### Table 1: Comparison of different Genetic Codings of the membership functions in a Fuzzy

"... In PAGE 5: ... Figure 4 shows the desired control surface and Fig.5 the evolution of the GA using four different codings for the fuzzy system ( Table1 ). Table 1 shows a comparison of the Mean Squared Error (MSE) and the number of parameters needed for different codings of the fuzzy system.... ..."

### Table 1 Parameters of fuzzy inference systems

"... In PAGE 1: ... Se- lection of important variables and adequate rules is critical for obtaining a good model. The parameters of fuzzy inference systems can be classi ed into four categories ( Table1 ): logic, struc- tural, connection, and operational. Generally speak- ing, this order also represents their relative in uence on system behavior (with logic being the most in u- ential and operational the least).... In PAGE 1: ... Our encoding of solutions (the genome) takes advantage of previous knowledge about the problem, thus reducing the search space while fa- voring the extraction of the most signi cant variables in order to provide more human-comprehensible rules. Referring to Table1 , the evolved parts of the fuzzy system in this work are: the relevant variables, the antecedents and consequents of rules, and the values of input membership functions. Thus, we evolve struc- tural, connection, and operational parameters at the same time.... In PAGE 2: ... Fuzzy system parameters Previous knowledge about the WBCD problem repre- sents valuable information to be used for our choice of fuzzy parameters. Following Table1 , we delineate below the fuzzy system set-up: Low d P High 1 Value 0 Degree of membership Figure 1 Orthogonal membership functions and their pa- rameters, plotted above as degree of membership versus input values. The orthogonality condition means that the sum of all membership functions at any point is one.... ..."

### Table 9 Accuracy of system grading for 50 documents using rough-member- ship vs. rough-fuzzy document grading scheme [18] Domain Accuracy using Accuracy using rough fuzzy membership membership (%)

2005

"... In PAGE 14: ...6% with the ID3 approach. Table9 summarizes the accuracy of our grading function for top 50 documents taken from the misclassification matrices presented earlier. As we can see even for 50 documents the average accuracy across the five domains is 79.... ..."

Cited by 1

### Table 1. Number of truck angle membership functions

"... In PAGE 8: ... Table1 . Number of rules and compression for learned TBU systems #28a#29 Jenkins-Yuhas hand-crafted neural system #28b#29 Learned fuzzy system Fig.... ..."

### Table 1: Parameter classi cation of fuzzy inference systems.

"... In PAGE 1: ... Fuzzy modeling is the task of identifying the parameters of a fuzzy inference system so that a desired behavior is attained. The parameters of fuzzy inference systems can be classi ed into four categories ( Table1 ): logical, structural, connective, and operational. Generally speaking, this order also represents their relative in uence on performance, from most in uential (logical) to least in uential (operational).... In PAGE 3: ... This motivated us to take into account the following ve semantic criteria, de ning constraints on the fuzzy parameters [10,11]: (1) distinguishability; (2) justi able number of elements; (3) coverage; (4) normalization; and (5) orthogonality. Referring to Table1 , and taking into account the above criteria, we delineate below the fuzzy system setup: Logical parameters: singleton-type fuzzy systems; min-max fuzzy operators; orthogonal, trapezoidal input membership functions; weighted-average defuzzi cation. Structural parameters: two input membership functions (Low and High); two output singletons (benign and malignant); a user-con gurable number of rules (based on our previous results [9], we limited the number of rules to be between 1{5).... ..."

### Table 2 details a obtained initial fuzzy system with 146 correctly classified patterns and 2 features and 15 rules. Fig. 5 gives the membership functions of the fuzzy classification system.

"... In PAGE 6: ...ules. Fig. 5 gives the membership functions of the fuzzy classification system. Table2 Initial fuzzy classification system (Iris) The genetic algorithm is used to select fuzzy rules to compose compact fuzzy system from the initial fuzzy system detailed in Table2. The parameters of the genetic algorithm are: the population size is 20, the ... In PAGE 6: ...ules. Fig. 5 gives the membership functions of the fuzzy classification system. Table 2 Initial fuzzy classification system (Iris) The genetic algorithm is used to select fuzzy rules to compose compact fuzzy system from the initial fuzzy system detailed in Table2 . The parameters of the genetic algorithm are: the population size is 20, the ... ..."

### Table 4: Trapezoidal membership function de nitions of the fuzzy controller. point compliance. The FC was implemented in ANSI-C, and was compiled with a Logical Systems C compiler. A real-time sampling frequency of 150 Hz was attained. To achieve this frequency, the rules and fuzzi cation and defuzzi cation procedures were implemented as macros. This avoids the time wasted with parameter passing and stack operations due to function calls.

### Table 1 Parameter classi cation of fuzzy inference systems. Class Parameters

"... In PAGE 4: ... One of the major problems in fuzzy modeling is the curse of dimensionality, meaning that the computation requirements grow exponentially with the number of variables. The parameters of fuzzy inference systems can be classi ed into four categories ( Table1 ): logical, structural, connective, and operational. Generally speaking, this order also represents their relative in uence on performance, from most in uential (logical) to least in uential (operational).... In PAGE 9: ...Table1 ). We then focus our attention on structural and connective parameters, presenting the three major evolutionary approaches: Michigan, Pittsburgh, and iterative rule learning.... In PAGE 9: ...1 Applying evolution to fuzzy modeling Depending on several criteria|including the available a priori knowledge about the system, the size of the parameter set, and the availability and com- pleteness of input/output data|arti cial evolution can be applied in di erent stages of the fuzzy parameters search. Three of the four types of fuzzy param- eters in Table1 can be used to de ne targets for evolutionary fuzzy modeling: structural parameters, connective parameters, and operational parameters. As noted in Subsection 1.... In PAGE 12: ...embership value of 0.8 entails a High membership value of 0.2). Referring to Table1 , and taking into account the above criteria, we delineate below the fuzzy system set up:... ..."

### Table 2 An example fuzzy membership matrix

"... In PAGE 10: ... Example 2. Let the output of a fuzzy analysis performed on the dissimilarity matrix of a CMSD problem is as presented in Table2 , where c1, c2, c3 represent the possible clusters of the system. In this output, we read that it is 50% beneficial for the part 1 to be in cluster c1, 20% beneficial to be in cluster c2 and 30% beneficial to be in cluster c3 in terms of operational similarities.... In PAGE 11: ...nvolved in the FMS cell (writing new CNC programs, new fixtures, tools, etc.). Example 3. Let the threshold value be 15 and the product variety costs and fuzzy membership matrix values of a problem be as given in Table2 . Each part is assigned to the cluster where it has the greatest membership value.... In PAGE 13: ... Example 5. Let the parts, p8, p9 and p11 of Table2 have an operation on a candidate machine, and hence they are the candidates to change clusters. Let f 2 = 3, and all the cells be open.... ..."