An entropy construction inspired by fuzzy sets

 Fuzzy dynamics is considered as a model of a general algebraic scheme based on two binary operations fulfilling a very weak distributive law. The main result is the existence of the limit defining the entropy of the general dynamical system. Present address: Katedra matematiky Fakulty prírodnych vied UMB, Tajovského 40, SK-97 401 Banská Bystrica, Slovakia E-mail: riecan@fpv.umb.sk Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday Supported by grant VEGA 1/9056/02.     

An agent system for managing uncertainty in the integration of spatio-environmental data

 Recent applications in environmental systems have necessitated the integration of data from multiple, heterogeneous sources. The integration process involves challenges related to issues of uncertainty and imprecision associated with both the data and the process itself. While the handling of uncertainty in geographical information systems (GIS) has been a focal point of research in recent years, the additional challenges of dealing with multiple data sources and types, as well as specific fields of analysis, lead to much more complex situations. In this paper, we present a framework for the use of fuzzy mobile agents to address these additional challenges from the standpoint of large-scale environmental systems. We would like to thank the National Imagery and Mapping Agency, the Marine Corps Warfighting Lab, PE 0603640M, and the Office of Naval Research, PE 0603238N, for sponsoring this research.     

Interpolation and extrapolation of fuzzy quantities – the multiple-dimensional case

 This paper deals with the problem of rule interpolation and rule extrapolation for fuzzy and possibilistic systems. Such systems are used for representing and processing vague linguistic If-Then-rules, and they have been increasingly applied in the field of control engineering, pattern recognition and expert systems. The methodology of rule interpolation is required for deducing plausible conclusions from sparse (incomplete) rule bases. The interpolation/extrapolation method which was proposed for one-dimensional input space in [4] is extended in this paper to the general n-dimensional case by using the concept of aggregation operators. A characterization of the class of aggregation operators with which the extended method preserves all the nice features of the one- dimensional method is given.     

Rainfall prediction model using soft computing technique

 Rainfall prediction in this paper is a spatial interpolation problem that makes use of the daily rainfall information to predict volume of rainfall at unknown locations within area covered by existing observations. This paper proposed the use of self-organising map (SOM), backpropagation neural networks (BPNN) and fuzzy rule systems to perform rainfall spatial interpolation based on local method. The SOM is first used to separate the whole data space into some local surface automatically without any knowledge from the analyst. In each sub-surface, the complexity of the whole data space is reduced to something more homogeneous. After classification, BPNNs are then use to learn the generalization characteristics from the data within each cluster. Fuzzy rules for each cluster are then extracted. The fuzzy rule base is then used for rainfall prediction. This method is used to compare with an established method, which uses radial basis function networks and orographic effect. Results show that this method could provide similar results from the established method. However, this method has the advantage of allowing analyst to understand and interact with the model using fuzzy rules.     

An fMUX architecture: data modularization and mixed-mode system modeling

 In this study, we introduce a concept of a fuzzy multiplexer (fMUX) generalizing a well-known idea of multiplexers existing in two-valued logic and digital systems. A generic topology of the fMUX is presented and its functional behavior studied. We show that a design process with fMUXs is concerned with their supervised learning. A detailed learning scheme is discussed. Numerical illustration is included. It is shown that fMUX support an idea of mixed-mode modeling in which we encounter data-information granules quite often exhibiting variable granularity and this diversity lends itself to a modular way of model development.     

Automatic fuzzy-rule assessment and its application to the modelling of nitrogen leaching for large regions

 Diffuse nutrient emissions from agricultural land is one of the major sources of pollution for ground water, rivers and coastal waters. The quantification of pollutant loads requires mathematical modelling of water and nutrient cycles. The deterministic simulation of nitrogen dynamics, represented by complicated highly non-linear processes, requires the application of detailed models with many parameters and large associated data bases. The operation of those models within integrated assessment tools or decision support systems for large regions is often not feasible. Fuzzy rule based modelling provides a fast, transparent and parameter parsimonious alternative. Besides, it allows regionalisation and integration of results from different models and measurements at a higher generalised level and enables explicit consideration of expert knowledge. In this paper an algorithm for the assessment of fuzzy rules for fuzzy modelling using simulated annealing is presented. The fuzzy rule system is applied to simulate nitrogen leaching for selected agricultural soils within the 23687 km² Saale River Basin. The fuzzy rules are defined and calibrated using results from simulation experiments carried out with the deterministic modelling system SWIM. Monthly aggregated time series of simulated water balance components (e.g. percolation and evapotranspiration), fertilization amounts, resulting nitrogen leaching and crop parameters are used for the derivation of the fuzzy rules. The 30-year simulation period was divided into 20 years for training and 10 years for validation, with the latter taken from the middle part of the period. Three specific fuzzy rule systems were created from the simulation experiments, one for each selected soil profile. Each rule system includes 15 rules as well as one prescribed rules from expert knowledge and 7 input variables. The performance of the fuzzy rule system is satisfactory for the assessment of nitrate leaching on annual to long term time steps. The approach allows rapid scenario analysis for large regions and has the potential to become part of decision support systems for generalised integrated assessment of water and nutrients in macroscale regions.     

Multilevel fuzzy relational systems: structure and identification

 Existing fuzzy relational equations (FRE) typically possess an evident single-level structure, where no consequence part of the rule being modeled, is used as a fact to another rule. Corresponding to multistage fuzzy reasoning, a natural extension of traditional fuzzy relational systems (FRS) is to introduce some intermediate levels of processing governed by enhanced FRE's so that the structure resulted becomes multilevel or multistage. Three basic multilevel FRS structures, namely, incremental, aggregated, and cascaded, are considered in this paper and they correspond to different reasoning mechanisms being frequently used by human beings in daily life. While the research works on multilevel FRS are sparse and our ability to solve a system of multilevel FRE's in a purely analytical manner is very limited, we address the identification problem from an optimization approach and introduce three fuzzy neural models. The proposed models consist of single-level FRS modules that are arranged in different hierarchical manners. Each module can be realized by Lin and Lee's fuzzy neural model for implementing the Mamdani fuzzy inference. We have particularly addressed the problem of how to distribute the input variables to different (levels of) relational modules for the incremental and aggregated models. In addition, the new models can learn a complete multistage fuzzy rule set from stipulated data pairs using structural and parameter learning. The effectiveness of the multilevel models has been demonstrated through various benchmarking problems. It can be generally concluded that the new models are distinctive in learning, generalization, and robustness.     

An intelligent information sharing strategy within a swarm for unconstrained and constrained optimization problems

 In this paper we present a new multilevel information sharing strategy within a swarm to handle single objective, constrained and unconstrained optimization problems. A swarm is a collection of individuals having a common goal to reach the best value (minimum or maximum) of a function. Among the individuals in a swarm, there are some better performers (leaders) those that set the direction of search for the rest of the individuals. An individual that is not in the better performer list (BPL) improves its performance by deriving information from its closest neighbor in BPL. In an unconstrained problem, the objective values are the performance measures used to generate the BPL while a multilevel Pareto ranking scheme is implemented to generate the BPL for constrained problems. The information sharing strategy also ensures that all the individuals in the swarm are unique as in a real swarm, where at a given time instant two individuals cannot share the same location. The uniqueness among the individuals result in a set of near optimal individuals at the final stage that is useful for sensitivity analysis. The benefits of the information sharing strategy within a swarm are illustrated by solving two unconstrained problems with multiple equal and unequal optimum, a constrained optimization problem dealing with a test function and a well studied welded beam design problem.     

Perception-based hidden Markov models: a theoretical framework for data mining and knowledge discovery

 The combination of objective measurements and human perceptions using hidden Markov models with particular reference to sequential data mining and knowledge discovery is presented in this paper. Both human preferences and statistical analysis are utilized for verification and identification of hypotheses as well as detection of hidden patterns. As another theoretical view, this work attempts to formalize the complementarity of the computational theories of hidden Markov models and perceptions for providing solutions associated with the manipulation of the internet.     

A new evolutionary algorithm combining simulated annealing and genetic programming for relevance feedback in fuzzy information retrieval systems

 Relevance feedback techniques have demonstrated to be a powerful means to improve the results obtained when a user submits a query to an information retrieval system as the world wide web search engines. These kinds of techniques modify the user original query taking into account the relevance judgements provided by him on the retrieved documents, making it more similar to those he judged as relevant. This way, the new generated query permits to get new relevant documents thus improving the retrieval process by increasing recall. However, although powerful relevance feedback techniques have been developed for the vector space information retrieval model and some of them have been translated to the classical Boolean model, there is a lack of these tools in more advanced and powerful information retrieval models such as the fuzzy one. In this contribution we introduce a relevance feedback process for extended Boolean (fuzzy) information retrieval systems based on a hybrid evolutionary algorithm combining simulated annealing and genetic programming components. The performance of the proposed technique will be compared with the only previous existing approach to perform this task, Kraft et al.'s method, showing how our proposal outperforms the latter in terms of accuracy and sometimes also in time consumption. Moreover, it will be showed how the adaptation of the retrieval threshold by the relevance feedback mechanism allows the system effectiveness to be increased.