![]() In this image, the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. These truth values can then be used to determine how the brakes should be controlled. Each function maps the same temperature value to a truth value in the 0 to 1 range. For instance, a temperature measurement for anti-lock brakes might have several separate membership functions defining particular temperature ranges needed to control the brakes properly. Applying truth valuesĪ basic application might characterize subranges of a continuous variable. It is essential to realize that fuzzy logic uses truth degrees as a mathematical model of the vagueness phenomenon while probability is a mathematical model of ignorance. Another designer might equally well design a set membership function where the glass would be considered full for all values down to 50 ml. Note that the concept of emptiness would be subjective and thus would depend on the observer or designer. Then one might define the glass as being 0.7 empty and 0.3 full. The meaning of each of them can be represented by a certain fuzzy set. Then we may consider two concepts: Empty and Full. For example, let a 100 ml glass contain 30 ml of water. The notion of truth doesn't fall by the wayside, but rather a means of representing and reasoning over partial knowledge is afforded, by aggregating all possible outcomes into a dimensional spectrum.īoth degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first. However, there exist certain propositions with variable answers, such as asking various people to identify a color. The notion of whether 1+1=2 is absolute, immutable, mathematical truth. ![]() OverviewĬlassical logic only permits propositions having a value of truth or falsity. Fuzzy logics however had been studied since the 1920s as infinite-valued logics notably by Łukasiewicz and Tarski. Fuzzy logic has been applied to many fields, from control theory to artificial intelligence. The term "fuzzy logic" was introduced with the 1965 proposal of fuzzy set theory by Lotfi A. Irrationality can be described in terms of what is known as the fuzzjective. Furthermore, when linguistic variables are used, these degrees may be managed by specific functions. Fuzzy logic has been extended to handle the concept of partial truth, where the truth value may range between completely true and completely false. Compared to traditional binary sets (where variables may take on true or false values) fuzzy logic variables may have a truth value that ranges in degree between 0 and 1. Fuzzy logicįuzzy logic is a form of many-valued logic it deals with reasoning that is approximate rather than fixed and exact. Reading session at the bottom of this page.
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