Temporal fuzzy association rule mining with 2-tuple linguistic representation

This paper reports on an approach that contributes towards the problem of discovering fuzzy association rules that exhibit a temporal pattern. The novel application of the 2-tuple linguistic representation identifies fuzzy association rules in a temporal context, whilst maintaining the interpretability of linguistic terms. Iterative Rule Learning (IRL) with a Genetic Algorithm (GA) simultaneously induces rules and tunes the membership functions. The discovered rules were compared with those from a traditional method of discovering fuzzy association rules and results demonstrate how the traditional method can loose information because rules occur at the intersection of membership function boundaries. New information can be mined from the proposed approach by improving upon rules discovered with the traditional method and by discovering new rules

Global Optimization strategies for two-mode clustering

Two-mode clustering is a relatively new form of clustering that clusters both rows and columns of a data matrix. To do so, a criterion similar to k-means is optimized. However, it is still unclear which optimization method should be used to perform two-mode clustering, as various methods may lead to non-global optima. This paper reviews and compares several optimization methods for two-mode clustering. Several known algorithms are discussed and a new, fuzzy algorithm is introduced. The meta-heuristics Multistart, Simulated Annealing, and Tabu Search are used in combination with these algorithms. The new, fuzzy algorithm is based on the fuzzy c-means algorithm of Bezdek (1981) and the Fuzzy Steps approach to avoid local minima of Heiser and Groenen (1997) and Groenen and Jajuga (2001). The performance of all methods is compared in a large simulation study. It is found that using a Multistart meta-heuristic in combination with a two-mode k-means algorithm or the fuzzy algorithm often gives the best results. Finally, an empirical data set is used to give a practical example of two-mode clustering.algorithms;fuzzy clustering;multistart;simulated annealing;simulation;tabu search;two-mode clustering

Evaluation of fuzzy inference systems using fuzzy least squares

Efforts to develop evaluation methods for fuzzy inference systems which are not based on crisp, quantitative data or processes (i.e., where the phenomenon the system is built to describe or control is inherently fuzzy) are just beginning. This paper suggests that the method of fuzzy least squares can be used to perform such evaluations. Regressing the desired outputs onto the inferred outputs can provide both global and local measures of success. The global measures have some value in an absolute sense, but they are particularly useful when competing solutions (e.g., different numbers of rules, different fuzzy input partitions) are being compared. The local measure described here can be used to identify specific areas of poor fit where special measures (e.g., the use of emphatic or suppressive rules) can be applied. Several examples are discussed which illustrate the applicability of the method as an evaluation tool

The application of ANFIS prediction models for thermal error compensation on CNC machine tools

Thermal errors can have significant effects on CNC machine tool accuracy. The errors come from thermal deformations of the machine elements caused by heat sources within the machine structure or from ambient temperature change. The effect of temperature can be reduced by error avoidance or numerical compensation. The performance of a thermal error compensation system essentially depends upon the accuracy and robustness of the thermal error model and its input measurements. This paper first reviews different methods of designing thermal error models, before concentrating on employing an adaptive neuro fuzzy inference system (ANFIS) to design two thermal prediction models: ANFIS by dividing the data space into rectangular sub-spaces (ANFIS-Grid model) and ANFIS by using the fuzzy c-means clustering method (ANFIS-FCM model). Grey system theory is used to obtain the influence ranking of all possible temperature sensors on the thermal response of the machine structure. All the influence weightings of the thermal sensors are clustered into groups using the fuzzy c-means (FCM) clustering method, the groups then being further reduced by correlation analysis. A study of a small CNC milling machine is used to provide training data for the proposed models and then to provide independent testing data sets. The results of the study show that the ANFIS-FCM model is superior in terms of the accuracy of its predictive ability with the benefit of fewer rules. The residual value of the proposed model is smaller than ±4 μm. This combined methodology can provide improved accuracy and robustness of a thermal error compensation system

Improving land change detection based on uncertain survey maps using fuzzy sets

In this paper we present a method for correcting inherent classification bias in historical survey maps with which subsequent land cover change analysis can be improved. We linked generalized linear modelling techniques for spatial uncertainty prediction to fuzzy set based operations. The predicted uncertainty information was used to compute fuzzy memberships of forest and non-forest classes at each location. These memberships were used to reclassify the original map based on decision rules, which take into consideration the differences in identification likelihood during the historical mapping. Since the forest area was underestimated in the original mapping, the process allows to correct this bias by favouring forest, especially where uncertainty was high. The analyses were performed in a cross-wise manner between two study areas in order to examine whether the bias correction algorithm would still hold in an independent test area. Our approach resulted in a significant improvement of the original map as indicated by an increase of the Normalized Mutual Information from 0.26 and 0.36 to 0.38 and 0.45 for the cross-wise test against reference maps in Pontresina and St. Moritz, respectively. Consequently subsequent land cover change assessments could be considerably improved by reducing the deviations from a reference change by almost 50 percent. We concluded that the use of logistic regression techniques for uncertainty modelling based on topographic gradients and fuzzy set operations are useful tools for predictively reducing uncertainty in maps and land cover change models. The procedure allows to get more reliable area estimates of crisp classes and it improves the computation of the fuzzy areas of classes. The approach has limitations when the original map shows high initial accurac