Blended intelligence of FCA with FLC for knowledge representation from clustered data in medical analysis

Formal concept analysis is the process of data analysis mechanism with emergent attractiveness across various fields such as data mining, robotics, medical, big data and so on. FCA is helpful to generate the new learning ontology based techniques. In medical field, some growing kids are facing the problem of representing their knowledge from their gathered prior data which is in the form of unordered and insufficient clustered data which is not supporting them to take the right decision on right time for solving the uncertainty based questionnaires. In the approach of decision theory, many mathematical replicas such as probability-allocation, crisp set, and fuzzy based set theory were designed to deals with knowledge representation based difficulties along with their characteristic. This paper is proposing new ideological blended approach of FCA with FLC and described with major objectives: primarily the FCA analyzes the data based on relationships between the set of objects of prior-attributes and the set of attributes based prior-data, which the data is framed with data-units implicated composition which are formal statements of idea of human thinking with conversion of significant intelligible explanation. Suitable rules are generated to explore the relationship among the attributes and used the formal concept analysis from these suitable rules to explore better knowledge and most important factors affecting the decision making. Secondly how the FLC derive the fuzzification, rule-construction and defuzzification methods implicated for representing the accurate knowledge for uncertainty based questionnaires. Here the FCA is projected to expand the FCA based conception with help of the objective based item set notions considered as the target which is implicated with the expanded cardinalities along with its weights which is associated through the fuzzy based inference decision rules. This approach is more helpful for medical experts for knowing the range of patient’s memory deficiency also for people whose are facing knowledge explorer deficiency

Gödel Description Logics

In the last few years there has been a large effort for analysing the computational properties of reasoning in fuzzy Description Logics. This has led to a number of papers studying the complexity of these logics, depending on their chosen semantics. Surprisingly, despite being arguably the simplest form of fuzzy semantics, not much is known about the complexity of reasoning in fuzzy DLs w.r.t. witnessed models over the Gödel t-norm. We show that in the logic G-IALC, reasoning cannot be restricted to finitely valued models in general. Despite this negative result, we also show that all the standard reasoning problems can be solved in this logic in exponential time, matching the complexity of reasoning in classical ALC

Fuzzy ontology representation using OWL 2

AbstractThe need to deal with vague information in Semantic Web languages is rising in importance and, thus, calls for a standard way to represent such information. We may address this issue by either extending current Semantic Web languages to cope with vagueness, or by providing a procedure to represent such information within current standard languages and tools. In this work, we follow the latter approach, by identifying the syntactic differences that a fuzzy ontology language has to cope with, and by proposing a concrete methodology to represent fuzzy ontologies using OWL 2 annotation properties. We also report on some prototypical implementations: a plug-in to edit fuzzy ontologies using OWL 2 annotations and some parsers that translate fuzzy ontologies represented using our methodology into the languages supported by some reasoners

One-variable fragments of intermediate logics over linear frames

A correspondence is established between one-variable fragments of (first-order) intermediate logics defined over a fixed countable linear frame and Gödel modal logics defined over many-valued equivalence relations with values in a closed subset of the real unit interval. It is also shown that each of these logics can be interpreted in the one-variable fragment of the corresponding constant domain intermediate logic, which is equivalent to a Gödel modal logic defined over (crisp) equivalence relations. Although the latter modal logics in general lack the finite model property with respect to their frame semantics, an alternative semantics is defined that has this property and used to establish co-NP-completeness results for the one-variable fragments of the corresponding intermediate logics both with and without constant domains

Semantic operations of multiple soft sets under conflict

AbstractMolodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. Description Logics (DLs) are a family of knowledge representation languages which can be used to represent the terminological knowledge of an application domain in a structured and formally well-understood way. Nowadays, properties and semantics of ontology constructs mainly are determined by DLs. In this paper we investigate semantic operations of multiple standard soft sets by using domain ontologies (i.e., DL intensional knowledge bases). Concretely, we give some semantic operations such as complement, restricted difference, extended union, restricted intersection, restricted union, extended intersection, AND, and OR for (multiple) standard soft sets from a semantic point of view. Especially, we also present an approach to deal with conflict from a semantic point of view when we define these semantic operations. Moreover, the basic properties and implementation methods of these semantic operations under conflict are also presented and discussed

Fuzzy Description Logics with General Concept Inclusions

Description logics (DLs) are used to represent knowledge of an application domain and provide standard reasoning services to infer consequences of this knowledge. However, classical DLs are not suited to represent vagueness in the description of the knowledge. We consider a combination of DLs and Fuzzy Logics to address this task. In particular, we consider the t-norm-based semantics for fuzzy DLs introduced by Hájek in 2005. Since then, many tableau algorithms have been developed for reasoning in fuzzy DLs. Another popular approach is to reduce fuzzy ontologies to classical ones and use existing highly optimized classical reasoners to deal with them. However, a systematic study of the computational complexity of the different reasoning problems is so far missing from the literature on fuzzy DLs. Recently, some of the developed tableau algorithms have been shown to be incorrect in the presence of general concept inclusion axioms (GCIs). In some fuzzy DLs, reasoning with GCIs has even turned out to be undecidable. This work provides a rigorous analysis of the boundary between decidable and undecidable reasoning problems in t-norm-based fuzzy DLs, in particular for GCIs. Existing undecidability proofs are extended to cover large classes of fuzzy DLs, and decidability is shown for most of the remaining logics considered here. Additionally, the computational complexity of reasoning in fuzzy DLs with semantics based on finite lattices is analyzed. For most decidability results, tight complexity bounds can be derived