Membership function

About: Membership function is a research topic. Over the lifetime, 15795 publications have been published within this topic receiving 418366 citations.

Compatible cluster merging for fuzzy modelling

Abstract: Making a fuzzy model of a dynamic process requires the tuning of many parameters. Doing this heuristically is tedious and time consuming. Clustering techniques provide an easier way for forming fuzzy model using measurements made on the system. However, the number of clusters and hence the number of rules the fuzzy rule-base must be determined a priori. It is usually not possible to determine beforehand the optimal number of rules in a rule-base. In this paper, a compatible cluster merging algorithm is suggested for finding the "optimal" number of rules in a rule base. It is based on the compatible cluster merging algorithm proposed recently. The original compatible cluster merging algorithm has certain undesired properties for fuzzy modelling. Hence, a modification is proposed and a modified compatible cluster merging algorithm is described. The new algorithm combines techniques from the original compatible cluster merging, fuzzy multicriteria decision making and heuristics. Examples are given that show the applicability of the proposed method. >

Interval valued strict preference with Zadeh triples

Abstract: Preference modelling and choice theory are common to many different areas including operational research, economics, artificial intelligence and social choice theory. We consider “vague preferences” and introduce a new technique to model this vagueness with the aim of making a choice at the final stage. Our basic tools of modelling will be fuzzy relations and interval valued fuzzy sets. Specifically, we propose that the initial vagueness in the weak preferences of a decision maker is represented by a fuzzy relation and further constructs from this concept introduce a higher-order vagueness which is represented by interval valued fuzzy sets. We derive necessary and sufficient conditions on the representation of this initial vagueness such that a complete ranking of the alternatives is possible. It is shown that conditions weaker than min-transitivity on the representation of initial vagueness are necessary and sufficient for the alternatives to be partially ranked. Furthermore, two linearity conditions are shown to make the ordering of the alternatives a complete order. Conditions for the existence of unfuzzy non-dominated alternatives are also explored.

Handling forecasting problems based on high-order fuzzy logical relationships

Abstract: People usually use many methods to predict the weather, the temperature, the stock index, the enrollments, the earthquake, the economy, etc. Based on these forecasting results, people can prevent damages to occur or get benefits from the forecasting activities. In this paper, we present a new method to forecast the Taiwan Stock Exchange Capitalization Weighted Stock Index (TAIEX), the enrollments of the University of Alabama and the inventory demand based on high-order fuzzy logical relationships. First, the proposed method fuzzifies the historical data into fuzzy sets to form high-order fuzzy logical relationships. Then, it calculates the value of the variable between the subscripts of adjacent fuzzy sets appearing in the antecedents of high-order fuzzy logical relationships. Then, it lets the high-order fuzzy logical relationships with the same variable value form a high-order fuzzy logical relationship group. Finally, it chooses a high-order fuzzy logical relationship group to forecast the TAIEX. The proposed method gets a higher average forecasting accuracy rate to forecast the TAIEX, the enrollments of the University of Alabama and the inventory demand than the existing methods.

Fuzzy relational classifier trained by fuzzy clustering

Abstract: A novel approach to nonlinear classification is presented, in the training phase of the classifier, the training data is first clustered in an unsupervised way by fuzzy c-means or a similar algorithm. The class labels are not used in this step. Then, a fuzzy relation between the clusters and the class identifiers is computed. This approach allows the number of prototypes to be independent of the number of actual classes. For the classification of unseen patterns, the membership degrees of the feature vector in the clusters are first computed by using the distance measure of the clustering algorithm. Then, the output fuzzy set is obtained by relational composition. This fuzzy set contains the membership degrees of the pattern in the given classes. A crisp decision is obtained by defuzzification, which gives either a single class or a "reject" decision, when a unique class cannot be selected based on the available information. The principle of the proposed method is demonstrated on an artificial data set and the applicability of the method is shown on the identification of live-stock from recorded sound sequences. The obtained results are compared with two other classifiers.