to form the Galois connections needed to build concept multilattices.
منابع مشابه
Fuzzy Formal Concept Analysis via Multilattices: First Prospects and Results
The most general algebraic structure of truth-values considered in the theory of fuzzy concept analysis to evaluate the attributes and objects has been a lattice. However, in some examples arises the necessity of a more general structure. In this paper we investigate the use of multilattices as underlying set of truth-values for these attributes and objects.
متن کاملResiduated Multilattices: a First Glimpse into Their Structures
We prove that when divisibility is added to a residuated multilattice, this causes the multilattice structure to collapse down to a residuated lattice. This motivates the study of semi-divisibility and regularity on residuated multilattices. The ordinal sum construction is also applied to residuated multilattices as a way to construct new examples of both residuated multilattices and consistent...
متن کاملAn algorithm for the arithmetic classification of multilattices.
A procedure for the construction and the classification of monoatomic multilattices in arbitrary dimension is developed. The algorithm allows one to determine the location of the points of all monoatomic multilattices with a given symmetry, or to determine whether two assigned multilattices are arithmetically equivalent. This approach is based on ideas from integral matrix theory, in particular...
متن کاملA note on variable threshold concept lattices: Threshold-based operators are reducible to classical concept-forming operators
The present paper deals with formal concept analysis of data with fuzzy attributes. We clarify several points of a new approach of [S.Q. Fan, W.X. Zhang, Variable threshold concept lattice, Inf. Sci., accepted for publication] which is based on using thresholds in concept-forming operators. We show that the extentand intent-forming operators from [S.Q. Fan, W.X. Zhang, Inf. Sci., accepted for p...
متن کاملUsing Linguistic Hedges in L-rough Concept Analysis
We enrich concept-forming operators in L-rough Concept Analysis with linguistic hedges which model semantics of logical connectives ‘very’ and ‘slightly’. Using hedges as parameters for the concept-forming operators we are allowed to modify our uncertainty when forming concepts. As a consequence, by selection of these hedges we can control the size of concept lattice.
متن کامل