Antecedent Part Research Articles

An algorithm to compute the degree of match in fuzzy systems

Abstract An algorithm is described for the computation of the degree of match (DM) between the antecedent part of a classification rule and an assertion given by a user when imprecise and precise propositions are mixed freely in a fuzzy expert classification system. In order to estimate to what extent the antecedent proposition X is A is matched against an assertion X is A∗, a value between −1 and +1 is computed from the truth relationship between A and A ∗ . The DM of each classification rule is used to indicate the certainty value of classification. The bigger the DM, the greater is the possibility that an object is classified to the class.

Construction of fuzzy inference rules by NDF and NDFL

Whereas conventional fuzzy reasoning lacks determining membership functions, a neural network driven fuzzy reasoning (NDF) capable of determining membership functions uniquely by an artificial neural network is formulated. In an NDF algorithm the optimum membership function in the antecedent part of fuzzy inference rules is determined by a neural network, while in the consequent parts an amount of reasoning for each rule is determined by other plural neural networks. On the other hand, we propose a new algorithm that can adjust inference rules to compensate for a change of inference environment. We call this algorithm a neural network driven fuzzy reasoning with learning function (NDFL). NDFL can determine the optimal membership function and obtain the coefficients of linear equations in the consequent parts by the searching function of the pattern search method. In this paper, inference rules for making a pendulum stand up from its lowest suspended point ar3 determined by the NDF algorithm for verifying its effectiveness. The NDFL algorithm is formulated and applied to a simple numerical example to demonstrate its effectiveness.

A FUZZY SCHEME WITH APPLICATION TO EXPERT CLASSIFICATION SYSTEMS FOR COMPUTING THE DEGREE OF MATCH BETWEEN A RULE AND AN ASSERTION

We propose a fuzzy scheme for the computation of the degree of match between the antecedent part of a production rule in a rule base and an assertion stored in working memory when imprecise and precise propositions are mixed freely. In order to estimate to what extent the antecedent part X is A is matched against an assertion X is A*. a value between -1 and + 1 is computed from the truth relationship between A and A*. The proposed scheme is computationally efficient and can be applied consistently for all combinations of precise and imprecise propositions. Furthermore, the scheme allows estimates of imprecision to be combined with certainty factors. The scheme consequently seems especially useful for application in expert classification systems.

Numerical Calculation of Incompressible Flow around a Moving Plate with an Adaptive Fuzzy Control using Chaotic Fluctuation.

A new adaptive control method for fuzzy reasoning is proposed, in which the fuzzy controller works with a fluctuation generator for adaptation. The fluctuation generator which produces Gaussian noise is combined with antecedent parts of a fuzzy controller to fluctuate membership functions in each processing time. The learning parts of the system update the membership functions if the output from the controller is more suitable for faster convergence of the Poisson equation. Two-dimensional numerical simulation of the flow around a moving plate is conducted with the fuzzy controller using this new technique. The control variables, i. e., input to the controller, are the interval of the time step and the over-relaxation parameter of the Poisson equation. As a results it is found that this method is adaptive and time effective. The new adaptive method reduced the computational time to 80% compared that for a fuzzy controller without learning.

Semantics and computation of the generalized modus ponens: The long paper

The generalized modus ponens is a fuzzy logic pattern of reasoning that permits inferences to be made with rules having imprecise information in both their antecedent and consequent parts. Several alternatives are available to represent the meaning one wishes to assign to a given rule. This paper first explores four of the most often encountered possibilities, in the case where a single rule is considered at a time. Second, the behavior of two of them (which seem sufficient for practical use in deduction systems) is investigated in the situation where the dependency between antecedent and consequent variables is described by a collection of rules rather than a single rule. Conjectures are made about what is semantically important in the result yielded by the exact computation of the generalized modus ponens. With these hypothesis it is shown that one can get a meaningful approximation of what is produced by the generalized modus ponens technique and also avoid the well-known inefficiency problem associated with its computation.