In this paper, we study the classical Sumudu transform in fuzzy environment, referred to as the fuzzy Sumudu transform (FST). We also propose some results on the properties of the FST, such as linearity, preserving, fuzzy derivative, shifting and convolution theorem. In order to show the capability of the FST, we provide a detailed procedure to solve fuzzy differential equations (FDEs). A numer...

Graphs with labeled vertices and edges play an important role in various applications, including chemistry. A model of learning from positive and negative examples, naturally described in terms of Formal Concept Analysis (FCA), is used here to generate hypotheses about biological activity of chemical compounds. A standard FCA technique is used to reduce labeled graphs to object-attribute repres...

We present a general formula for the intent–extent mappings of a Galois lattice generated by individual descriptions which lie in any arbitrary lattice. The formulation is unique if a natural maximality condition is required. This formulation yields, as particular cases, formal concept binary Galois lattices of Wille, those de0ned by Brito or Blyth–Janowitz, as well as fuzzy or stochastic Galoi...

Article history: Received 25 June 2010 Received in revised form 6 March 2012 Accepted 24 July 2012 Available online 8 August 2012

Several papers relate different alternative approaches to classical concept lattices: such as property-oriented and object-oriented concept lattices and the dual concept lattices. Whereas the usual approach to the latter is via a negation operator, this paper presents a fuzzy generalization of the dual concept lattice, the dual multi-adjoint concept lattice, in which the philosophy of the multi...

We propose a generalization of Formal Concept Analysis (FCA) in which sets of attributes are replaced by expressions of an almost arbitrary logic. We prove that all FCA can be reconstructed on this basis. We show that from any logic that is used in place of sets of attributes can be derived a contextualized logic that takes into account the formal context and that is isomorphic to the concept l...

The development of the theory of Formal Concept Analysis has been accompanied from its beginning by applications of the theory to real-world problems. Those applications gave rise to the implementation of the software Toscana and the creation of Toscanasystems. In this paper, we provide a mathematical model for these systems. This model—called Conceptual Data System— enables us to describe Tosc...

This paper presents a theoretical framework for exploring temporal data, using Relational Concept Analysis (RCA), in order to extract frequent sequential patterns that can be interpreted by domain experts. Our proposal is to transpose sequences within relational contexts, on which RCA can be applied. To help result analysis, we build closed partially-ordered patterns (cpo-patterns), that are sy...

1. This paper summarises the issues and ideas raised by participants in our roundtables. These points do not necessarily reflect the views of the FCA, but participants in the events. They are one source of evidence that the FCA may use to inform its views. We are now considering the issues raised further with a view to identifying opportunities for increasing access to alternatives and make rec...

This paper presents an approach to Concept Analysis of structured, multivalued and incomplete data currently present in life science knowledge bases. We are concerned with tree structured objects, whose size may be variable. We focus on the composition relations between attributes in the learning process. The interest of the method is the ability to take into account both structural and value p...