I Soft Computing Approach to Pattern Classification 1.1 Introductio As the primary concern of soft computing approach to pattern classification(object recognition)(Zadeh 1977; Pedrycz 1990) is to mimic the cognitive process of human reasoning for classification(recognition), we try to imitate the way human beings perceive(Newell and Simon 1972)different classes of objects(patterns) based on some rough(inexact) information of certain parameters(features). For instance, human being can easily distinguish between a poor person and a rich person just by looking at the individual,s standard of living which cannot be measured explicitly by any specific scale but can onsidering the area where the person lives, the kind of food he/she takes, the kind of education his/her family takes, the kind of clothes he/she wears, the kind of ommodities he/she uses, etc. And such information(knowledge) can be repre sented by a rule(law of implication) as given below RI: if standard of living of a person is high then the person is rich, R2: if standard of living of a person is low then the person is poor; where standard of living high, standard of living low, etc, are linguistic terms and rich, poor are different classes. Each primary linguistic term(i.e. high/low, etc. associated with a term set which is finite and where each primary term in the term set is defined on the same universe of discourse. the said universe of discourse is partitioned (in an overlapped manner) by the finite elements of the term set. For instance, if we place the standard of living between 0 and 10(by some arbitrary scale)then Fig. 1. 1 explains how the elements of the term set partition the universe on which each element of the term set is defined. Each primary term of the term set the degree of uncertainty of the elements of the said universe to become member of either of the fuzzy set(fuzzy set of low/fuzzy set of medium/fuzzy set of high Now, instead of having one-dimensional implications (i.e. R, and r2)we can have multidimensional implication for representing our knowledge(information) For instance R3: if(behavior of a person is smart, appearance of a person is beautiful)then he/she becomes a candidate for interview of a personal assistant of a firm where t is transpose Usually, the above type of rule is read as R4: if behavior of a person is smart and appearance of a person is beautiful ther he/she becomes a candidate for interview of a personal assistant of a firm Such one-dimensional implication (i.e. R4)is a kind of interpretation(see Eq (A 1)of Appendix-A) of the said multi-dimensional form (i.e. R3) of an plication Here, according to the one-dimensional form of an implication, we have two antecedent clauses(e.g. smart behavior and beautiful appearance)which can be represented by two fuzzy sets defined over two different universe of discourses In the consequent part, we always have single clause which can be represented by a1.1 Introduction As the primary concern of soft computing approach to pattern classification (object recognition) (Zadeh 1977; Pedrycz 1990) is to mimic the cognitive process of human reasoning for classification (recognition), we try to imitate the way human beings perceive (Newell and Simon 1972) different classes of objects (patterns) based on some rough (inexact) information of certain parameters (features). For instance, human being can easily distinguish between a poor person and a rich person just by looking at the individual’s standard of living which cannot be measured explicitly by any specific scale but can be indirectly estimated by considering the area where the person lives, the kind of food he/she takes, the kind of education his/her family takes, the kind of clothes he/she wears, the kind of commodities he/she uses, etc. And such information (knowledge) can be repre￾sented by a rule (law of implication) as given below. R1: if standard of living of a person is high then the person is rich, R2: if standard of living of a person is low then the person is poor; where standard of living high, standard of living low, etc., are linguistic terms and rich, poor are different classes. Each primary linguistic term (i.e. high/low, etc.) is associated with a term set which is finite and where each primary term in the term set is defined on the same universe of discourse. The said universe of discourse is partitioned (in an overlapped manner) by the finite elements of the term set. For instance, if we place the standard of living between 0 and 10 (by some arbitrary scale) then Fig. 1.1 explains how the elements of the term set partition the universe on which each element of the term set is defined. Each primary term of the term set is represented by a fuzzy set. Between partition there is an overlap which indicates the degree of uncertainty of the elements of the said universe to become member of either of the fuzzy set (fuzzy set of low/fuzzy set of medium/fuzzy set of high). Now, instead of having one-dimensional implications (i.e. R1 and R2) we can have multidimensional implication for representing our knowledge (information). For instance, R3: if (behavior of a person is smart, appearance of a person is beautiful)t then he/she becomes a candidate for interview of a personal assistant of a firm; where t is transpose. Usually, the above type of rule is read as R4: if behavior of a person is smart and appearance of a person is beautiful then he/she becomes a candidate for interview of a personal assistant of a firm. Such one-dimensional implication (i.e. R4) is a kind of interpretation (see Eq. (A.1) of Appendix-A) of the said multi-dimensional form (i.e. R3) of an implication. Here, according to the one-dimensional form of an implication, we have two antecedent clauses (e.g. smart behavior and beautiful appearance) which can be represented by two fuzzy sets defined over two different universe of discourses. In the consequent part, we always have single clause which can be represented by a 2 1 Soft Computing Approach to Pattern Classification