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Scaling the membership function
European Journal of Operational Research, 1986This paper contains an axiomatic treatment of the measurement of the fuzzy set membership function based on the measurement methodology of the Analytic Hierarchy Process (AHP). The set of axioms corresponding to hierarchic structures are a special case of axioms for priority setting in systems with feedback which allow for a wide class of dependencies.
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Building a hierarchical representation of membership functions
Proceedings Tenth IEEE International Conference on Tools with Artificial Intelligence (Cat. No.98CH36294), 2002Deriving inference rules from training examples is one of the most common machine-learning approaches. Fuzzy systems that can automatically derive fuzzy if-then rules and membership functions from numeric data have recently been developed. In this paper, we propose a new hierarchical representation for membership functions, and design a procedure to ...
Tzung-Pei Hong, Jyh-Bin Chen
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On fuzzy ellipsoid numbers and membership functions
Journal of Intelligent & Fuzzy Systems, 2016In this paper, the operations of fuzzy ellipsoid numbers and the direct relationship between the joint membership function and the edge membership functions are investigated. First, we prove that the general scalar multiplication (defined by Zadeh’s expansion) of fuzzy ellipsoid numbers preserves the closeness of the operation, but the general addition
Guixiang Wang +3 more
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Choosing membership functions of linguistic terms
The 12th IEEE International Conference on Fuzzy Systems, 2003. FUZZ '03., 2004The shapes of terms used in fuzzy systems have adopted several 'conventions'. Terms are almost invariably normalised (having a maximum membership value of 1), convex (having a single maximum or plateau maxima) and distinct (being restricted in their degree of overlap: often expressed as some variation on the concept that all membership values at any ...
Garibaldi, J. M., John, Robert, 1955-
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A CMOS PWL fuzzy membership function
Proceedings of ISCAS'95 - International Symposium on Circuits and Systems, 2002The membership function, classically constructed from piecewise linear (PWL) functions, is one of the most important components in fuzzy neural systems. Here we give an improved current mode CMOS circuit suitable for design of fuzzy membership PWL functions.
S. Ahmadi +2 more
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Finding relevant attributes and membership functions
Fuzzy Sets and Systems, 1999Fuzzy systems that automatically derive fuzzy if-then rules from numeric data have been developed. Most have to predefine membership functions in order to learn. Hong and Lee proposed a general learning method that automatically derives fuzzy if-then rules and membership functions from a set of given training examples using a decision table.
Tzung-Pei Hong, Jyh-Bin Chen
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The Membership Function and Its Measurement
2013Perhaps the most fundamental concept in fuzzy set theory is the membership function [24, 25]. Fuzzy sets allow for gradual degrees of membership and the membership function is a measure of that degree. The meaning of the membership function has been a question for everyone including Zadeh himself who advocated a linguistic approach [26–28] from the ...
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Measurement of Membership Functions
1986Abstract Empirical measurement of membership functions of fuzzy sets are considered with the fundamental axioms of measurement theory. An experimental construction of fuzzy set membership leads to a realization of stochastic fuzziness and a type II fuzzy set representation. Axioms of measurement can be validated with a probabilistic interpretation.
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Membership Functions and Their Assessment
1978Membership functions and their assessment present a problem of paramount importance. Its neglect would further delay any real applications of the fuzzy set theory. Membership functions are not ‘given’ and they can not be arbitrarily assumed. A systematic assessment procedure, designed to externalize decision maker’s perception of fuzziness is ...
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Tuning of Membership Functions
2001In the previous chapter, we discuss extraction of the three types of fuzzy rules: those with pyramidal membership functions, those with polyhedral regions, and those with ellipsoidal regions using the data included in the associated clusters. Since these fuzzy rules are generated without considering the overlap between classes, their classification ...
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