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Pablo D. Slemenson“Lógica de lo preconciente”goes considerably beyond its place in fuzzy logic. This more general theory leads totwo linked methodologies--granular computing (GrC) and computing with words(CW). In CW, words play the role of labels of granules and the initial and terminaldatasets are assumed to consist of propositions expressed in a natural language. Theinput interface serves to translate from a natural language (NL) to a generalizedconstraint language (GCL), while the output interface serves to re-translate from GLCto NL. Internally, granular computing is employed to propagate constraints frompremises to conclusions. The importance of the methodologies of granular computingand computing with words derives from the fact that they make it possible to conceiveand design systems that achieve high MIQ (machine intelligence quotient) bymimicking the remarkable human ability to perform complex tasks without anymeasurements and any computations. Although GrC and CW are intended to deal withimprecision, uncertainty, and partial truth, both are well-defined theories built on amathematical foundation. In coming years, they are likely to play an increasinglyimportant role in the conception, design, construction, and utilization ofinformation/intelligent systems.The Concept of Similarity in Diagnosis and RecognitionThe Concept of Similarity(Professor Lotfi A. Zadeh)(ARO) DAAH 04-961-0341, Berkeley Initiative on Soft Computing, British Telecom,(NASA) NAC2-1177, and (ONR) N00014-96-1-0556The concept of similarity plays a crucial role in object recognition and fault diagnosis.In object recognition, the process consists of comparing and contrasting the objectunder scrutiny with the elements in an object space. In fault diagnosis, e.g., indifferential diagnosis of diseases of an organ, the process consists of finding the best fitbetween the symptoms of the patient and the symptoms of various diseases of theorgan. We focus here on two general methods to define similarity of objects: settheoreticand metric. (1) In set-theoretic similarity, let a and b represent two objects andA and B represent the set of features of a and b, respectively. The similarity functions(a,b), representing the measure of similarity of a and b, is a function of AÇB, A-B andB-A, i.e., s(a,b) = f(AÇB, A-B, B-A). The function f must be defined so that it wouldreflect the semantics of similarity in the application. For instance, if a and b are twocampsites and A and B are their respective set of features, then a user-defined functionApendice 316
Pablo D. Slemenson“Lógica de lo preconciente”f will represent the degree to which a and b are considered similar. f is an increasingfunction of the size of AÇB, and a decreasing function of the size of A-B and B-A. (2)In metric similarity, objects are assumed to have features that are describable in crisp orfuzzy measures (linguistic variables). For instance, a human face has features such aseyes, lips, and nose, each of which may have one or more measures e.g., long curved(nose), fat (lips), and large brown (eyes). Similarity of objects is defined in terms ofsimilarity of their features. Similarity of features is defined with respect to similarity offeature measures. In most applications, one must apply both types of similarity. Type 1similarity is applicable in cases where presence or absence of features play a role. Type2 similarity is applicable in cases where a feature may have one or more measures andthe measures take on crisp or fuzzy values. The feature measures of an object arecombined to obtain a measure for the object to make decisions as the outcome ofdiagnosis or recognition. The combination method depends heavily on theapplication/user. 1StaffThe Roles of Soft Computing and Fuzzy Logic in the Conception, Design, andUtilization of Information/Intelligent Systems(Professor Lotfi A. Zadeh)(ARO) DAAH-04-961-0341, Berkeley Initiative on Soft Computing, British Telecom,(LLNL) B-291525, (NASA) NAC2-1177, and (ONR) N00014-96-1-0556Soft computing (SC) is a consortium of methodologies that provides a foundation forthe conception, design, and deployment of intelligent systems. The principal membersof SC are fuzzy logic (FL), neurocomputing (NC), evolutionary computing (EC), andprobabilistic computing (PC), with PC subsuming evidential reasoning, management ofuncertainty, and parts of machine learning theory. Within SC, the main contribution ofFL is a methodology for dealing with imprecision, approximate reasoning, fuzzyinformation granulation, and computing with words; that of NC is systemidentification, learning, and adaptation; that of EC is systematized random research,tuning, and optimization; and that of PC is decision analysis and management ofuncertainty. The essence of soft computing is that unlike the traditional, hardcomputing, soft computing is aimed at an accommodation with the pervasiveimprecision of the real world. Thus, the guiding principle of soft computing is: exploitthe tolerance for imprecision, uncertainty, and partial truth to achieve tractability,Apendice 317
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