H.R. van Nauta Lemke's research while affiliated with Delft University of Technology and other places

This paper reports the results of a general study conducted in cooperation with the Dutch ING Group to identify various fields of interaction between a financial institution and a technical university. A number of projects have been examined in terms of, amongst others, the length of the project and the possibility and term of measuring first results, in order to define the project(s) most suitable for an initial cooperation. It is found that in banking and insurance many possible fields of interaction with technology are available. Projects in these fields have a lot of potential for success, though not always fit for cooperation with technical universities, due to prioritization of issues or to a lack of of readiness for researching the possibilities of new techniques. This paper can give financial institutions as well as technical research institutes an insight into some of the possibilities of collective research

FAIR (fuzzy arithmetic-based interpolative reasoning)—a fuzzy reasoning scheme based on fuzzy arithmetic, is presented here. Linguistic rules of the Mamdani type, with fuzzy numbers as consequents, are used in an inference mechanism similar to that of a Takagi–Sugeno model. The inference result is a weighted sum of fuzzy numbers, calculated by means of the extension principle. Both fuzzy and crisp inputs and outputs can be used, and the chaining of rule bases is supported without increasing the spread of the output fuzzy sets in each step. This provides a setting for modeling dynamic fuzzy systems using fuzzy recursion. The matching in the rule antecedents is done by means of a compatibility measure that can be selected to suit the application at hand. Different compatibility measures can be used for different antecedent variables, and reasoning with sparse rule bases is supported. The application of FAIR to the modeling of a nonlinear dynamic system based on a combination of knowledge-driven and data-driven approaches is presented as an example.

In fuzzy multicriteria decision making, the evaluations for criteria are aggregated using a suitable decision function. Many of the aggregation operators from fuzzy set theory that can be used as decision functions assume that the criteria have equal importance. This paper considers the extension of these functions when the criteria are not equally weighted. The criteria weights are interpreted as factors influencing the sensitivity of the decision function to the corresponding criteria. A set of conditions is specified which a weighted decision function should satisfy. This leads to a systematic way of introducing the weight factors into the decision functions. The proposed analysis is applied to a class of operators in which the parameter may be interpreted as the decision maker's characteristic optimism index. In this context, it is shown that the well-known method of multiplication of weight factors with membership values is suitable for optimistic decision makers, while Yager's power raising method is suitable for pessimistic decision makers only. A geometric interpretation of the decision making process is also given.

Weighted aggregation of information in fuzzy set theory is considered The weighted aggregation plays an important role, especially in fuzzy decision making, where the decision criteria can have different degrees of importance. The weight factors, however, can not be used with most aggregation operators such as t-norms and t-conorms that are used in fuzzy set theory. The paper introduces a general framework based on sensitivity analysis for extending fuzzy set aggregation operators to their weighted counterparts. As an example, the framework is applied to the extension of t-norms to their weighted counterparts. It is shown that some of the methods that have been suggested in literature for weighted aggregation with t-norms apply only in particular situations. Conditions are given under which the previously proposed methods are valid

Discusses some essential requirements for the introduction of computational intelligence techniques in the field of financial services, and reports on an investigation carried out concerning the possibilities and expected success of using fuzzy systems in some business chapters of the Dutch ING group. Based on this investigation, the subject of direct marketing is chosen for a pilot study of the application of data-driven modeling techniques using fuzzy clustering and iterative gain-charts refinement. This is compared with the present practice using statistical tools

In fuzzy rule-based models acquired from numerical data, redundancy may be present in the form of similar fuzzy sets that represent compatible concepts. This results in an unnecessarily complex and less transparent linguistic description of the system. By using a measure of similarity, a rule base simplification method is proposed that reduces the number of fuzzy sets in the model. Similar fuzzy sets are merged to create a common fuzzy set to replace them in the rule base. If the redundancy in the model is high, merging similar fuzzy sets might result in equal rules that also can be merged, thereby reducing the number of rules as well. The simplified rule base is computationally more efficient and linguistically more tractable. The approach has been successfully applied to fuzzy models of real world systems.

A fuzzy logic rule-based system for assessing steady-state security of a power network with a ring structure is presented. The system uses the measurements of the network state, the information about the network configuration, physical knowledge about the system and rules to determine the security class. The security is determined in a hierarchical manner, first at the component level and then at the network level. The rules are obtained from experts in the field of power systems, and describe the approximate behavior of the network based on knowledge about the physical principles and the network topology. A new defuzzification operator is introduced, which allows the fuzzy logic system to follow different strategies such as risk aware operation. A graphical interface has been built for realizing effective interaction with the operators. The developed system has been tested on the 380 kV Dutch transmission network and it has been found that the classification corresponds to the opinion of experienced operators as to the security class.

FAIR - Fuzzy Arithmetic based Interpolative Reasoning is presented. Linguistic rules of the Mamdani type with fuzzy numbers as consequents are used in an inference mechanism similar to that of the Takagi-Sugeno model. The inference result is a weighted sum of fuzzy numbers calculated by means of the extension principle. Both fuzzy and crisp inputs and outputs can be used, and chaining of rule bases is supported without increasing the fuzziness in each step. This provides a setting for the modeling of dynamic fuzzy systems by fuzzy recursion. The matching in the rule antecedents is done by means of a compatibility measure. Different compatibility measures can be used for different antecedent variables, and reasoning with sparse rule bases is supported. Application of FAIR to the modeling of a nonlinear dynamic system is presented as an example.

Redundancy may be present in fuzzy models which are acquired from data by using techniques like fuzzy clustering and gradient learning. The redundancy may manifest itself in the form of a larger number of rules than necessary, or in the form of fuzzy sets that are very similar to one another. By reducing this redundancy, transparent fuzzy models with appropriate number of rules and distinct fuzzy sets are obtained. This chapter considers cluster validity and cluster merging techniques for determining the relevant number of rules for a given application when fuzzy clustering is used for modeling. Similarity based rule base simplification is then applied for reducing the number of fuzzy sets in the model. The techniques lead to transparent fuzzy models with low redundancy.

A type of nonlinear controller is introduced which is based on the aggregation of fuzzy sets using decision functions. The fuzzy sets are defined on the domain of discourse of individual input variables of the controller. The nonlinear control surface is formed by an aggregation suitable for the process that is controlled. The nonlinearity of the control surface can be specified explicitly by the selection of the membership functions and the aggregation operator. By keeping the number of fuzzy sets to one per variable, the number of controller parameters is reduced considerably compared to a more conventional fuzzy controller especially when the number of inputs is large. The resulting controller belongs to a more restrictive class of controllers, but the ease of implementation and the reduced complexity often compensates for the loss of generality