Encyclopedia of Computer Science and Technology

204 fuzzy logicdefining and arranging functions until the desired processingis accomplished. (The decision making accomplishedby branching statements in imperative languages is accomplishedby incorporating conditionals in function definitions.)Many functional languages (including LISP) for convenienceincorporate some features of imperative languages.The ML language, for example, includes data type declarations.A similar language, Haskell, however, eschews allsuch imperative features.ApplicationsFunctional languages have generally been used for specializedpurposes, although they can in principle perform anytask that an imperative language can. APL, which is basicallya functional language, has devotees who appreciate itscompact and powerful syntax for performing calculations(see apl). LISP and its variants have long been favored formany artificial intelligence applications, particularly naturallanguage processing, where its representation of data aslists and the facility of its list-processing functions seems anatural fit.Proponents of functional languages argue that they freethe programmer from having to be concerned with explicitlysetting up and using variables. In a functional language,problems can often be stated in a more purely mathematicalway. Further, because functional programs are not organizedas sequentially executed tasks, it may be easier toimplement parallel processing systems using functionallanguages.However, critics point out that imperative languages aremuch closer to how computers actually work (employingactual storage locations and sequential operation) and thusproduce code likely to be much faster and more efficientthan that produced by functional languages.Further ReadingBird, R. Introduction to Functional Programming Using Haskell. 2nded. London: Prentice Hall, 1998.Hudak, Paul. The Haskell School of Expression: Learning FunctionalProgramming through Multimedia. New York: Cambridge UniversityPress, 2000.Michaelson, Greg, Phil Trinder, and Hans-Wolfgang. Loidl, eds.Trends in Functional Programming. 2 vols. Portland, Oreg.:Intellect, 2000.Thompson, S. Haskell. Miranda: The Craft of Functional Programming.2nd ed. Reading, Mass.: Addison-Wesley, 1996.fuzzy logicAt bottom, a data bit in a computer is “all or nothing”(1 or 0). Most decisions in computer code are also all ornothing: Either a condition is satisfied, and execution takesone specified path, or the condition is not satisfied and itgoes elsewhere. In real life, of course, many situations fallbetween the cracks. For example, a business might want totreat a credit applicant who almost qualifies for “A” statusdifferent from one who barely made “B.” While a programcould be refined to include many gradations between B andA, another approach is to express the degree of “closeness”(or certainty) using fuzzy logic.In 1965, mathematician L. A. Zadeh introduced the conceptof the fuzzy set. In a fuzzy set, a given item is notsimply either a member or not a member of a specified set.Rather, there is a degree of membership or “suitability”somewhere between 0 (definitely not a member) and 1 (definitelya member). A program using fuzzy logic must includea variety of rules for determining how much certainty toassign in a given case. One way to create rules is to askexperts in a given field (such as credit analysis) to articulatethe degree of certainty or confidence they would feel in agiven set of circumstances. For physical systems, data canalso be correlated (such as the relationship of temperatureto the likelihood of failure of a component) and used to createa rule to be followed by, for example, a chemical processcontrol system.Fuzzy logic is particularly applicable to the creation ofprograms (see expert system) that are better able to copewith uncertainty and the need to weigh competing factorsin coming to a decision. It can also be used in engineeringto allow designers to specify which factors they wantto tightly constrain (such as for safety reasons) and whichcan be allowed more leeway. The system can then come upwith optimized design specifications. Fuzzy logic has alsobeen applied to areas such as pattern recognition and imageanalysis where a number of uncertain observations mustoften be accumulated and a conclusion drawn about theoverall object.Further ReadingBojadziev, George, and Maria Bojadziev. Fuzzy Logic for Business,Finance, and Management. 2nd ed. Hackensack, N.J.: WorldScientific Publishing Co., 2007.“Fuzzy Logic Tutorial.” Encoder (Seattle Robotics Society). March1998. Available online. URL: http://www.seattlerobotics.org/encoder/mar98/fuz/flindex.html. Accessed August 4,2007.Mendel, Jerry M. Uncertain Rule-Based Fuzzy Logic Systems: Introductionand New Directions. Upper Saddle River, N.J.: PrenticeHall PTR, 2000.Nguyen, Hung T., and Elbert A. Walker. A First Course in FuzzyLogic. 3rd ed. Bocal Raton, Fla.: Chapman & Hall/CRC,2006.Sanchez, E. Fuzzy Logic and the Semantic Web. Amsterdam: Elsevier,2006.