Fuzzy Membership Function Generation Research Articles

A method for automatic generation of fuzzy membership functions for mobile device’s characteristics based on Google Trends

While creating a framework for adaptive mobile interfaces for m-learning applications we found that in order to ease the use of our framework we needed to present the mobile device characteristics to non-expert users in a easy to understand manner. Using fuzzy sets to represent the characteristics of mobile devices, non-expert developers such as teachers or instructional designers can actively participate in the development or adaptation of the educational tools. To be able to automatically generate the fuzzy membership functions of the sets we needed the data of the mobile device market, regrettably this information is not publicly available. To tackle this problem we have developed a method to estimate the market share of each mobile device based on the popularity metrics recovered from Google Trends and then we use that estimated value as the input to generate the fuzzy set of each characteristic. The proposed method allows us to not only model the state of the market in different periods of time, but also to localize the results to adapt them to the mobile market of specific countries. In this paper we will describe the proposed algorithm and we will discuss the obtained results.

Fuzzy Membership Function Generation: A Modified Approach with Improved Performance

This paper presents a new approach to generate fuzzy membership functions. We propose to use learning vector quantization (LVQ) before using FCM to initialize it with number and initial location of cluster centers. We also propose to use modified fuzzy C-means algorithm (MCM) to provide modified shapes of membership functions at extremes. The simulation has shown that the proposed algorithm has better performance as it provide the optimum solution, speeds up the rate of convergence, does not require to specify the number of clusters beforehand, does not require to specify the partition matrix randomly and generates membership functions that provide a smooth variation of the control action when the parameters are at extreme. Keywords: Fuzzy C-Means (FCM), Learning vector Quantization (LVQ), Modified Fuzzy C-Means (MCM).

An information theoretic approach to generating fuzzy hypercubes for if-then classifiers

In this paper, a framework for automatic generation of fuzzy membership functions and fuzzy rules from training data is proposed. The main focus of this paper is designing fuzzy if-then classifiers; however the proposed method can be employed in designing a wide range of fuzzy system applications. After the fuzzy membership functions are modeled by their supports, an optimization technique, based on a multi-objective real coded genetic algorithm with adaptive cross over and mutation probabilities, is implemented to find near optimal supports. Employing interpretability constraint in parameter representation and encoding, we ensure that the generated fuzzy membership function does have a semantic meaning. The fitness function of the genetic algorithm, which estimates the quality of the generated membership functions, consists of two elements: (i) the Shannon entropy and mutual information measures to measure diversity of the data distribution in a hypercube; and (ii) the number of generated fuzzy rules addressing the measure of compactness of the fuzzy system. Finally membership functions are tuned to yield optimal classifier hypercubes, which represent the predictivity and discriminating power of the classifier. Fuzzy rules of the classifier are derived from the optimal hypercubes. Using the proposed approach to designing fuzzy if-then classifiers, we are also able to evaluate the generated membership functions and compare the results with that of other techniques which have been previously reported in the literature.Using the experimental result, we show that the proposed approach outperforms other techniques in low resolutions. It means that theproposed approach can achieve satisfying result with lower complexity.