On the incorporation of interval-valued fuzzy sets into the Bousi-Prolog system: declarative semantics, implementation and applications

In this paper we analyse the benefits of incorporating interval-valued fuzzy sets into the Bousi-Prolog system. A syntax, declarative semantics and im- plementation for this extension is presented and formalised. We show, by using potential applications, that fuzzy logic programming frameworks enhanced with them can correctly work together with lexical resources and ontologies in order to improve their capabilities for knowledge representation and reasoning

From fuzzy to annotated semantic web languages

The aim of this chapter is to present a detailed, selfcontained and comprehensive account of the state of the art in representing and reasoning with fuzzy knowledge in Semantic Web Languages such as triple languages RDF/RDFS, conceptual languages of the OWL 2 family and rule languages. We further show how one may generalise them to so-called annotation domains, that cover also e.g. temporal and provenance extensions

Parameterizing the semantics of fuzzy attribute implications by systems of isotone Galois connections

We study the semantics of fuzzy if-then rules called fuzzy attribute implications parameterized by systems of isotone Galois connections. The rules express dependencies between fuzzy attributes in object-attribute incidence data. The proposed parameterizations are general and include as special cases the parameterizations by linguistic hedges used in earlier approaches. We formalize the general parameterizations, propose bivalent and graded notions of semantic entailment of fuzzy attribute implications, show their characterization in terms of least models and complete axiomatization, and provide characterization of bases of fuzzy attribute implications derived from data

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Modelling causal reasoning

PhDAlthough human causal reasoning is widely acknowledged as an object of scientific enquiry, there is little consensus on an appropriate measure of progress. Up-to-date evidence of the standard method of research in the field shows that this method has been rejected at the birth of modern science. We describe an instance of the standard scientific method for modelling causal reasoning (causal calculators). The method allows for uniform proofs of three relevant computational properties: correctness of the model with respect to the intended model, full abstraction of the model (function) with respect to the equivalence of reasoning scenarios (input), and formal relations of equivalence and subsumption between models. The method extends and exploits the systematic paradigm [Handbook of Logic in Artificial Intelligence and Logic Programming, volume IV, p. 439-498, Oxford 1995] to fit with our interpretation of it. Using the described method, we present results for some major models, with an updated summary spanning seventy-two years of research in the field

Foundations of Fuzzy Logic and Semantic Web Languages

This book is the first to combine coverage of fuzzy logic and Semantic Web languages. It provides in-depth insight into fuzzy Semantic Web languages for non-fuzzy set theory and fuzzy logic experts. It also helps researchers of non-Semantic Web languages get a better understanding of the theoretical fundamentals of Semantic Web languages. The first part of the book covers all the theoretical and logical aspects of classical (two-valued) Semantic Web languages. The second part explains how to generalize these languages to cope with fuzzy set theory and fuzzy logic

Multiobjective programming for type-2 hierarchical fuzzy inference trees

This paper proposes a design of hierarchical fuzzy inference tree (HFIT). An HFIT produces an optimum tree-like structure. Specifically, a natural hierarchical structure that accommodates simplicity by combining several low-dimensional fuzzy inference systems (FISs). Such a natural hierarchical structure provides a high degree of approximation accuracy. The construction of HFIT takes place in two phases. Firstly, a nondominated sorting based multiobjective genetic programming (MOGP) is applied to obtain a simple tree structure (low model’s complexity) with a high accuracy. Secondly, the differential evolution algorithm is applied to optimize the obtained tree’s parameters. In the obtained tree, each node has a different input’s combination, where the evolutionary process governs the input’s combination. Hence, HFIT nodes are heterogeneous in nature, which leads to a high diversity among the rules generated by the HFIT. Additionally, the HFIT provides an automatic feature selection because it uses MOGP for the tree’s structural optimization that accept inputs only relevant to the knowledge contained in data. The HFIT was studied in the context of both type-1 and type-2 FISs, and its performance was evaluated through six application problems. Moreover, the proposed multiobjective HFIT was compared both theoretically and empirically with recently proposed FISs methods from the literature, such as McIT2FIS, TSCIT2FNN, SIT2FNN, RIT2FNS-WB, eT2FIS, MRIT2NFS, IT2FNN-SVR, etc. From the obtained results, it was found that the HFIT provided less complex and highly accurate models compared to the models produced by most of the other methods. Hence, the proposed HFIT is an efficient and competitive alternative to the other FISs for function approximation and feature selectio