Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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01 Jan 1995
TL;DR: This paper extends the method for extracting fuzzy rules directly from numerical input-output data for pattern classification to function approximation, and compares the approximation performance of the fuzzy system with the function approximation approach based on neural networks.
Abstract: In our previous work (1993) we developed a method for extracting fuzzy rules directly from numerical input-output data for pattern classification. In this paper we extend the method to function approximation. For function approximation, first, the universe of discourse of an output variable is divided into multiple intervals, and each interval is treated as a class. Then the same as for pattern classification, using the input data for each interval, fuzzy rules are recursively defined by activation hyperboxes which show the existence region of the data for the interval and inhibition hyperboxes which inhibit the existence region of data for that interval. The approximation accuracy of the fuzzy system derived by this method is empirically studied using an operation learning application of a water purification plant. Additionally, we compare the approximation performance of the fuzzy system with the function approximation approach based on neural networks. >
190 citations
TL;DR: Techniques for processing simple fuzzy queries expressed in the relational query language SEQUEL are introduced and the feasibility of implementing such techniques in a real environment is studied.
Abstract: This paper is concerned with techniques for fuzzy query processing in a database system. By a fuzzy query we mean a query which uses imprecise or fuzzy predicates (e.g. AGE = “VERY YOUNG”, SALARY = “MORE OR LESS HIGH”, YEAR-OF-EMPLOYMENT = “RECENT”, SALARY ⪢ 20,000, etc.). As a basis for fuzzy query processing, a fuzzy retrieval system based on the theory of fuzzy sets and linguistic variables is introduced. In our system model, the first step in processing fuzzy queries consists of assigning meaning to fuzzy terms (linguistic values), of a term-set, used for the formulation of a query. The meaning of a fuzzy term is defined as a fuzzy set in a universe of discourse which contains the numerical values of a domain of a relation in the system database. The fuzzy retrieval system developed is a high level model for the techniques which may be used in a database system. The feasibility of implementing such techniques in a real environment is studied. Specifically, within this context, techniques for processing simple fuzzy queries expressed in the relational query language SEQUEL are introduced.
189 citations
TL;DR: The method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems and it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting.
Abstract: A fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure. This extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods, while remaining easily interpretable. Fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a CART decision tree. A training rule for fuzzy trees, similar to backpropagation in neural networks, is designed. This rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits. The method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems. In regression problems, it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting. In classification, fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space. This allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate, sometimes even below the Bayes misclassification rate.
189 citations
TL;DR: The linguistic score index and linguistic accuracy index of the LIFN are introduced in order to process the multiple attribute decision making (MADM) with LIFNs, and an approach to handle MADM under LifNs environment is proposed.
Abstract: Motivated by intuitionistic fuzzy sets and fzzy linguistic approach, this article proposes the concept of linguistic intuitionistic fuzzy numbers (LIFNs) where membership and and nonmembership are represented as linguistic terms. In order to process the multiple attribute decision making (MADM) with LIFNs, we introduce the linguistic score index and linguistic accuracy index of the LIFN. Simultaneously, the operation laws for LIFNs are defined and the related properties of the operation laws are studied. Further, some aggregation operators are developed, involving the linguistic intuitionistic fuzzy weighted averaging (LIFWA) operator, linguistic intuitionistic fuzzy ordered weighted averaging (LIFOWA) operator and linguistic intuitionistic fuzzy hybrid averaging (LIFHA) operator, etc., which can be utilized to aggregate preference information taking the form of LIFNs. Based on the LIFWA and the LIFHA operators, we propose an approach to handle MADM under LIFNs environment. Finally, an illustrativ...
188 citations
TL;DR: A theory of almost periodic fuzzy functions, i.e. of the almost periodic functions of real variable and with values fuzzy real numbers, is developed and applications to fuzzy differential equations and to (fuzzy) dynamical systems are given.
188 citations