This paper mainly studies attribute reduction which keeps the lattice structure in formal contexts based on the property pictorial diagram. Firstly, the property pictorial diagram of a formal context is defined. Based on such diagram, an attribute reduction approach of concept lattice is achieved. Then, through the relation between an original formal context and its complementary context, an at...

In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...

Property-oriented concept lattices are systems of conceptual clusters called property-oriented concepts, which are partially ordered by the subconcept/superconcept relationships. Property-oriented concept lattices are basic structures used in formal concept analysis. In general, a property-oriented concept lattice may contain overlapping clusters and is not to be a tree construction. Additional...

In this paper the Archimedean property of t-norms on the lattice L is investigated, where L is the underlying lattice of interval-valued fuzzy set theory (Sambuc, 1975) and intuitionistic fuzzy set theory (Atanassov, 1983). We discuss also two additional variations on this property: the weak and strong Archimedean property.

structure of alpha lattice designs makes removing the effects of incomplete blocks from residual effect of plots, and maximizes precision of comparison between genotypes at the same incomplete block. this investigation was conducted to study the international chickpea germplasm, for finding desirable lines regarding seed yield and other traits. two trials including cien-la-2010 and cien-s-2010 ...