1.1 Introduction Fig. 1.1 Overlapped Elements of the term set discourse by the elements of he term set medium Standord of liv ing fuzzy set defined over a finite universe of different classes. The cardinality of the term set of each antecedent clause of an implication determines the number of rules that can be generated. For instance, if we have two antecedent clauses in an implication each having the cardinality 3(say, low, medium and high), then we will have total 3 x 3=9 rules. Note, that the cardinality of a term set defined over a given universe is not unique. Depending upon the need of the problem it determined. It simply indicates the granularity(see Fig. 1. 2) by which we want to partition the given universe to facilitate our representation of perception about grouping of objects(patterns) Depending on whether the universe of discourse is continuous or discrete, we an define the fuzzy sets of the antecedent clause of an implication by two ways. In ase universe is continuous, we may go by functional definition, e.g. a bell-shaped function(see Fig. 1. 1), triangle shaped function( see Fig. 1. 2), trapezoid shaped function or any arbitrary shaped function. In case of discrete universe, we may go by numerical definition. In this case, the grade of membership function of a fuzzy et is represented by a one-dimensional array of numbers. The length of the array depends on the degree of discretization. Discretization of a universe of discourse is frequently referred to as quantiza- on. In effect quantization discretizes a universe into a certain number of segments (quantization levels). Each segment is labeled as a generic element of a discrete niverse. A fuzzy set is then defined over the said discrete universe by assigning grade of membership values to each generic element of the discrete universe. The consequent clause of an implication basically represents different classes of objects(patterns) existing over the finite range of the pattern space as shown in Fig. 1.3. The possibility of occurrence of different classes of patterns in the pattern space under a particular observation(it may be imprecise observation, like feature FI is high and feature F2 is low, etc ) may be represented by a fuzzy set defined over the pattern space which is treated as universe of different classes of patterns Now, we try to give a more meaningful discussion on the correspondence between conventional approach to pattern classification and soft computin approach to pattern classification. Note that recognition of the occluded scene consists of model objects is based on the features of few dominant points of the occluded and model objects. The features of patterns and objects are un fiedly treated on a feature(pattern) space spanned by the individual feature axis Further note that the basic concept of supervised approach to pattern classificationfuzzy set defined over a finite universe of different classes. The cardinality of the term set of each antecedent clause of an implication determines the number of rules that can be generated. For instance, if we have two antecedent clauses in an implication each having the cardinality 3 (say, low, medium and high), then we will have total 3 9 3 = 9 rules. Note, that the cardinality of a term set defined over a given universe is not unique. Depending upon the need of the problem it is determined. It simply indicates the granularity (see Fig. 1.2) by which we want to partition the given universe to facilitate our representation of perception about grouping of objects (patterns). Depending on whether the universe of discourse is continuous or discrete, we can define the fuzzy sets of the antecedent clause of an implication by two ways. In case universe is continuous, we may go by functional definition, e.g. a bell-shaped function (see Fig. 1.1), triangle shaped function (see Fig. 1.2), trapezoid shaped function or any arbitrary shaped function. In case of discrete universe, we may go by numerical definition. In this case, the grade of membership function of a fuzzy set is represented by a one-dimensional array of numbers. The length of the array depends on the degree of discretization. Discretization of a universe of discourse is frequently referred to as quantiza￾tion. In effect quantization discretizes a universe into a certain number of segments (quantization levels). Each segment is labeled as a generic element of a discrete universe. A fuzzy set is then defined over the said discrete universe by assigning grade of membership values to each generic element of the discrete universe. The consequent clause of an implication basically represents different classes of objects (patterns) existing over the finite range of the pattern space as shown in Fig. 1.3. The possibility of occurrence of different classes of patterns in the pattern space under a particular observation (it may be imprecise observation, like feature F1 is high and feature F2 is low, etc.) may be represented by a fuzzy set defined over the pattern space which is treated as universe of different classes of patterns. Now, we try to give a more meaningful discussion on the correspondence between conventional approach to pattern classification and soft computing approach to pattern classification. Note that recognition of the occluded scene consists of model objects is based on the features of few dominant points of the occluded scene and model objects. The features of patterns and objects are uni- fiedly treated on a feature (pattern) space spanned by the individual feature axis. Further note that the basic concept of supervised approach to pattern classification Fig. 1.1 Overlapped partition of the universe of discourse by the elements of the term set 1.1 Introduction 3