Fuzzy Logics have been applied successfully within both Formal Concept Analysis and Description Logics. Especially in the latter field, Fuzzy Logics have been gaining significant momentum during the last two years. Unfortunately, the research on fuzzy logics within the two communities has been conducted independently from each other, leading to different approaches being pursued. We show that i...

Sometimes we have to work with  $L$-fuzzy context sequences where one or more values are missing. These sequences can represent, among other things, the evolution in time of an $L$-fuzzy context. The studies of tendencies that we have done so far used tools that are not valid when the $L$-fuzzy context has unknown values. In this work we address such situations and we propose new methods to tac...

Using a gradation of openness in a (Chang fuzzy) I-topological space, we introduce degrees of compactness that we call α-fuzzy compactness (where α belongs to the unit interval), so extending the concept of compactness due to C. L. Chang. We obtain a Baire category theorem for α-locally compact spaces and construct a one-point α-fuzzy compactification of an I-topological space. 1. Introduction....

We present a new approach for handling fuzzy triadic data in the setting of Formal Concept Analysis. The starting point is a fuzzyvalued triadic context (K1,K2,K3, Y ), where K1,K2 and K3 are sets and Y is a ternary fuzzy relation between these sets. First, we generalise the methods of Triadic Concept Analysis to our setting and show how they fit other approaches to Fuzzy Triadic Concept Analys...

Presented is a reduction of fuzzy Galois connections and fuzzy concept lattices to (crisp) Galois connections and concept lattices: each fuzzy concept lattice can be viewed as a concept lattice (in a natural way). As a result, a simple proof of the characterization theorem for fuzzy concept lattices is obtained. The reduction enables us to apply the results worked out for concept lattices to fu...

We focus on two approaches to formal concept analysis (FCA) of data with fuzzy attributes recently proposed in the literature, namely, on the approach via hedges and the approach via thresholds. Both of the approaches present parameterized ways to FCA of data with fuzzy attributes. Our paper shows basic relationships between the two of the approaches. Furthermore, we show that the approaches ca...

In this paper, we discussed about the intuitionistic fuzzy linear transformations (IFLT) and shown that the set of all linear transformations ) (V L defined over an intuitionistic fuzzy vector space V does not form an vector space. Here we determine the unique intuitionistic fuzzy matrix associated with an intuitionistic fuzzy linear transformation with respect to an ordered standard basis for ...

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In previous work (Nescolarde-Selva and Usó-Doménech, 2014a,b) discussed the theory that complex belief systems have a topological structure. In this paper it is suggested that this structure is also fuzzy. They introduce the concepts of fuzzy sets in the context of beliefs (substantive and derived) , and between derived beliefs themselves. Also introduced are the concepts of fuzzy covering, fuz...

In this paper we propose the extension of some aggregation or arithmetic operations between discrete fuzzy numbers to discrete fuzzy number-valued multisets such as the addition, the union and the intersection and, even, the order. For this reason, we prove or recall some properties of discrete fuzzy numbers and we undertake their study on multisets.