This paper proposes the FOGA (Fuzzy Ontology Generation frAmework) for automatic generation of fuzzy ontology on uncertainty information. The FOGA framework comprises the following components: Fuzzy Formal Concept Analysis, Fuzzy Conceptual Clustering and Fuzzy Ontology Generation. First, Fuzzy Formal Concept Analysis incorporates fuzzy logic into Formal Concept Analysis (FCA) to form a fuzzy c...

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI...

Fuzzy description logics can be used to model vague knowledge in application domains. This paper analyses the consistency and satisfiability problems in the description logic SHI with semantics based on a complete residuated De Morgan lattice. The problems are undecidable in the general case, but can be decided by a tableau algorithm when restricted to finite lattices. For some sublogics of SHI...

Computational Intelligence (CI) consists of an evolving collection of methodologies often inspired from nature (Bonissone, Chen, Goebel & Khedkar, 1999, Fogel, 1999, Pedrycz, 1998). Two popular methodologies of CI include neural networks and fuzzy systems. Lately, a unification was proposed in CI, at a “data level”, based on lattice theory (Kaburlasos, 2006). More specifically, it was shown tha...

We present a logic, called fuzzy attribute logic, for reasoning about formulas describing particular attribute dependencies. The formulas are of a form A ⇒ B where A and B are collections of attributes. Our formulas can be interpreted in two ways. First, in data tables with entries containing degrees to which objects (table rows) have attributes (table columns). Second, in database tables where...

In this paper, the notions of fuzzy soft subalgebra and fuzzy soft convex subalgebra of a residuated lattice are introduced and some related properties are investigated. Then, we define fuzzy soft congruence on a residuated lattice and obtain the relation between fuzzy soft convex subalgebras and fuzzy soft congruence relations on residuated lattices. The concept of soft homomorphism is defined...

In this paper we study a representation of a fuzzy subgroup $mu$ of a group $G$, as a product of indecomposable fuzzy subgroups called the components of $mu$.  This representation is unique up to the number of components and their isomorphic copies. In the crisp group theory, this is a well-known Theorem attributed to Remak, Krull, and Schmidt. We consider the lattice of fuzzy subgroups and som...

In this paper, we study some properties of the near SR-compactnessin L-topological spaces, where L is a fuzzy lattice. The near SR-compactness isa kind of compactness between Lowen’s fuzzy compactness and SR-compactness,and it preserves desirable properties of compactness in general topologicalspaces.

This paper proposes a new fuzzy FCA-based approach to conceptual clustering for automatic generation of concept hierarchy on uncertainty data. The proposed approach first incorporates fuzzy logic into Formal Concept Analysis (FCA) to form a fuzzy concept lattice. Next, a fuzzy conceptual clustering technique is proposed to cluster the fuzzy concept lattice into conceptual clusters. Then, hierar...

This chapter introduces a rule-based perspective on the framework of fuzzy lattices, and the Fuzzy Lattice Reasoning (FLR) classifier. The notion of fuzzy lattice rules is introduced, and a training algorithm for inducing a fuzzy lattice rule engine from data is specified. The role of positive valuation functions for specifying fuzzy lattices is underlined and non-linear (sigmoid) positive valu...