Some notes on Zadeh’s extensions

This paper shows that the Zadeh’s extensions of sendograph-metric-continuous fuzzy-valued functions are sendograph-metric-continuous fuzzy functions.     

Growing fuzzy topology adaptive resonance theory models with a push-pull learning algorithm

A new incrementally growing neural network model, called the growing fuzzy topology ART (GFTART) model, is proposed based on integrating the conventional fuzzy ART model with the incremental topology-preserving mechanism of the growing cell structure (GCS) model. This is in addition, to a new training algorithm, called the push-pull learning algorithm. The proposed GFTART model has two purposes: First, to reduce the proliferation of incrementally generated nodes in the F2 layer by the conventional fuzzy ART model based on replacing each F2 node with a GCS. Second, to enhance the class-dependent clustering representation ability of the GCS model by including the categorization property of the conventional fuzzy ART model. In addition, the proposed push-pull training algorithm enhances the cluster discriminating property and partially improves the forgetting problem of the training algorithm in the GCS model.     

A fuzzy-based interleaved multi-hop authentication scheme in wireless sensor networks

In sensor networks, a compromised node can either generate fabricated reports with false votes or inject false votes into real reports, which causes severe damage such as false alarms, energy drain and information loss. An interleaved hop-by-hop authentication (IHA) scheme addresses the former attack by detecting and filtering false reports in a deterministic and hop-by-hop fashion. Unfortunately, in IHA, all en-route nodes must join to verify reports while only a few are necessary to the authentication procedure. In this paper, we propose a fuzzy-based interleaved multi-hop authentication scheme based on IHA. In our scheme, the fuzzy logic system only selects some nodes for verification based on the network characteristics. Moreover, we apply a voting method and a hash-based key assignment mechanism to improve network security. Through performance evaluation, the proposed scheme is found to save up to 13% of the energy consumption and to provide more network protection compared to IHA.     

Loss and gain functions for CBR retrieval

The method described in this article evaluates case similarity in the retrieval stage of case-based reasoning (CBR). It thus plays a key role in deciding which case to select, and therefore, in deciding which solution will be eventually applied. In CBR, there are many retrieval techniques. One feature shared by most is that case retrieval is based on attribute similarity and importance. However, there are other crucial factors that should be considered, such as the possible consequences of a given solution, in other words its potential loss and gain. As their name clearly implies, these concepts are defined as functions measuring loss and gain when a given retrieval case solution is applied. Moreover, these functions help the user to choose the best solution so that when a mistake is made the resulting loss is minimal. In this way, the highest benefit is always obtained.     

A systematic approach to improve multiple Lyapunov function stability and stabilization conditions for fuzzy systems

This paper presents a systematic approach for decreasing conservativeness in stability analysis and control design for Takagi-Sugeno (TS) systems. This approach is based on the idea of multiple Lyapunov functions together with simple techniques for introducing slack matrices. Unlike some previous approaches based on multiple Lyapunov functions, both the stability and the stabilization conditions are written as linear matrix inequality (LMI) problems. The proposed approach reduces the number of inequalities and guarantees extra degrees of freedom to the LMI problems. Numeric examples illustrate the effectiveness of this method.