The concept of a linguistic variable and its application to approximate reasoning - I

By a linguistic variable we mean a variable whose values are words or sentences in a natural or artificial language. I:or example, Age is a linguistic variable if its values are linguistic rather than numerical, i.e., young, not young, very young, quite young, old, not very oldand not very young, etc., rather than 20, 21, 22, 23, In more specific terms, a linguistic variable is characterized by a quintuple (&?, T(z), U, G,M) in which &? is the name of the variable; T(s) is the term-set of2 , that is, the collection of its linguistic values; U is a universe of discourse; G is a syntactic rule which generates the terms in T(z); and M is a semantic rule which associates with each linguistic value X its meaning, M(X), where M(X) denotes a fuzzy subset of U The meaning of a linguistic value X is characterized by a compatibility function, c : l/ + [0, I], which associates with each u in U its compatibility with X. Thus, the COItIpdtibiiity of age 27 with young might be 0.7, while that of 35 might be 0.2. The function of the semantic rule is to relate the compdtibihties of the socalled primary terms in a composite linguistic value-e.g.,.young and old in not very young and not very old-to the compatibility of the composite value. To this end, the hedges such as very, quite, extremely, etc., as well as the connectivesand and or are treated as nonlinear operators which modify the meaning of their operands in a specified fashion. The concept of a linguistic variable provides a means of approximate characterization of phenomena which are too complex or too ill-defined to be amenable to description in conventional quantitative terms. In particular, treating ZFuth as a linguistic variable with values such as true, very true, completely true, not very true, untrue, etc., leads to what is called fuzzy logic. By providing a basis for approximate reasoning, that is, a mode of reasoning which is not exact nor very inexact, such logic may offer a more realistic framework for human reasoning than the traditional two-valued logic. It is shown that probabilities, too, can be treated as linguistic variables with values such as likely, very likely, unlikely, etc. Computation with linguistic probabilities requires the solution of This work was supported in part by the Navy Electronic Systems Command under Contract N00039-71-C-0255, the Army Research Office, Durham, N.C., under Grant DA-ARO-D-31-124-7 l-G1 74, and the National Science Foundation under Grant GK-VP610656X3. The writing of the paper was completed while the author was participating in a Joint Study Program with the Systems Research Department, IBM Research Ldboratory, San Jose, California. Parts II and III of this paper will appear in forthcoming issues of Information Sciences. @American Elsevier Publishing Company, Inc., 1975