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The brain and fuzzy logic

Our brain gathers information constantly. The processing of this information is not governed by “crisp” ON/OFF, black/white logic. Rather, it is based on “fuzzy inputs” (truths, perceptions and inferences) which result in an averaged, summarized, normalized output. We then assign to this output a precise number or decision value which we verbalize, write down or act upon. The goal of fuzzy logic control systems is to perform this kind of process.

What is fuzzy logic?

Fuzzy logic is a problem-solving control system methodology that incorporates a simple, rule-based IF X AND Y THEN Z approach rather than attempting to model a system mathematically. The fuzzy logic model is empirically-based, relying on an operator's experience rather than their technical understanding of the system.

In this sense, ‘fuzzy logic’ does not mean ‘inaccurate’ or ‘inexact’ logic. Fuzzy logic is not any less precise than any other form of logic: it is an organized method for handling complex concepts.

The applications of fuzzy logic systems are countless: from automobile subsystems like ABS and cruise-control, ‘intelligent’ home appliances and air-traffic control to digital imaging processing, microprocessors and biomedical systems.

Fuzzy set theory

Classical logic relies on something being either true or false. Thus, something either completely belongs to a set or it is completely excluded from it. For example, considering a set of tall people in the classical logic, one has to decide where is the border between tall people and people who are not tall. If the border is set to, say, 6 feet, then if a person is 6’1’’ tall, he belongs to the set of tall people. If the person is 5’11’’ tall he does not belong to the set.

Unlike in "crisp" sets, where membership is full or none, an object is allowed to belong only partly to one set. Using fuzzy sets, the person being 6’1’’ tall can still have a full membership of the set of tall people, but the person that is 5’11’’ tall, can have 90% membership of the set. This person thus can have what can be described as a "quite tall" representation in a model.

The membership of an object to a particular set is described by a real value from the range between 0 and 1. Thus, for instance, an element can have a membership value 0.5, which describes a 50% membership in a given set. Such logic allows a much easier application of many problems that cannot be easily implemented using classical approach.

Such a classification certainly allows a single object to be a member of two mutually exclusive in the "crisp" sense sets. For example a person 5’5’’tall can be classified as 0.5 tall and also 0.3 short, thus it could be described as "rather tall" and at the same time "sort of short".

Implementing Models using Fuzzy Logics

Fuzzy reasoning allows the implementation of very complex processes, where a simple mathematical model cannot be obtained. Fuzzy logic can also be successfully applied to highly nonlinear processes, where it is observed to greatly simplify the modeling.
The power of fuzzy logic is to perform reasonable and meaningful operations on concepts that cannot be easily coded using a classical approach. Such modification allows for a much more flexible and widespread use of reliable and consistent logic in a variety of applications.
One of the most successful fuzzy logic implementations is the control of a subway in Sendai, Japan. The fuzzy system controls acceleration, deceleration, and breaking of the train. Since its introduction, it not only reduced energy consumption by 10%, but the passengers hardly notice now when the train is changing its velocity. In the past neither conventional, nor human control could have achieved such performance. Therefore, the subway management only allow human drivers outside peak hours because the fuzzy controlled system is safer.

The Cerebral State Monitor’s fuzzy system

The Cerebral State Monitor is driven by an Adaptive Neuro-Fuzzy Inference System (ANFIS). ANFIS is a fuzzy inference system tuned with a back propagation algorithm from a neural network in order to accurately calculate the Cerebral State Index (CSI) for depth of anesthesia.  
The system is ‘data-driven’, meaning that the ANFIS parameters are defined by the causal relation between input-output data.

CSI calculation process: the CSM uses a set of four input parameters calculated from the EEG.

Further reading

  • Henneberg SW, Jensen EW. Fuzzy Logic- a review of the limitless?. Ugeskr Laeger 2000, 18, 162(51):7021
  • Erik W Jensen, Angela Nebot, Pere Caminal , Steen W Henneberg. Identification of causal relations between haemodynamic parameters, auditory evoked potentials and isoflurane by means of fuzzy logic. British Journal of Anaesthesia 1999: 82: 25-32
  • Erik W Jensen, Angela Nebot. Comparison of FIR and ANFIS Methodologies for Prediction of Mean Blood Pressure and Auditory Evoked Potentials index during Anaesthesia. Proceedings of the IEEE congress of Biomedical engineering, Hong Kong 1998, ISSN 1094-687x, pp. 1385-1388
  • Erik W Jensen, Angela Nebot. Comparison of FIR and ANFIS Methodologies for the Prediction of Physiologic Parameters in Anaesthesiology. Proceedings of EUFIT, Aachen 1998, p. 1809-1814
  • Jang JSR: ANFIS: Adaptive-Network-Based Fuzzy Inference System. IEEE Transactions on Systems, Man and Cybernetics 1993; 23:665-685.
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