Therefore, this temperature has 0.2 membership in the fuzzy set "warm" and 0.8 membership in the fuzzy set "cold". The orange arrow (pointing at 0.2) may describe it as "slightly warm" and the blue arrow (pointing at 0.8) "fairly cold". this temperature has zero membership in the fuzzy set "hot". Since the red arrow points to zero, this temperature may be interpreted as "not hot" i.e. The vertical line in the image represents a particular temperature that the three arrows (truth values) gauge. A point on that scale has three "truth values"-one for each of the three functions. These fuzzy sets are typically described by words, and so by assigning the system input to fuzzy sets, we can reason with it in a linguistically natural manner.įor example, in the image below the meanings of the expressions cold, warm, and hot are represented by functions mapping a temperature scale. Any value between 0 and 1 represents the degree of uncertainty that the value belongs in the set. If it is 0 then the value does not belong to the given fuzzy set, and if it is 1 then the value completely belongs within the fuzzy set. This degree of membership may be anywhere within the interval. De-fuzzify the fuzzy output functions to get "crisp" output values.įuzzification is the process of assigning the numerical input of a system to fuzzy sets with some degree of membership.Execute all applicable rules in the rulebase to compute the fuzzy output functions.Fuzzify all input values into fuzzy membership functions.The most well-known system is the Mamdani rule-based one. For example, we can use the hedges rather and somewhat to construct the additional values rather old or somewhat young. Because natural languages do not always contain enough value terms to express a fuzzy value scale, it is common practice to modify linguistic values with adjectives or adverbs. Ī linguistic variable such as age may accept values such as young and its antonym old. In fuzzy logic applications, non-numeric values are often used to facilitate the expression of rules and facts. Fuzzy set theory provides a means for representing uncertainty. 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 values Ī basic application might characterize various sub-ranges of a continuous variable. īoth degrees of truth and probabilities range between 0 and 1 and hence may seem similar at first, but fuzzy logic uses degrees of truth as a mathematical model of vagueness, while probability is a mathematical model of ignorance. In such instances, the truth appears as the result of reasoning from inexact or partial knowledge in which the sampled answers are mapped on a spectrum. However, there are also propositions with variable answers, such as one might find when asking a group of people to identify a color. įuzzy logic has been applied to many fields, from control theory to artificial intelligence.Ĭlassical logic only permits conclusions that are either true or false. These models have the capability of recognising, representing, manipulating, interpreting, and using data and information that are vague and lack certainty. Fuzzy models or fuzzy sets are mathematical means of representing vagueness and imprecise information (hence the term fuzzy). įuzzy logic is based on the observation that people make decisions based on imprecise and non-numerical information. Fuzzy logic had, however, been studied since the 1920s, as infinite-valued logic-notably by Łukasiewicz and Tarski. The term fuzzy logic was introduced with the 1965 proposal of fuzzy set theory by Iranian Azerbaijani mathematician Lotfi Zadeh. By contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. It is employed to handle the concept of partial truth, where the truth value may range between completely true and completely false. For other uses, see Fuzzy logic (disambiguation).įuzzy logic is a form of many-valued logic in which the truth value of variables may be any real number between 0 and 1. This article is about the scientific theory of that name.
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