Some Considerations and a Benchmark Related to the CNF Property of the Koczy-Hirota Fuzzy Rule Interpolation

The goal of this paper is twofold. Once to highlight some basic problematic properties of the KH Fuzzy Rule Interpolation through examples, secondly to set up a brief Benchmark set of Examples, which is suitable for testing other Fuzzy Rule Interpolation (FRI) methods against these ill conditions. Fuzzy Rule Interpolation methods were originally proposed to handle the situation of missing fuzzy rules (sparse rule-bases) and to reduce the decision complexity. Fuzzy Rule Interpolation is an important technique for implementing inference with sparse fuzzy rule-bases. Even if a given observation has no overlap with the antecedent of any rule from the rule-base, FRI may still conclude a conclusion. The first FRI method was the Koczy and Hirota proposed "Linear Interpolation", which was later renamed to "KH Fuzzy Interpolation" by the followers. There are several conditions and criteria have been suggested for unifying the common requirements an FRI methods have to satisfy. One of the most common one is the demand for a convex and normal fuzzy (CNF) conclusion, if all the rule antecedents and consequents are CNF sets. The KH FRI is the one, which cannot fulfill this condition. This paper is focusing on the conditions, where the KH FRI fails the demand for the CNF conclusion. By setting up some CNF rule examples, the paper also defines a Benchmark, in which other FRI methods can be tested if they can produce CNF conclusion where the KH FRI fails

Fuzzy Modeling of Thermoplastic Composites' Melt Volume Rate

Melt volume-flow rate (MVR) is one of the most important quality indicators of composite materials, which depends on the proportion of the component materials. This paper reports the development of a low complexity fuzzy model that describes the relation between percentage amount of multiwall carbon nanotube (MWCNT), acrylonitrile-butadiene-styrene (ABS), polycarbonate (PC) and MVR of the resulting composite. The rule base was generated from a sample data set obtained from experiments by the rule base extension using default set shapes (RBE-DSS) method, and the applied fuzzy inference technique was the least squares method based fuzzy rule interpolation (LESFRI). The resulting model was validated against a separate test data set as well, and it was compared to a fuzzy model generated by a traditional commercial software tool

Fuzzy Rule Interpolation and SNMP-MIB for Emerging Network Abnormality

It is difficult to implement an efficient detection approach for Intrusion Detection Systems (IDS) and many factors contribute to this challenge. One such challenge concerns establishing adequate boundaries and finding a proper data source. Typical IDS detection approaches deal with raw traffics. These traffics need to be studied in depth and thoroughly investigated in order to extract the required knowledge base. Another challenge involves implementing the binary decision. This is because there are no reasonable limits between normal and attack traffics patterns. In this paper, we introduce a novel idea capable of supporting the proper data source while avoiding the issues associated with the binary decision. This paper aims to introduce a detection approach for defining abnormality by using the Fuzzy Rule Interpolation (FRI) with Simple Network Management Protocol (SNMP) Management Information Base (MIB) parameters. The strength of the proposed detection approach is based on adapting the SNMP-MIB parameters with the FRI.  This proposed method eliminates the raw traffic processing component which is time consuming and requires extensive computational measures. It also eliminates the need for a complete fuzzy rule based intrusion definition. The proposed approach was tested and evaluated using an open source SNMP-MIB dataset and obtained a 93% detection rate. Additionally, when compared to other literature in which the same test-bed environment was employed along with the same number of parameters, the proposed detection approach outperformed the support vector machine and neural network. Therefore, combining the SNMP-MIB parameters with the FRI based reasoning could be beneficial for detecting intrusions, even in the case if the fuzzy rule based intrusion definition is incomplete (not fully defined)