Wolfram-Manfred Lippe

The fuzzy neural network approximation lemma

Abstract It is well known that artificial neural networks are universal approximators. But what about fuzzy neural networks? Only Buckley and Hayashi [1] presented a theoretical result for these networks: They showed that there are fuzzy functions which cannot be approximated by a certain fuzzy neural network. In this paper we answer the question for a special type of fuzzy neural networks — especially with regard to the fuzzy arithmetic that is used: It is simplified in order to minimize the computational expense as well as to simplify the theoretical examinations. We prove that the class of fuzzy functions which is identical to the class of all continuous real functions extended by means of the extension principle can be approximated by certain fuzzy neural networks.

Stability analysis of neural net controllers using fuzzy neural networks

Neural networks can only be trained with a crisp and finite data set. Therefore, the approximation quality of a trained network is hard to verify. So, a common way in proving stability of a trained neural net controller is to demonstrate the existence of a Lyapunov function. In this article we propose a new method how stability of a neural net controller, used as a closed-loop feedback controller, can be proven. Instead of finding a Lyapunov function, conditions for a fuzzy training set are developed. If a fuzzy neural net is trained using this training set special properties of fuzzy neural nets can be used for estimating the generalization error. After defuzzification of the fuzzy net finite stability of the process can be concluded.

A model of inhomogeneity for ad hoc networks

The major prerequisites for successful wireless ad hoc networking are an almost homogeneous distribution of a nontrivial number of nodes and the determination of an almost ideal selective connectivity of the nodes in the network. To give a basic characterization of network connectivity, an ad hoc network model based on planar graphs is introduced. According to this underlying mathematical network description, the features of homogeneous connectivity for ad hoc networks are defined. Due to a specific physical layer ratio of wireless capacity utilization, a condition of isolation gives the opportunity to maintain isolated areas in any given ad hoc network distribution. To support identified isolated regions is a main goal of a hybrid transfer network.

Error prediction for neural networks by fuzzification

In classical “crisp” neural networks the output cannot be estimated for arbitrary input data. This situation can be overcome if fuzzy neural nets are trained with fuzzy data. These “continuous” data often better describe certain situations. Because fuzzy neural networks map fuzzy numbers to fuzzy numbers, a criterion for choosing a “good” training set can be formulated. Together with an important fuzzy neural network property, the output for arbitrary crisp input data can be estimated based on the fuzzy training set.

Context specific entity based modeling of organizational structures

An entity based modeling technique is presented to specify organizational structures. Our context specific approach describes this kind of structures with communication and information domains. Environmental factors differentiate a system of communicators. The model components are defined with their semantical interactions and applied in a detailed example for an operational structure with informational security requirements. The semantics of the model components are defined axiomatically. A context specific model is a multi-relational network between communicators and environmental factors and depicts organizational structures with the focus on communicational interaction and informational content.

Efficiency increase of fuzzy query languages by using indexes for selected operations

The relatively weak performance of fuzzy database management systems is a major reason for the clear lack of commercial variants. A very important component of a database management system is the query language whose performance is improved amongst others by using indexes. Consequently, the applicability of indexes, designed for the management of fuzzy data, for several operations of a fuzzy query language, in particular a fuzzy equi-join and a fuzzy projection, is examined in this paper. In doing so, the advantages achieved with the integration of a specific index are compared with the benefits resulting from the utilization of a fuzzy equality indicator which is another approach for the efficiency increase of fuzzy query languages. The results will demonstrate that the use of an index can definitely enhance the performance of a fuzzy query language.

Optimization of the normalization of fuzzy relational databases by using alternative methods of calculation for the Fuzzy Functional Dependency

Although, in comparison to standard databases, a tremendous benefit is often derived by using fuzzy databases, their distribution is very low. A reason for the relatively poor acceptance of fuzzy relational databases is to be seen in the difficulty to carry out an adequate normalization. The various procedures discussed in the literature possess miscellaneous weaknesses. In this work a normalization method is regarded whose most significant deficit lies in the fuzzy functional dependency (FFD) because thereby comprehensible results are not produced. Therefore, it is registered which alternatives for the determination of the degree of FFD exist. Furthermore, it is examined with which of these methods the just addressed disadvantage can be eliminated. For this purpose, the presented methods are applied to several examples in order to identify their characteristics.

A local optimum selection criterion for the physical neighbor connectivity of ad hoc networks

According to the common underlying mathematical model of ad hoc networks introduced elsewhere, a selective network model is defined to analyze local node connectivity. Based on a system architecture with a predetermined number of independent and simultaneous links of each network node, the different optimization degrees of the selection of neighbors are presented. A higher relaying efficiency gives the main opportunity for an ad hoc net to be an essential part of a future networking system. The efficiency of a selective network connectivity is compared to pure range controlled connectivity.

Low cost environment changing in a shallow binding system

This paper presents a general approach to the optimization of function calls. We define the class of “low cost calls” and introduce a technique of detecting and executing these calls in a modified shallow binding system known as “standardized shallow binding”. We show that by this technique the overhead expenses of changing environments for low cost calls are nearly cut down to zero. The new method can be applied to any imperative or applicative language. In this paper LISP is taken as an example; it is shown how the technique has been applied in the implementation of a LISP interpreter. We prove that our method exceeds a number of optimizations that have been proposed recently. Finally, we find that standardized shallow binding is also well suited for an efficient implementation of static scoping.

Modeling communicational and informational content in Facebook with context specific methods

In this paper, we apply context specific methods to formalize communicational parameters for different profile groups in Facebook. Information is posted or shared to distinct user groups. Our context specific approach is used to describe the privacy settings of user data in a formalized way. Communicational and informational parameters of a social graph are specified in a context specific model. Relations are defined to model communicational and informational interactions as well as environmental factors taking influence on the profile groups. The textual representation is introduced to describe models in a text-based form.