Boriana Vatchova

Advanced modelling of complex processes by rule based networks

This work presents an application of the novel theory of rule based networks for building models of processes characterised by uncertainty, non-linearity, modular structure and internal interactions. The application of the theory is demonstrated for a flotation process in the context of converting a multiple rule based system into an equivalent single rule based system by linguistic composition of the individual rule bases. During the conversion process, the transparency of the multiple rule based system is fully preserved while its accuracy is improved to a level comparable with the accuracy of the single rule based system.

Complexity management methodology for fuzzy systems with feedback rule bases

This paper proposes a complexity management methodology for fuzzy systems with feedback rule bases. The methodology is based on formal methods for presentation, manipulation and transformation of fuzzy rule bases. First, Boolean matrices are used for formal presentation of rule bases. Then, binary merging operations are used for formal manipulation of rule bases. Finally, repetitive merging operations are used for formal transformation of rule bases. The formal methods facilitate the understanding and modelling of fuzzy systems in terms of interacting subsystems. In particular, the methods reduce the qualitative complexity in fuzzy systems by improving the transparency of the rule bases.

Fuzzy networks with feedback rule bases for complex systems modelling

This paper proposes a novel approach for modelling complex interconnected systems by means of fuzzy networks with feedback rule bases. The nodes in these networks are rule bases connected in a feedback manner whereby outputs from some rule bases are fed as inputs to the same or preceding rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks, basic operations in such networks, their properties and advanced operations. These models, operations and properties are used for defining several types of networks with single or multiple local and global feedback. The proposed approach facilitates the understanding of complex interconnected systems by improving the transparency of their models.

Multi-valued logical method for knowledge extraction and updating in real time

Familiar methods for knowledge derivation are based on statistical procedures, which are not accompanied by algorithms for updating of knowledge in real time. In this work, the algorithms are implemented successfully using both logical and statistical procedures whereby flexible arrays of experimental data is entered such that older data is removed and newer data is added. These data are packed together in groups and transformed into logical values of functions of multi-valued logic. The functions are accompanied by probability of occurrence of its values, which is evaluated in real time. In this way, a new construction is formed called multi-valued logical probability function (MLPF), which expresses simultaneously two mutually related correspondences-logical and probabilistic. The correspondences are updated in real time. MLPF is a system of production rules, which are updated in real time.

Modular rule base fuzzy networks for linguistic composition based modelling

This paper proposes a linguistic composition based modelling approach by networked fuzzy systems that are known as fuzzy networks. The nodes in these networks are modules of fuzzy rule bases and the connections between these modules are the outputs from some rule bases that are fed as inputs to other rule bases. The proposed approach represents a fuzzy network as an equivalent fuzzy system by linguistic composition of the network nodes. In comparison to the known multiple rule base approaches, this networked rule base approach reflects adequately the structure of the modelled process in terms of interacting sub-processes and leads to more accurate solutions. The approach improves significantly the transparency of the associated model while ensuring a high level of accuracy. Another advantage of this fuzzy network approach is that it fits well within the existing approaches with single rule base and multiple rule bases.

Mamdani fuzzy networks with feedforward rule bases for complex systems modelling

This paper proposes a novel approach for modelling complex interconnected systems by means of Mamdani fuzzy networks with feedforward rule bases. The nodes in these networks are rule bases connected in a feedforward manner whereby outputs from some rule bases are fed as inputs to subsequent rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent Mamdani fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks, basic operations in such networks, their properties and advanced operations. These models, operations and properties are used for defining several types of networks with single or multiple horizontal levels and vertical layers. The proposed approach facilitates the understanding of complex interconnected systems by improving the transparency of their models.

Knowledge extraction methods for complex processes operating under uncertainty

This paper considers processes with many inputs and outputs from different application areas. Some parts of the inputs are measurable and others are not because of the presence of stochastic environmental factors. This is the reason why processes of this kind operate under uncertainty. As some factors cannot be measured and reflected into the process model, data mining methods cannot be applied. The proposed approach which can be applied in this case is based on artificial intelligence methods.

Production Rule and Network Structure Models for Knowledge Extraction from Complex Processes Under Uncertainty

This paper considers processes with many inputs and outputs from different application areas. Some parts of the inputs are measurable and others are not because of the presence of stochastic environmental factors. This is the reason why processes of this kind operate under uncertainty. As some factors cannot be measured and reflected into the process model, data mining methods cannot be applied. The proposed approach which can be applied in this case is based on artificial intelligence methods[1].

Boolean matrix equations for node identification in fuzzy rule based networks

This paper proposes a novel approach for modelling complex interconnected systems by means of fuzzy networks. The nodes in these networks are interconnected rule bases whereby outputs from some rule bases are fed as inputs to other rule bases. The approach allows any fuzzy network of this type to be presented as an equivalent fuzzy system by linguistic composition of its nodes. The composition process makes use of formal models for fuzzy networks and basic operations in such networks. These models and operations are used for defining several node identification cases in fuzzy networks. In this case, the unknown nodes are derived by solving Boolean matrix equations in a way that guarantees a pre-specified overall performance of the network. The main advantage of the proposed approach over other approaches is that it has better transparency and facilitates not only the analysis but also the design of complex interconnected systems.

Space-Independent Community Detection in Airport Networks

This research explores the topology and passenger flows of the United States Airport Network (USAN) over two decades. The network model consists of a time-series of six network snapshots for the years 1990, 2000 and 2010, which capture bi-monthly passenger flows among US airports. Since the network is embedded in space, the volume of these flows is naturally affected by spatial proximity, and therefore, a model (recently proposed in the literature) accounting for this phenomenon is used to identify the communities of airports that have particularly high flows among them, given their spatial separation. This research results highlight the fact that some general techniques from network theory, such as network modelling and analysis, can be successfully applied for the study of a wide range of complex systems, while others, such as community detection, need to be tailored for a specific system.