Uncertain Knowledge Reasoning Based on the Fuzzy Multi-Entity Bayesian Network

With the rapid development of the semantic web and the ever-growing size of uncertain data, representing and reasoning uncertain information has become a great challenge for the semantic web application developers. In this paper, we present a novel reasoning framework based on the representation of fuzzy PR-OWL. Firstly, the paper gives an overview of the previous research work on uncertainty knowledge representation and reasoning, incorporates Ontology into the fuzzy Multi Entity Bayesian Networks theory, and introduces fuzzy PR-OWL, an Ontology language based on OWL2. Fuzzy PR-OWL describes fuzzy semantics and uncertain relations and gives grammatical definition and semantic interpretation. Secondly, the paper explains the integration of the Fuzzy Probability theory and the Belief Propagation algorithm. The influencing factors of fuzzy rules are added to the belief that is propagated between the nodes to create a reasoning framework based on fuzzy PR-OWL. After that, the reasoning process, including the SSFBN structure algorithm, data fuzzification, reasoning of fuzzy rules, and fuzzy belief propagation, is scheduled. Finally, compared with the classical algorithm from the aspect of accuracy and time complexity, our uncertain data representation and reasoning method has higher accuracy without significantly increasing time complexity, which proves the feasibility and validity of our solution to represent and reason uncertain information

Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes

Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of periodic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction. The initial formulation of these terms stems from the definition of complex fuzzy grade of membership. The problem, however, with these definitions are twofold: 1) the complex fuzzy membership is limited to polar representation with only one fuzzy component. 2) The definition is based on grade of membership and is lacking the rigor of axiomatic formulation. A new interpretation of complex fuzzy membership enables polar and Cartesian representation of the membership function where the two function components carry uncertain information. Moreover, the new interpretation is used to define complex fuzzy classes and develop an axiomatic based theory of complex propositional fuzzy logic. Additionally, the generalization of the theory to multidimensional fuzzy grades of membership has been demonstrated. In this paper we propose an axiomatic framework for first order predicate complex fuzzy logic and use this framework for axiomatic definition of complex fuzzy classes. We use these rigorous definitions to exemplify inference in complex economic systems. The new framework overcomes the main limitations of current theory and provides several advantages. First, the derivation of the new theory is based on axiomatic approach and does not assume the existence of complex fuzzy sets or complex fuzzy classes. Second, the new form significantly improves the expressive power and inference capability of complex fuzzy logic and class theory. The paper surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides an axiomatic basis for first order predicate complex fuzzy logic and complex class theory

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

Embedded fuzzontological model for document interpretation in attribute-value-pair annotation in economic intelligent systems

Two popular views about the concept of information are the "information as a process" and "information as a product". While there has been much research about the two paradigms, one recurrent question has been where is the place of interpretation in information utilization? A growing trend is the concept of annotation which encourages individual interpretation on a subject of interest and keeps such information for future use. The problem of interpretation is not new, as it was clearly pointed out in the infological equation. With several attempt at resolving this imbroglio in place, we are of the opinion that misinterpretation results from differences in individual knowledge and cognitive ability amongst other factors. Consequently, we developed an attribute-value-pair (AVP) document representation metadata to interface directly with the ontology domain, and extend interpretation via fuzzy inference system

On the similarity relation within fuzzy ontology components

Ontology reuse is an important research issue. Ontology merging, integration, mapping, alignment and versioning are some of its subprocesses. A considerable research work has been conducted on them. One common issue to these subprocesses is the problem of defining similarity relations among ontologies components. Crisp ontologies become less suitable in all domains in which the concepts to be represented have vague, uncertain and imprecise definitions. Fuzzy ontologies are developed to cope with these aspects. They are equally concerned with the problem of ontology reuse. Defining similarity relations within fuzzy context may be realized basing on the linguistic similarity among ontologies components or may be deduced from their intentional definitions. The latter approach needs to be dealt with differently in crisp and fuzzy ontologies. This is the scope of this paper.ou