Fuzzy inferences

Using these operators, fuzzy inference mechanisms are then developed to manipulate rules that include fuzzy values. The largest difference between fuzzy inference and ordinary inference is that fuzzy inference aUows partial match of input and produces an interpolated output. This technology is useml in control also. See Ref. 94. 

Fuzzy Logic Control The apphcation of fuzzy logic to process control requires the concepts of Fuzzy rules and fuzzy inference. A fuzzy rule, also known as a fuzzy IF-THEN statement, has the form ... 

Fuzzy inference is therefore the process of mapping membership values from the input windows, through the rulebase, to the output window(s). 

Fig. 10.11 Clipped fuzzy output window due to fuzzy inference.

MATLAB Fuzzy Inference System (FIS) editor can be found in Appendix 1. Figure 10.16 shows the control surface for the 11 set rulebase fuzzy logic controller. 

The Adaptive Network based Fuzzy Inference System (ANFIS)... 

The ANFIS neurofuzzy controller was implemented by Jang (1993) and employs a Takagi-Sugeno-Kang (TSK) fuzzy inference system. The basic ANFIS architecture is shown in Figure 10.31. 

If the fuzzy inference system has inputs xi and X2 and output /as shown in Figure 10.31, then a first-order TSK rulebase might be... 

Fig. A1.5 Main menu of Fuzzy Inference System (FIS) editor.

Jang, J.S.R. (1993) ANFIS Adaptive Network-based Fuzzy Inference System, IEEE Transactions on Systems, Man and Cybernetics, 23, pp. 665-685. 

Fault Detection Based on Fuzzy Inference Systems... 

In order to combine the conclusions of several such Fuzzy Inference Systems, they will be translated into belief structures, according to the method proposed in [22]. Each Fuzzy Inference System presented Figure 12 is the association of fuzzification functions (providing a numerical evaluation of the membership of a variable to fuzzy sets) and of rules linking these observations to different classes which can be states or disjunctions of states of the process. 

The rules of a Fuzzy Inference System link observations on the space of observed variables to singletons or disjunctions of singletons from the frame of discernment 17. It means that a rule can be expressed by ... 

In this paper we describe the application of an adaptive network based fuzzy inference system (ANFIS) predictor to the estimation of the product compositions in a binary methanol-water continuous distillation column from available on-line temperature measurements. This soft sensor is then applied to train an ANFIS model so that a GA performs the searching for the optimal dual control law applied to the distillation column. The performance of the developed ANFIS estimator is further tested by observing the performance of the ANFIS based control system for both set point tracking and disturbance rejection cases. 

ANFIS—adaptive neuro-fuzzy inference system... 

Fuzzy inference systems are also known as fuzzy associative memories, fuzzy models, fuzzy-rule-based systems, or fuzzy controllers. 

In Example 8.9, the performance of this adaptive neuro-fuzzy inference system is demonstrated for classification of two-dimensional data. 

Another important area of application is approximate reasoning based on fuzzy logic. Fuzzy inferences are applied in analytical expert systems or for controlling chemical or biotechnological reactors. 

Jang, J.S.R., ANFIS Adaptive-network-based fuzzy inference systems, IEEE Trans. Syst. Man... 

Lee, K.M., Kwak, D.K., and Lee-Kwang, H., Fuzzy inference neural network for fuzzy model tuning, IEEE Trans. Syst. Man Cybern. SMC-26 637-645,1996. 

M.M. Gupta J. Qi 1991. Theory of T-norms and fuzzy inference methods, Fuzzy Sets and Systems. 40 431-450. 

The results of this rule-base operation are then post-processed using a fuzzy inference engine to obtain the final prediction. 

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