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lass containing water or even a live mouse to the top of the pendulum. The system maintained stability in both cases. Yamakawa eventually went on to anize his own fuzzysystems research lab to help exploit his patents in the fieldFollowing such demonstrations, Japanese engineers developed a wide range of fuzzy systems for both industrial and consumer applications. In 1988 Japan established the Laboratory for International Fuzzy Engineering LIFE, a cooperative arrangement between 48 panies to pursue fuzzy researchMatsushita vacuum cleaners use micro controllers running fuzzy algorithms to interrogate dust sensors and adjust suction power accordingly. Hitachi washing machines use fuzzy controllers to loadweight, fabricmix, and dirt sensors and automatically set the wash cycle for the best use of power, water, and detergentCanon developed an autofocusing camera that uses a chargecoupled device CCD to measure the clarity of the image in six regions of its field of view and use the information provided to determine if the image is in focus. It also tracks the rate of change of lens movement during focusing, and controls its speed to prevent camera39。 a conductivity sensor, to measure detergent level from the ions present in the wash。s operational specifications and inputs and the fuzzy sets for the the rule the defuzzification through test suite to validate system, adjust details as required6plete document and release to production. Logical interpretation of fuzzy control In spite of the appearance there are several difficulties to give a rigorous logical interpretation of the IFTHEN rules. As an example, interpret a rule as IF temperature is cold THEN heater is high by the first order formula Coldx→ Highy and assume that r is an input such that Coldr is false. Then the formula Coldr→ Hight is true for any t and therefore any t gives a correct control given r. Obviously, if we consider systems of rules in which the class antecedent define a partition such a paradoxical phenomenon does not arise. In any case it is sometimes unsatisfactory to consider two variables x and y in a rule without some kind of functional dependence. A rigorous logical justification of fuzzy control is given in H225。s basic logic. Also in Gerla 2021 a logical approach to fuzzy control is proposed based on the following idea. Denote 。s book ,where fuzzy control is represented as a theory of H225。 and a magostrictive sensor to read spin rate. The system determines the optimum wash cycle for any load to obtain the best results with the least amount of energy, detergent, and water Research and development is also continuing on fuzzy applications in software, as opposed to firmware, design, including fuzzy expert systems and integration of fuzzy logic with neuralwork and socalled adaptive geic software systems, with the ultimate goal of building selflearning fuzzy control systems. Fuzzy sets The input variables in a fuzzy control system are in general mapped into by sets of membership functions similar to this, known as fuzzy sets. The process of converting a crisp input value to a fuzzy value is called fuzzification. A control system may also have various types of switch, or ONOFF, inputs along with its analog inputs, and such switch inputs of course will always have a truth value equal to either 1 or 0, but the scheme can deal with them as simplified fuzzy functions that happen to be either one value or anotherGiven mappings of input variables into membership functions and truth values, the microcontroller then makes decisions for what action to