A Hybrid Artificial Immune Genetic Algorithm with Fuzzy Rules for Breast Cancer Diagnosis Emad Nabil Department of Computer Science, Faculty of Information Technology, MISR University for Science & Technology, Egypt.
[email protected]
Amr Badr Department of Computer Science, Faculty of Computers and Information, Cairo University, Egypt.
[email protected]
ABSTRACT The automatic diagnosis of breast cancer is an important, real-world medical problem. In this paper we give an introduction to fuzzy systems, genetic algorithms and artificial immune system, and then we introduce a hybrid algorithm that gathers the genetic algorithms with the artificial immune system in one algorithm. The genetic algorithm, the artificial immune system and the hybrid algorithm were implemented and tested on the Wisconsin breast cancer diagnosis (WBCD) problem in order to generate a fuzzy rule system for breast cancer diagnosis. The hybrid algorithm generated a fuzzy system which reached the maximum classification ratio earlier than the two other ones. The motivations of using fuzzy rules incorporate with evolutionary algorithms in the underline problem are attaining high classification performance with the possibility of attributing a confidence measure (degree of benignity or malignancy) to the output diagnosis beside the simplicity of the diagnosis system which means that the system is human interpretable. Key Words: artificial immune system, genetic algorithms, fuzzy systems, breast cancer diagnosis.
1. Introduction
Ibrahim Farag Department of Computer Science, Faculty of Computers and Information, Cairo University, Egypt.
[email protected]
Mohamed Osama Khozium Faculty of Information Technology, MISR University for Science & Technology (MUST), Egypt.
[email protected]
computing with biological mechanisms, which involves the use of information processing capabilities of biological systems to replace or supplement the current silicon-based computers (e.g. Quantum and DNA computing) [12]. Our research point will be under the umbrella of the first approach. In this paper we combine two methodologies which are Genetic algorithms and artificial immune system so as to automatically produce a fuzzy system for breast cancer diagnosis. The major advantage of fuzzy systems is that they favor interpretability [3] and provide what is called confidence measure which means in our case the degree of benignity or malignancy. Finding good fuzzy systems is quite a hard task so; this is where GA and AIS algorithms work, enabling the automatic production of fuzzy systems, based on a database of training cases. In the next three sections we provide a brief overview of fuzzy systems, artificial immune system and genetic algorithms. In section 5 we present our proposed hybrid algorithm between GA and AIS which will be tested on the Wisconsin breast cancer diagnosis (WBCD) problem described in section 6. Section 7 speaks about the evolutionary fuzzy modeling and our algorithm setup. The algorithm testing is delineated in section 8, followed by concluding remarks in Section 9.
2. The fuzzy systems
Computing and engineering have been enriched by the introduction of the biological ideas to help developing solutions for various problems. This can be exemplified by the artificial neural networks (ANN), evolutionary algorithms (EA), artificial life (ALife), and cellular automata (CA). There exist three different approaches, the first is: biologically motivated computing, under this umbrella the EA, ANN and artificial immune system (AIS), the second is computationally motivated biology, where computing provides models and inspiration for biology (i.e. ALife and CA). The third approach is
Fuzzy logic is a computational paradigm that provides a mathematical tool for representing and manipulating information in a way that resembles human communication and reasoning processes [21]. Fuzzy logic is based on the assumption that there is no 100% certainty, i.e. a statement is partially true or false and composed of imprecise concepts. For example, “this person is tall”, see figure 1, where the fuzzy value “tall” applied to the fuzzy variable “length”, the uncertainty is subject to interpretation [3]. A fuzzy variable (also called a linguistic variable) is characterized by: Its tag (i.e.
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length), a set of fuzzy values (also known as linguistic values or labels) and the membership functions of these labels. These latter assign a membership value, µlabel (u) to a given real value within some predefined range called the universe of discourse. In fuzzy logic, Boolean logic operations do not hold, new ones can be defined. There are three basic operations, and, or, and not, which can be defined in fuzzy logic as follows: µA and B (u) = µ A (u) B
3. 4.
The defuzzifier, which translates this latter output into a crisp value. The knowledge base, which contains a set of fuzzy rules (rule base) and a set of membership functions (database).
µ B (u) = min {µ A (u), µ B (u)} B
B
µA or B (u) = µ A (u) µ B (u) = max {µ A (u), µ B (u)} µ not A (u) = ¬ µ A (u)=1- µ A (u) B
B
Where A and B are fuzzy variables [3].
Figure 2: Basic structure of a fuzzy inference system
The decision-making process is performed by the inference engine using the rules contained in the rule base. These fuzzy rules define the connection between input and output fuzzy variables. A fuzzy rule has the form: If antecedent then consequent.
2.1. Automatic approaches to fuzzy modeling The task of identifying the parameters of a fuzzy inference system so that a desired behavior is attained is called fuzzy modeling [22]. With the direct approach, a fuzzy model is constructed using knowledge from a human expert. This task becomes difficult when search space is very large; this is why automatic approaches are used in fuzzy modeling. Selection of relevant variables and adequate rules is critical for obtaining a good system. 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. Fuzzy inference systems parameters can be classified into four categories (Table 1 [14]): logical, structural, connective, and operational. This order is from most influential (logical) to least influential (operational).
Figure 1: Example of a fuzzy variable length which has two possible fuzzy values, labeled short and tall, and orthogonal membership functions, plotted above as degree of membership versus input values. P and d define the start point and the length of membership function respectively. The orthogonality condition means that the sum of all membership functions at any point is one. In the figure, an example: value u is assigned the membership values µshort (u) =0.8 and µtall (u) = 0.2 (as it can be seen µshort (u) + µtall (u) =1). A fuzzy inference system is a rule-based system that uses fuzzy logic, rather than Boolean logic, to reason about data [21]. Its basic structure includes (as depicted in Figure. 2 [3]) four main components: 1. The fuzzifier, which translates crisp (real-valued) inputs into fuzzy values. 2. An inference engine that applies a fuzzy reasoning mechanism to obtain a fuzzy output.
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Table 1: Parameter inference systems
Class Logical Structural
classification
of
fuzzy
Parameters Reasoning mechanism Fuzzy operators Membership function types Defuzzification method Relevant variables Number of membership functions
Connective Operational
selected as memory cells for future pathogens attacks and the rest mature into antibody secreting cells called plasma cells [8, 11, 13].
Number of rules Antecedents of rules Consequents of rules Rule weights Membership function values
3. The Artificial Immune System
Figure 3: Multi-layer structure of the immune system
Figure 4: The clonal selection principle
There are two inter-related systems by which the body identifies foreign materials: the innate immune system and the adaptive immune system, explained in figure 3 [3]. The innate immune system: this name comes from the fact that the human body is born with the ability to recognize certain microbes and immediately destroys them. Our innate immune system can destroy many pathogens on first encounter. The innate immunity is based on a set of receptors known as pattern recognition receptors (PRRs). The adaptive immune system: uses somatically generated antigen receptors which are clonally distributed on the two types of lymphocytes: B cells and T cells. These antigen receptors are generated by random processes and, as a consequence, the general design of the adaptive immune response is based upon the clonal selection of lymphocytes expressing receptors with particular specificities according to the antigens nature [5, 6, 8].
3.2. Somatic hypermutation and repertoire diversity Mutation is random changes, these changes are introduced into the variable region genes and occasionally one such change will lead to an increase in the affinity of the antibody. These higher-affinity variants are selected to enter the pool of memory cells [16]. Due to the random nature of the somatic mutation process, large proportions of mutating genes become non-functional or develop harmful anti-self specificities. Those cells with low affinity receptors, or the self reactive cells, must be eliminated so that they do not significantly contribute to the pool of memory cells. The killing process here maintained by the selection algorithms. For this algorithm to work the receptor population or repertoire has to be diverse enough to recognize any foreign shape, we maintain the diversity by metadynamics. A mammalian immune system contains a heterogeneous repertoire of approximately 1012 lymphocytes in human [8, 9, 10, 12].
3.1. An overview of the clonal selection principle 3.3. Pattern recognition in the immune system The clonal selection principle, or theory, is the algorithm used by the immune system to describe the basic features of an immune response to an antigenic stimulus [7]. Clonal selection establishes the idea that only cells that recognize the antigens will proliferate where the rest will not, as depicted in figure 4 [12]. The most triggered cells
Recognition in the immune system occurs at the molecular level and is based on shape complementarily between the binding site of the receptor and a portion of the antigen called an epitope. While antibodies posses a single kind of receptor, antigens may have multiple
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epitopes, meaning that a single antigen can be recognized by different antibody molecules (figure 5).
Begin t=0; Initialize the initial population p(t) randomly; Identify antigen S; Evaluate affinity p(t)versus S; While (not finished) do Begin t= t+1; Select C(t) from p(t-1); Proportional cloning of C(t) forming C’(t); Mutation C’(t) forming c”(t); Select P(t) from c”(t) and P(t-1); Select memory cell from P(t); Metadymanics; End.
Figure 5: antigen epitope is recognized by an antibody
3.4. Shape-space model and affinities The antigen (Ag) and antibody (Ab) representations will partially determine which distance measure shall be used to calculate their degree of interaction or complementarily (figure 6). The affinity between an antigen and an antibody is related to their distance that can be estimated via any distance measure between two strings (or vectors). If the coordinates of an antibody are given by and the coordinates of an antigen are given by , if antigens and antibodies are represented as sequences of symbols then we can use Hamming shape-space, (Equation 1). When the distance D between two sequences is maximal, the molecules constitute a perfect complement of each other and their affinity is maximal. Equ. (1)
Figure 6: the complementarily relation between the antigen and antibody Shape-spaces that use real-valued coordinates can measure distance in the form of equation (2) which called Euclidean distance. In our algorithms we use the hamming distance (equation 1) Equ. (2)
3.5. The clonal selection algorithm The standard clonal selection algorithm CLONALG [12] can be summarized as follows.
End.
4. Genetic Algorithms (GAs) The Genetic Algorithms (GAs) constitute stochastic evolutionary techniques whose search methods model some natural phenomena which are the genetic inheritance and Darwinian strife for survival [2, 5, 8, 18]. GAs perform a search through a space of potential solutions, which are distinguished by the definition of an evaluation (fitness) function, which plays the role of an environment feedback. GA can be described as follows. Begin t=0; Initialize the initial population p(t) randomly; Evaluate structures in p (t); While (not finished) do Begin t= t+1; Select parents C(t) from p(t1); Crossover and mutate structures in C (t) forming C’ (t); Replace C’ (t) by P (t-1); End. End The genetic algorithm has many variables as the population size, the selection methods, mutation rate and crossover rate. The previous factors have a heavy effect on the GAs performance, i.e., A large population size can enhance the exploration of the landscape, a strong selection algorithm stress the exploitation, the choice of the crossover operator influences the tension between the exploration and exploitation[1, 20] and the mutation rate also affects the GA exploration and exploitation. The
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optimal mutation rate is not only different for every problem but will vary with evolutionary time according to the state of the search and the landscape being searched [14]. This problem will be recovered in our algorithm.
5. The Proposed hybrid algorithm The proposed algorithm modifies clonal selection algorithm mutation method. The mutation in nature occurs at small percentage value = 0.002 and this is rational from the computational point of view to ensure that the good solutions are not distorted too match. However, researches have shown that an initial large mutation rate that decreases exponentially as a function of the generation number improves the convergence speed and accuracy [14]. The initial large mutation rate ensures that a large space is covered, while the mutation rate becomes smaller when the individuals start to converge to the optimum. This is accepted solution for the tradeoff between the exploration and exploitation [12].We used the timeis a positive decaying formula in equation (3) where constant, m(0) is the initial large mutation rate and t is the generation number. The equation is depicted in figure 7. We have imported the crossover operator from the genetic algorithms in order to increase the exploration of the landscape and to add a recombination operator in the clonal selection algorithm.
Begin 1. t= t+1; 2. Select C(t) from p(t-1); 3. Proportional cloning of C(t) forming C’(t); 4. Degraded Proportional Mutation C’(t) forming c”(t); 5. Crossover c”(t) forming C*(t); 6. Select P(t) from c*(t) and P(t1); 7. Select memory cell from P(t); 8. Metadymanics; End. End. As the standard clonal selection algorithm, first the populations of antibodies are randomly generated of certain size then, identify the antigen S after that evaluate the affinity of every antibody versus the antigen S. the algorithm in details is described as follows. 1. 2. 3. 4.
Equ. (3) 5.
6.
Figure 7: The effect of the degraded function on mutation value
7.
The proposed algorithm can be summarized as follows.
8.
Begin t=0; Initialize the initial population p(t) randomly; Identify antigen S; Evaluate fitness p (t) versus S; While (not finished) do
Increments the generation number t by one. Select the highest affinity antibodies from P(t-1) forming C(t). Clone individuals in C(t) proportional to their affinity forming C’ (t). The mutation is applied to C’(t) taking into consideration that the mutation rate are proportional with the affinity of individuals of C’(t) in the same generation, also the mutation degraded from one generation to another. Crossover operator applied after the mutation forming C*(t), and it must be after mutation, this is as if we apply crossover over two clones of same antibody then; no changes will take place. We applied two point crossover for recombination. As a future work adapted crossover can be merged in clonal selection instead of two point crossover. The maturated clones C*(t) plus the previous generation P(t-1) is merged to compose the new population P(t). The new population P(t) is the highest affinity antibodies and this ensure that the elitism principle was taken into consideration. The highest affinity antibodies are selected from P(t) as memory cells in order to be recognizers for future antigens . To keep the diversity of the repertoire and the learning ability for new antigens we replace the lowest affinity members by random generated individuals, this is what called metadynamics.
6. The Wisconsin breast cancer diagnosis problem
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In this section we present the Wisconsin breast cancer diagnosis problem [3] which is the test case of our proposed algorithm. Breast cancer is the most common cancer among women, excluding skin cancer. The presence of a breast mass is an alert sign of a cancer, but it does not always indicate a malignant one. Fine needle aspiration (FNA) is an outpatient procedure that involves using a small-gauge needle to extract fluid directly from a breast mass. FNA procedure over breast masses is a costeffective, non-traumatic, and mostly non-invasive diagnostic test that obtains information needed to evaluate malignancy. The Wisconsin breast cancer diagnosis (WBCD) database [17] is the result of the efforts made at the university of Wisconsin Hospital for accurately diagnosing breast masses based solely on an FNA test. Nine visually assessed characteristics of an FNA sample considered relevant for diagnosis were identified, and assigned an integer value between 1 and 10. The measured variables are as follows: (1) (2) (3) (4) (5) (6) (7) (8) (9)
problem where part or all of the parameters of a fuzzy system constitute the search space.
7.1 Applying evolution to fuzzy modeling Three of the four types of fuzzy parameters in Table 1 can be used to define targets for evolutionary fuzzy modeling: structural parameters, connective parameters, and operational parameters. Logical parameters are usually predefined by the designer based on experience. The evolutionary algorithm is used to tune the knowledge contained in the fuzzy system by finding membership function values (p, d values) and the relevant variables. Evolutionary structure learning is carried out by encoding within the genome an entire fuzzy system this is known as the Pittsburgh approach.
Clump thickness (V1); Uniformity of cell size (V 2); Uniformity of cell shape (V 3); Marginal adhesion (V 4); Single epithelial cell size (V 5); Bare nuclei (V 6); Bland chromatin (V 7); Normal nucleoli (V 8); Mitosis (V 9).
Figure 8: The proposed diagnosis system. Note that the fuzzy subsystem displayed to the left is in fact the entire fuzzy inference system of Figure 2.
The database itself consists of 683 cases; the general form of the database is described in table 2. There exit some previous systems that achieved high classification ration but, these systems look alike black boxes and with no explanation or interpretation about how the decision was taken further, there is no providing with the degree of benignity or malignancy. These two points are covered in this study besides high performance classification ratio. Table 2: the WCBD data representation Case V1 V2 ……. V9 Diagnosis 1 1 2 ……. 8 Benign 2 2 4 ……. 3 Benign … …… ….. ….. …. …. 683 4 8 ….. 1 malignant
7.2. Evolving fuzzy systems for the WBCD problem The solution scheme we propose for the WBCD problem is depicted in Figure 8. It consists of a fuzzy system and a threshold unit. The fuzzy system computes a malignancy value of the malignancy of a case, based on the input values, the threshold unit then outputs a benign or malignant diagnostic according to the fuzzy system’s output. If the malignancy value is less than or equals to 3 it is considered benign case other than diagnosed as malignant one.
7.3. Fuzzy system parameters
7. Evolutionary fuzzy modeling Evolutionary algorithms are used to search large, and often complex, search spaces. They have proven worthwhile on numerous diverse problems and able to find near-optimal solutions with an adequate performance measure. Fuzzy modeling can be seen as an optimization
According to information obtained from previous work [3], we have deduced the following points. • Small number of rules: Systems with no more than four rules have been shown to obtain high performance [4, 19]. • Small number of variables: Rules with no more than four antecedents have proven adequate [4]. • Nature of the input variables: higher-valued variables are associated with malignancy. Some
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• •
•
fuzzy models forgo interpretability in the interest of improved performance. Where medical diagnosis is concerned, interpretability, also called linguistic integrity, is the major advantage of fuzzy systems. This motivated us to take into account the following semantic criteria, defining constraints on the fuzzy parameters [15]: Distinguishability: To what extend the system is understood and has interpretability Justifiable number of elements: The number of membership functions of a variable. This number should not exceed the limit of 7 ± 2 distinct terms. The same criterion is applied to the number of variables in the rule antecedent; this is to be familiar for humans. Orthogonality. For each element of the universe of discourse, the sum of all its membership values should be equal to one (e.g. in figure 1 a short membership value of 0.8 and a tall membership value of 0.2 so summation =1).
7.4. The fuzzy system setup Logical parameters • • • •
Reasoning mechanism: singleton-type fuzzy system, i.e. Output membership functions are real values, rather than fuzzy ones. Fuzzy operators: min. Input membership function type: orthogonal, trapezoidal (like Figure 1). Defuzzification method: weighted average.
Structural parameters • • • •
Relevant variables: there is insufficient a priori knowledge to define them; therefore this will be one of the algorithm’s objectives. Number of input membership functions: two membership functions, denoted Low and High Number of output membership functions: two singletons are used, corresponding to the benign and malignant diagnostics. Number of rules: in our approach, this is a userconfigurable parameter. Will be only one rule. The rule itself is to be found by the genetic algorithm.
Connective parameters • • •
Antecedents of rules: to be found by the algorithm. Consequent of rules: the algorithm finds rules for the benign diagnostic; the malignant diagnostic is an else condition. Rule weights: active rules have a weight of value 1 and the else condition has a weight of 0.25.
Operational parameters
• •
Input membership function values: to be found by the evolutionary algorithm. Output membership function values: following the WBCD database, we used a value of 2 for benign and 4 for malignant.
7.5. The evolutionary algorithm setup We apply Pittsburgh-style structure learning, using our algorithm to search for three parameters. The relevant variables, the input membership function values, and the antecedents of rules. They are constructed as follows: • Membership function parameters. There are nine variables (V1–V9), each with two parameters P and d, defining the start point and the length of the membership function edges, respectively. • Antecedents. The i-th rule has the form:if (V1 is Ai 1 )and…and (V9 is Ai 9 ) then (output is benign) where Aij represents the membership function applicable to variable Vj. Aij can take the values: 1 (Low), 2 (High), or 0 or 3 (Other). • Relevant variables are searched for implicitly by letting the algorithm choose non-existent membership functions as valid antecedents; in such a case the respective variable is considered irrelevant. Parameter Values Bits Quantity Total bits P 1-8 3 9 27 d 1-8 3 9 27 A 0-3 2 9 18 Table 3: Parameters encoding of a genome, Total genome length is 54+18= 72 The parameters encoding are described in table 3, which form a single individual’s genome. Figure 8 shows a sample genome. We used a genetic algorithm with a fixed population size of 200 individuals to evolve the fuzzy inference system, and fitness-proportionate selection. The algorithm terminates when the maximum number of generations is reached.
8. Algorithm Testing The proposed algorithm has been tested on the WSBC problem. The three algorithms have been implemented and have been tested in Wisconsin database. The three algorithms have reached a valid classification ratio equal to 97.36% i.e. 665 valid diagnosis cases from 683 cases. And the results of the three algorithms were depicted in figure 9 and table 7. It is clear that the hybrid algorithms reached the maximum classification ratio in the earlier generations before the GA and the AIS. Also the AIS reached before the GA. Table 4, 5, and 6 represents the
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best fuzzy system developed by the GA, AIS and the hybrid algorithms respectively, including in each system both the database and the rule base.
Table 4: The best evolved fuzzy diagnostic system by the GA
Table 5: The best evolved fuzzy diagnostic system by the AIS
Figure 8: Example of a genome for a rule system. (a) Represents genome encoding. The first 18 positions encode the parameters P and d for the nine variables V1–V9. The rest encode the membership function applicable for the nine antecedents of the rule; (b) is an interpretation of the database and the rule base of the rule system encoded in (a). Table 6: The best evolved fuzzy diagnostic system by the hybrid algorithm
9. Conclusion and Future Work We proposed a modification to the clonal selection algorithm CLONALG [10] which is inspired from the clonal selection principle and affinity maturation of the immune responses. We introduced the adaptability of the mutation rate by simple degrading function as it is not logic that the mutation rate is static through all generations; also we merged the crossover into the CLONALG, Two point crossover applied after the mutation process to increase the exploration of the landscape. The algorithm was tested on Wisconsin breast cancer diagnosis (WBCD) problem and reached the maximum classification ratio in the earlier generations before the GA and the AIS. In fact, there are many parameters which still need for adaptation as the optimal population size, optimal selection method, the number of clones, the number of selected individuals to be cloned, the start mutation rate that degraded with time, the degradation rate, the crossover points (one point, two point…, uniform), the crossover rate, the number of randomly generated individuals in metadynamics and the optimal number of memory cells. . The future work can refine the hybrid algorithm more and more for adaptation to these factors. The number of fuzzy ruled can also be more than one, this increase the classification ratio for sure HBI-38
Table 7: the maturation of the best element of GA, AIS and hybrid algorithm (H) the numbers in table represent the number of valid classification cases according to the WBCD through generations (GN). GN GA AIS H GN GA AIS H 1 235 231 237 14 661 661 665 2 641 639 653 15 661 662 665 3 641 650 657 16 661 662 665 4 652 651 658 17 661 664 665 5 652 654 663 18 661 664 665 6 652 659 665 19 663 664 665 7 660 659 665 20 663 664 665 8 660 661 665 21 664 665 665
9 10 11 12 13
660 660 660 661 661
661 661 661 661 661
665 665 665 665 665
22 23 24 25 26
664 664 664 664 665
665 665 665 665 665
Polytechniques ET Universitaires Romandes, 369–372, 1998.
665 665 665 665 665
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Figure 9: The run of the three algorithms, it is clear that the hybrid algorithm reaches the highest classification ration earlier than both the genetic algorithm and artificial immune system
[12] De Castro L. N. and Timmis J., Artificial Immune Systems A new computational approach, Springer, 2002.
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