### Table 1. Complementary features of ANN and FIS

"... In PAGE 5: ... Neuro-Fuzzy (NF) System We define a NF [6] system as a combination of ANN and Fuzzy Inference System (FIS) [9] in such a way that neural network learning algorithms are used to determine the parameters of FIS. As shown in Table1 , to a large extent, the drawbacks pertaining to these two approaches seem largely complementary. Table 1.... ..."

### Table 5: Fuzzy and neuro-fuzzy software systems.

2003

"... In PAGE 22: ...upports independent rules (i.e., changes in one rule do not effect the result of other rules). FSs and NNs differ mainly on the way they map inputs to outputs, the way they store information or make inference steps. Table5 lists the most popular software and hardware tools based on FSs as well as on merged FSs and NNs methodologies. Neuro-Fuzzy Systems (NFS) form a special category of systems that emerged from the integration of Fuzzy Systems and Neural Networks [65].... ..."

Cited by 2

### 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. Simulation results of fuzzy system. Fuzzy Inference System

"... In PAGE 5: ... First, the fuzzy system and the PNN are exploited for the comparison of the proposed model, which has high accuracy and superior generalization capabilities. Table2 provides simulation results of the fuzzy sys- tem only. Triangular and Gaussian MF, and conse- quent polynomials of fuzzy rules are considered as modeling options.... ..."

### 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 IV: The confusion matrix of the fuzzy inference system

### Table 5 Fuzzy inference rules for FIA

2003

"... In PAGE 8: ... In this article, we use the algebraic product operation to compute the matching degree. Table5 shows the fuzzy logic rules defined by the domain experts for FIA. The output term layer performs the fuzzy OR operation to integrate the fired rules which have the same Fig.... ..."

Cited by 3

### TABLE I NAME, TYPE, AND PARAMETERS OF THE LINGUISTIC VARIABLES FOR EACH FUZZY INFERENCE SISTEM. THE FIRST EIGHT ROWS ARE FOR THE AGREEMENT SIDE, THE REST ARE FOR THE NONAGREEMENT SIDE. NOTE: TRAP=TRAPEZOIDAL, TRIANG=TRIANGULAR. FIS

### 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).... ..."