This paper presents a comparative study of concept lattices of fuzzy contexts based on formal concept analysis and rough set theory. It is known that every complete fuzzy lattice can be represented as the concept lattice of a fuzzy context based on formal concept analysis [R. Bělohlávek, Concept lattices and order in fuzzy logic, Ann. Pure Appl. Logic 128 (2004) 277–298]. This paper shows that ...

Rough relation algebras were introduced by S. Comer as a generalisation of algebras of Pawlak's rough sets and Tarski's relation algebras. In this paper, some algebraic and arithmetical properties of rough relation algebras are studied and the representable rough relation algebras are characterised. 1. Definitions and preliminary results We assume that the reader is familiar with the basic fact...

Since the appearance of the first paper on fuzzy sets proposed by Zadeh in 1965, the relationship between probability and fuzziness in the representation of uncertainty has been discussed among many people. The question is whether probability theory itself is sufficient to deal with uncertainty. In this paper the relationship between probability and fuzziness is analyzed by the process of perce...

In this paper, we first review existing fuzzy extensions of the dominance-based rough set approach (DRSA), and advance theory considering additional properties. Moreover, examine application Ordered Weighted Average (OWA) operators to DRSA. OWA have shown a lot potential in handling outliers noisy data decision tables, when they are combined with indiscernibility-based (IRSA). We theoretical pr...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

We extend the standard rough set-based approach to be able to deal with huge amounts of numeric attributes versus small amount of available objects. We transform the training data using a novel way of non-parametric discretization, called roughfication (in contrast to fuzzification known from fuzzy logic). Given roughfied data, we apply standard rough set attribute reduction and then classify t...

This paper introduces a novel clustering scheme employing a combination of Rough set theory and Fuzzy set theory to generate meaningful abstractions from web access logs. Our experimental results show that the proposed scheme is capable of capturing the semantics involved in web access logs at an acceptable computational expense.

This paper is devoted to the discussion of the relationship between fuzzy rough set models and fuzzy topologies on a finite universe. The (TC) axiom for fuzzy topology is proposed. It is proved that the set of all lower approximation sets based on a reflexive and transitive fuzzy relation consists of a fuzzy topology which satisfies (TC) axiom; and conversely, a fuzzy topology which obey (TC) a...

This article introduces interior and closure operators with inclusion degree considered within a crisp or fuzzy topological framework. First, inclusion degree is introduced in an extension of the interior and closure operators in crisp topology. This idea is then introduced in fuzzy topology by incorporating a relaxed version of fuzzy subsethood. The introduction of inclusion degree leads to a ...