Size reduction by interpolation in fuzzy rule bases

Fuzzy control is at present still the most important area of real applications for fuzzy theory. It is a generalized form of expert control using fuzzy sets in the definition of vague/linguistic predicates, modeling a system by If...then rules. In the classical approaches it is necessary that observations on the actual state of the system partly match (fire) one or several rules in the model (fired rules), and the conclusion is calculated by the evaluation of the degrees of matching and the fired rules. Interpolation helps reduce the complexity as it allows rule bases with gaps. Various interpolation approaches are shown. It is proposed that dense rule bases should be reduced so that only the minimal necessary number of rules remain still containing the essential information in the original base, and all other rules are replaced by the interpolation algorithm that however can recover them with a certain accuracy prescribed before reduction. The interpolation method used for demonstration is the Lagrange method supplying the best fitting minimal degree polynomial. The paper concentrates on the reduction technique that is rather independent from the style of the interpolation model, but cannot be given in the form of a tractable algorithm. An example is shown to illustrate possible results and difficulties with the method.     

Fuzzy if... then rule models and their transformation into oneanother

The two most essential fuzzy rule-based models used in the literature and in the industrial applications are briefly described. The way of reasoning in these models is shown. Interpolative reasoning for the case of sparse rule bases is also discussed. Rule base compression by eliminating redundant rules whose information can be reconstructed within a set accuracy interval from the remaining rules by using the previous interpolation method is shown. A general fuzzy model is discussed that contains the previous fuzzy models (as well as the nonfuzzy one) as special cases. Ways of transforming the different approximative models into each other via the general model and interpolation are presented     

Performance Evaluation of Supervised Machine Learning Techniques for Efficient Detection of Emotions from Online Content

Emotion detection from the text is a challenging problem in the text analytics. The opinion mining experts are focusing on the development of emotion detection applications as they have received considerable attention of online community including users and business organization for collecting and interpreting public emotions. However, most of the existing works on emotion detection used less efficient machine learning classifiers with limited datasets, resulting in performance degradation. To overcome this issue, this work aims at the evaluation of the performance of different machine learning classifiers on a benchmark emotion dataset. The experimental results show the performance of different machine learning classifiers in terms of different evaluation metrics like precision, recall ad f-measure. Finally, a classifier with the best performance is recommended for the emotion classification.     

Representing membership functions as points in high-dimensionalspaces for fuzzy interpolation and extrapolation

This paper introduces a new approach for fuzzy interpolation and extrapolation of sparse rule base comprising of membership functions with finite number of characteristic points. The approach calls for representing membership functions as points in high-dimensional Cartesian spaces using the locations of their characteristic points as coordinates. Hence, a fuzzy rule base can be viewed as a set of mappings between the antecedent and consequent spaces and the interpolation and extrapolation problem becomes searching for an image in the consequent space upon given an antecedent observation. The present approach divides observations into two groups: 1) observations within the antecedent spanning set contain the same geometric properties as the given antecedents; and 2) observations lying outside the antecedent spanning set contain new geometric properties beyond those of the given rules. Heuristic reasoning must therefore be applied. In this case, a two-step approach with certain flexibility to accommodate additional criteria and design objectives is formulated     

Fuzzy rule interpolation for multidimensional input spaces with applications: a case study

Fuzzy rule based systems have been very popular in many engineering applications. However, when generating fuzzy rules from the available information, this may result in a sparse fuzzy rule base. Fuzzy rule interpolation techniques have been established to solve the problems encountered in processing sparse fuzzy rule bases. In most engineering applications, the use of more than one input variable is common, however, the majority of the fuzzy rule interpolation techniques only present detailed analysis to one input variable case. This paper investigates characteristics of two selected fuzzy rule interpolation techniques for multidimensional input spaces and proposes an improved fuzzy rule interpolation technique to handle multidimensional input spaces. The three methods are compared by means of application examples in the field of petroleum engineering and mineral processing. The results show that the proposed fuzzy rule interpolation technique for multidimensional input spaces can be used in engineering applications.     

Improvements and critique on Sugeno's and Yasukawa's qualitative modeling

Investigates Sugeno's and Yasukawa's (1993) qualitative fuzzy modeling approach. We propose some easily implementable solutions for the unclear details of the original paper, such as trapezoid approximation of membership functions, rule creation from sample data points, and selection of important variables. We further suggest an improved parameter identification algorithm to be applied instead of the original one. These details are crucial concerning the method's performance as it is shown in a comparative analysis and helps to improve the accuracy of the built-up model. Finally, we propose a possible further rule base reduction which can be applied successfully in certain cases. This improvement reduces the time requirement of the method by up to 16% in our experiments.