P. Thrift. Fuzzy logic synthesis with genetic algorithms. In Proc. Fourth International Conference on Genetic Algorithms (ICGA'91), pages 509--513, San Diego, USA, 1991. Morgan Kaufmann.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... an evolution strategy example, and [97] 201] for genetic algorithm examples) Similarly, both the rule base and membership functions of fuzzy systems can be optimized by evolutionary algorithms, typically yielding improvements of the performance of the fuzzy system (e.g. 202] 203] 204] [205], 206] The interaction of computational intelligence techniques and hybridization with other methods such as expert systems and local optimization techniques certainly opens a new direction of research towards hybrid systems that exhibit problem solving capabilities approaching those of ....

P. Thrift, "Fuzzy logic synthesis with genetic algorithms," In Belew and Booker [59], pp. 514--518.

....Though simple, this is a typical optimal control problem and has a well known solution (the bang bang rule [2] This system is simulated using Euler s method, i.e. taking time steps of t sec. and applying Newton s Laws: x t x t v t ( t t F t m ( t t As in [4] and [5] we consider t=0.02 sec. and m=2.0 kg. 3.2. Designing a Fuzzy Logic Controller As an optimal control problem, the cart centering problem is well suited for fuzzy control. The development of an FLC for this system involves the following three steps [6] a) Determine condition (input) ....

....PL IF pos IS NS THEN for IS PL IF pos IS NL THEN for IS PL where pos, vel and for stand for position, velocity and force respectively. The FLC described above is not the optimal one. Improvements in the rule base or in the interpretation of the linguistic terms may be done by means of GAs (see [4], 5] 6] 7] We propose the use of GP to produce rulebases that can be used as a starting point for further refinements by a human expert or even as a final solution. 4. Evolutionary Approach The genetic programming model is exposed in this section. First, the encoding is described. Next, ....

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Thrift, P. Fuzzy Logic Synthesis with Genetic Algorithms. In Belew R.K., Booker L.B. (Eds.), Procs. of the Fourth International Conference on Genetic Algorithms, Morgan Kaufmann Pub., San Mateo CA. Pages 509-513, 1991.

....backward, turn left or turn fight) The genetic competition occurs among sets of behavior rules (plan) after testing the plans. The main problem in this approach is that it has only been tested on a simulator. Some works have also been made in the genetic evolution of fuzzy rules. For instance, in [14] a genetic algorithm for the design of the fuzzy rules is presented to center a cart by applying a single force. The robot that has been used is the mini robot Khepera [9] which is a commercial mini robot developed at LAMI (EPFL, Lausanne, Switzerland) This robot has a circular shape with a ....

....laws of a real robot such as inertia, friction, failures of the hardware, etc. 3.2. Adaptation of fuzzy rules Our first goal was to test if the rules obtained by means of genetic evolution were able to control successfully an autonomous robot as it has been probed in other environments, [6,14]. So, the robot was given some fixed concepts such as near, far, etc. for the sensors and slow and fast for the motors. The genetic program should be able to successfully combine these concepts. The robot was located in a simple environment. It consisted of a rectangular area with two obstacles ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms, in: Proceedings of the Third International Conference on Genetic Algorithms 1993, pp. 509-513.

....in general decisions taken using crisp thresholds are dangerous in a number of real world applications, we have moved our attention to fuzzy rules, for their intrinsic interpolative behavior. The idea of using evolutionary algorithms to design fuzzy systems date from the beginning of the Nineties [5,12] and a fair body of work has been carried out throughout the past decade [6,7,4] The approach we followed is largely based on the development of a previous work on the evolution of fuzzy controllers [11] Based on that work, we define a classifier as a rule base, of up to 256 rules, each ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo, CA, 1991. Morgan Kaufmann.

....techniques such as neural networks [9] 17] or genetic algorithms (GAs) 7] 13] 19] have been developed to perform this task. Within them, we can distinguish between two di erent deriving approaches: Learning process: It relates to the task of directly obtaining the fuzzy rule surface [20], 25] or deep structures [21] from the available data. Tuning process: It assumes the existing of a previous definition for both structures provided by learning processes or experts and adjusts them with slight modi cations to increase the system performance [14] 15] Traditionally, the ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms, in R.K. Belew, L.B. Booker (Eds.), Proceedings of the 4th International Conference on Genetic Algorithms, San Mateo, CA, USA (Morgan Kaufmann Publishers, 1991) 509-513.

....However, the rules learnt by classical classifier systems are purely symbolic and rely on two valued classical logic their left hand side is either true or false. The only exception to this point is research in fuzzy controllers. For example, Valenzuela [VA91] and similarly Thrift [TH91] and Karr [KA91] use genetic algorithms to learn fuzzy rules and membership functions of fuzzy sets for designing control strategies. However, although their research is similar to our research in the sense that it integrates approximate reasoning techniques and genetic algorithms, there are two ....

Thrift, P.: "Fuzzy Logic Synthesis with Genetic Algorithms", in Proc. Fourth Int. Conf. on Genetic Algorithms, Morgan Kaufmann Publishers, pp. 509-513, 1991.

....KB depends on the concrete application. This makes the accuracy of the FRBS directly depend on its composition. Many approaches have been proposed to automatically learn the KB from numerical information. Most of them have focused on the Rule Base (RB) learning, using a predefined Data Base (DB) [2, 6, 12, 19, 24, 25, 26, 36, 38]. This operation mode makes the DB have a significant influence on the FRBS performance. In fact, some studies have showed that the system performance is much more sensitive to the choice of the semantics in the DB than to the composition of the RB [4, 11, 39] The usual solution to improve the ....

....the values of the system parameters by an uniform distribution of the linguistic terms into the variable universe of discourse. The RB learning methods are based on different techniques such as ad hoc data driven algorithms [2, 12, 26, 38] least square methods [2] Simulated Annealing [6] and GAs [19, 24, 25, 36]. Figure 1 a graphically shows this type of KB learning. This operation mode makes the DB have a significant influence on the FRBS performance. In fact, studies such as the ones developed in [4, 39] show, for the case of Fuzzy PI Controllers, that the system performance is much more sensitive to ....

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P. Thrift, Fuzzy logic synthesis with genetic algorithms, Proc. Fourth International Conference on Genetic Algorithms (ICGA'91) (1991) 509513

....may have similar performance) and deceptive, since a little modi cation may cause huge e ects on the performance of each system. The use of genetic algorithms to automatically adjust (part of) the parameters of a fuzzy system has attracted attention of researches from di erent engineering areas [3], 4] 5] 6] 7] 8] As shown in Herrera and Verdegay [9] genetic algorithms can be considered as ecient techniques for selecting high performance parameters to design a fuzzy system. However, some factors must be carefully analyzed in the process of fuzzy system design. The most important ....

P. Thrift, \Fuzzy logic synthesis with genetic algorithms," in Proceedings of the Fourth International Conference on Genetic Algorithms, 1991, pp. 509 - 513.

.... user defined membership function and rules) With the availability of a versatile yet efficient optimization method (GA) optimal FLCs for dynamic motion planning problems can be developed, like they have been used in other applications of FLCs, such as the cart pole balancing [10] cart centering [19], and others [9, 13] In the present study, we concentrate on dynamic motion planning (DMP) problem, where the objective is to find an obstacle free path between a starting point and a destination point, requiring the minimum possible time of travel. Since the DMP problem is unrealistic to solve ....

Thrift P., Fuzzy logic synthesis with genetic algorithms, Proc. of the Fourth Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo CA, 509-513, 1991.

....It is a classical representation used in different GFSs. A chromosome is obtained from the decision table by going row wise and coding each output fuzzy set as an integer or any other kind of label. It is possible to include the no output definition in a certain position, using a null label ([62, 78]) Relational matrices. Occasionally GAs are used to modify the fuzzy relational matrix (R) of a Fuzzy System with one input and one output. The chromosome is obtained by concatenating the m n elements of R, where m and n are the number of fuzzy sets associated with the input and output ....

....evaluate P(t 1) and (c) t = t 1. 4. Stop. 6.5 An Example of GFS with Pittsburgh Approach This section describe, in a few lines, one of the GFSs previously cited, specifically a GFS learning RBs and representing the rule base with a decision table. This method was proposed by Philip Thrift ([78]) This example will be analyzed according to the keys of the learning process, the population of potential solutions, the set of evolution operators and the performance index. Given a single output FRBS with n input variables, a fuzzy partition is defined for each variable (n 1 fuzzy ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proc. ICGA'91, pages 509--513, Los Altos, CA, 1991. Morgan Kaufmann.

....1 shows the main characteristics of the methods considered (a short description to each of them can be consulted in Appendix A) Table 1: Summary on the analyzed learning methods and their main characteristics Ref. Method Modeling Type Algorithm Type [34] WM LM AHDD [7] COR LM AHDD SA [32] T LM GA IL IS TBP TAP ET PT LH GH SC DC WR [11] M L Tun ILM GA X X X [21] LMe ILM GA X X X X [11] M L ILM AHDD GA X X X X X [9] LH Tun ILM GA X X X X XRB [12] ALM ILM AHDD GA X Xs [25] NIT ILM AHDD X XKB Xa X WR ILM GA X X Constrains in the learning (see [1] 3] WCA FM AHDD Hard ....

....does, a combinatorial process (performed by a Simulated Annealing algorithm in this case) is developed to obtain the combination of rules (one per group) with the best global performance, even though they are not the best in the corresponding groups. The method proposed by Thrift (T method) [32] is based on a Genetic Algorithm (GA) that encodes all the cells of the complete decision table in the chromosome. In this way, the method establishes a mapping between the set of linguistic terms associated to the output variable and an ordered integer set (containing one more element encoding ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms, in R.K. Belew, L.B. Booker (Eds.), Proceedings of the 4th International Conference on Genetic Algorithms, San Mateo, CA, USA (Morgan Kaufmann Publishers, 1991) 509-513.

....develop automatic techniques for performing this task. In this sense, a large quantity of methods has been proposed to automatically generate fuzzy rules from numerical data. Usually they make use of complex rule generation mechanisms such as neural networks [10, 11] genetic algorithms [2, 4, 5, 17], fuzzy clustering [3, 20] etc. Opposite to them, a family of ecient and simple methods guided by covering criteria of the data in the example set, called ad hoc data driven methods , has been proposed in the literature [6, 9, 12, 19] They are characterized by being methods based on a short ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms, Proceedings of the 4th International Conference on Genetic Algorithms, 1991, pp. 509-513.

....develop automatic techniques for performing this task. In this sense, a large quantity of methods has been proposed for automatically generating fuzzy rules from numerical data. Usually they make use of complex rule generation mechanisms such as neural networks [7, 8] genetic algorithms [3, 4, 12], fuzzy clustering [2, 15] etc. Opposite to them, a family of ecient and simple methods, called Ad Hoc Data Driven Methods , has been proposed in the literature [1, 9, 14] Under this name, those methods are collected which are based on processes where the learning of the fuzzy rules is guided ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms, Proc. of the 4th Int. Conf. on Genetic Algorithms, 1991, pp. 509-513.

.... any inductive LGR method to build the HRB, based on the existence of a set of input output data E TDS and a previously de ned DB(1;n(1) In order to illustrate this situation, two LRG methods have been used in [7] the one proposed by Wang and Mendel in [14] and the one proposed by Thrift in [13]. This Two level HSLR LM was extended in [8] by considering it as an iterative process. While the former methodology was thought as a simple descriptive re nement of linguistic models, the Iterative HSLR LM (I HSLR LM) is viewed as an accurate re nement of those models, which preserves HSLR LM ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms. Proceedings of Fourth International Conference on Genetic Algorithms (ICGA'91), Morgan Kauman Pub. (1991) 509-513.

....depends on the concrete application, and this makes the accuracy of the FRBS directly depend on its composition. Many approaches have been proposed to automatically learn the KB from numerical information. Most of them have focused on the Rule Base (RB) learning, using a prede ned Data Base (DB) [2, 6, 12, 17, 21, 22, 23, 31, 33]. This operation mode makes the DB have a signi cant in uence on the FRBS performance. In fact, some studies have showed that the system performance is much more sensitive to the choice of the semantics in the DB than to the composition of the RB [4, 11, 34] The usual solution for improving the ....

....the values of the system parameters by an uniform distribution of the linguistic terms into the variable universe of discourse. The RB learning methods are based on di erent techniques such as ad hoc data driven algorithms [2, 12, 23, 33] least square methods [2] Simulated Annealing [6] and GAs [17, 21, 22, 31]. Figure 1 a graphically shows this type of KB learning. This operation mode makes the DB have a signi cant in uence on the FRBS performance. In fact, studies such as the ones developed in [4, 34] show, for the case of Fuzzy PI Controllers, that the system performance is much more sensitive to ....

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P. Thrift, Fuzzy logic synthesis with genetic algorithms, Proc. Fourth International Conference on Genetic Algorithms (ICGA'91) (1991) 509513 21

.... formed by the rule best covering 11 Table 1: Learning and Tuning Methods used Reference Author(s) of the Method Technique used [35] Wang and Mendel Ad hoc Data Covering [36] Nozaki, Ishibuchi, and Tanaka Ad hoc Data Covering [37] Shann and Fu Neural Network [38] Jang (ANFIS) Neural Network [39] Thrift Genetic Algorithm [40] Liska and Melsheimer Genetic Algorithm [15] Gonz alez and P erez (SLAVE) Genetic Algorithm [20] Cord on and Herrera (D MOGUL) Ad hoc DC Genetic Algorithm a [18] Cord on and Herrera (WM ALM) Ad hoc DC Genetic Algorithm a [38] Jang (ANFIS for tuning) Neural ....

....Fuzzy Systems is presented in Appendix B. In the following we shall review several methods based on GAs under the Pittsburgh and IRL approaches. III.C.1 Thrift s Learning Method This method is based on encoding all the cells of the complete decision table in the chromosomes. In this way, Thrift [39] establishes a mapping between the label set associated to the system output variable and an ordered integer set (containing one more element and taking 0 as its rst element) representing the allele set. An example is shown to clarify the concept. Let fNB;NS;ZR;P S; PBg be the term set associated ....

Thrift, P. (1991). Fuzzy logic synthesis with genetic algorithms. Proc. of the 4th Int. Conf. on Genetic Algorithms, pp. 509-513.

....85, 227, 238] Tarng, Y. S. 592, 231, 717] Tautz, Wilfried, 481] Tazaki, Eiichiro, 118] Teller, Astro, 452] Terano, Toshiro, 186] Tettamanzi, Andrea G. B. 732] Tettamanzi, Andrea, 45] Teuber, P. 609] Themlin, Jean Marc, 709] Thompson, Wiley E. 469, 106] Thrift, Philip, [453] Toliyat, H. A. 504] Tomassini, Marco, 45] Tomizuka, M. 695] Tong, Fu, 209] T orm anen, Pasi, 593, 652, 663] Tozawa, Tatsumi, 708, 716] Trebi Ollennu, A. 614] Tresp, Christopher, 15] Troya, Jos e Ma, 566] Troyo, Jose J. 558] Tsai, C. F. 628] Tsai, Ching Chih, 210] ....

.... lters active, 504] fuzzy, 48] tness fuzzy, 335, 410, 637] food storage, 388] fussy systems rule based, 633] fuzzy , 658] fuzzy rules, 618] fuzzy classi cation, 22, 639] fuzzy control, 71] fuzzy data, 671] fuzzy GA, 506, 655] fuzzy inference, 470, 477] fuzzy logic, [319, 320, 345, 353, 453, 672, 687, 448, 355, 363, 439, 341, 690, 349, 694, 356, 27, 473, 30, 33, 37, 41, 491, 377, 69, 89, 96, 515, 516, 382, 109, 524, 527, 142, 163, 164, 567, 180, 198, 586, 587, 418, 635, 269, 270, 273, 668] fuzzy logic contraints, 193] control, 704, 471, 67, 72, 86, 383, 124] controllers, 469, 44] ne tuning, 248] production rules, 526] squared, 512] tutorial, 676] fuzzy modeling, 590, 290] fuzzy modelling, 55] fuzzy programming, 300] fuzzy reasoning, 468, 131] fuzzy ....

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Philip Thrift. Fuzzy logic synthesis with genetic algorithms. In Belew and Booker [781], pages 509-513. ga:Thrift91.

....to learn symbolic descriptions instead of numerical values not too much research has been performed in learning production rules, whose semantics deviate from two valued logic. The only exception to this point is research in fuzzy controllers. For example, Valenzuela [20] and similarly Thrift [17] and Karr [13] use genetic algorithms to learn fuzzy rules and membership functions of fuzzy sets for designing control strategies. However, although their research is similar to our research in the sense that it integrates approximate reasoning techniques and genetic algorithms, there are two ....

P. Thrift, "Fuzzy logic synthesis with genetic algorithms," in Proc. 4th Int. Conf. Genetic Algorithms, Morgan Kaufmann Publishers, 1991, pp. 509-513.

....behaviour. All they need is an efficient representation scheme for the chromosome structure as well as a capable fitness function that will lead the genetic search into optimum solutions. After that, it is possible to design the controller. Genetic algorithms can be used to find fuzzy rules [100], to find high performance membership functions for a controller [53] or for both [42, 96] Apart from these approaches, the genetic mechanism has also been used to improve the performance of a specific desicionmaking system built by fuzzy logic [81] A number of heuristic parameters concerning ....

.... a possible chromosome structure can be formed as a string of integers, each of which describes the corresponding output set that is related to the input set (chromosome position) 53] A similar but more complicated method is to use a new special label upon some slots of the chromosome string [100]. This label will indicate that the position with this value has not a fuzzy set entry or in other words it is not needed in the fuzzy rule. With this representation the GA determines the number of necessary rules, since the rules having the value in the action condition can be ignored. ....

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P. Thrift. Fuzzy Logic Synthesis with Genetic Algorithms. Proc. of the Fourth Int. Conf. on Genetic Algorithms, pp. 509--513, 1991.

....[60] in the first stage, and tuning the definition of the membership functions by means of the descriptive genetic tuning process presented in [12, 23] see Section 6) in the second one, and D2. a two stage GFRBS based on obtaining a preliminary FRB by means of Thrift s genetic learning process [58] in the first stage, and refining the definition of the membership functions by means of the same descriptive genetic tuning process used above. On the other hand, when working with the approximate one, the following two multi stage GFRBSs are employed: A1. a two stage GFRBS based on obtaining a ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms. Proc. Fourth International Conference on Genetic Algorithms (ICGA'91) (1991) 509-513.

....is a classical representation used in different GFSs. A chromosome is obtained from the decision table by going row wise and coding each output fuzzy set as an integer or any other kind of label. It is possible to include the no output definition in a certain position, using a null label ( 41, 49] Relational matrices. Occasionally GAs are used to modify the fuzzy relational matrix (R) of a Fuzzy System with one input and one output. The chromosome is obtained by concatenating the m Theta n elements of R, where m and n are the number of fuzzy sets associated with the input and output ....

....ideas may be found in [10, 11, 23, 26] 6 An example of GFS This section will describe, in a few lines, one of the GFSs previously cited, specifically a GFS learning RBs using a Pittsburgh approach and representing the rule base with a decision table. This method was proposed by Philip Thrift ( 49] This example will be analyzed according to the keys of the learning process described in subsection 3.2. Given a single output FRBS with n input variables, a fuzzy partition is defined for each variable (n 1 fuzzy partitions) In this case each fuzzy partition contains five or seven fuzzy ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. Proceedings 4th. International Conference on Genetic Algorithms, Morgan Kaufmann, 1991, 509513.

....some encouraging experimental results are described. 1. Introduction The idea of using evolutionary algorithms to tune parameters of fuzzy software components is relatively recent. The first attempts in this direction were aimed to the synthesis and optimization of fuzzy controllers (Karr 1991, Thrift 1991). Besides control, another area of research is data mining, where evolutionary algorithms are used to optimize queries. This optimization task becomes particularly interesting when queries are vague, database indexing is fuzzy and the data themselves are uncertain (Sanchez and Pierre 1994) ....

....results obtained in the preceding decade by fuzzy controllers hand crafted by experts. The task of using a genetic algorithm or, broadly speaking, an evolutionary algorithm for the design of fuzzy controllers was first undertaken at the beginning of this decade by C. L. Karr (Karr 1991) and P. Thrift (Thrift 1991). Similar work has been conducted by Michael Lee and Hideyuki Takagi (Lee and Takagi 1993a, 1993b) at University of California, Berkeley and by Cezary Janikow (Janikow 1994) at University of Missouri, St. Louis. A common trait among these approaches is that they use very simple shapes for the ....

Thrift, P. (1991) Fuzzy logic synthesis with genetic algorithms. In Proceedings of the Fourth International Conference on Genetic Algorithms (San Mateo, CA, 1991), R. K. Belew and L. B. Booker, Eds., Morgan Kaufmann.

....show some applications of ELF to conceptually interesting problems. EVOLUTIONARY LEARNING AGORITHMS AND FUZZY SYSTEMS Since 1989 [15] GAs have been adopted to identify sub optimal FLCs [20] 18] 16] 19] There have been also proposals to extend the LCS approach to Fuzzy Classifier Systems [21][22][23] Learning could be applied to at least 3 different aspects of an FLC: concept definition, state relevance, and the relationship between state and action. Concept definition People tend to describe behaviors of systems in terms of interpretations of the observed data. In an FLC, labels ....

....it should avoid to waste its time to learn it elsewhere. Learning the state relevance for an FLC corresponds to learning the relevant configurations of the input values. Usually, the approaches concerning Evolutionary Learning of FLCs consider that the FLC covers all the input space (e.g. [22][18] 10] In an FLC, the number of 3 rules covering all the possible combinations of the antecedent values is equal to the product the number of possible values of each antecedent. For three variables with the typical seven values each, we have 343 antecedent configurations. Since we have to ....

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P. Thrift, Fuzzy logic synthesis with genetic algorithms. Proc. of the 4th Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, pp. 509--513, 1991.

....a consequent (rules for a system with two input variables need three coefficients to obtain the output value, as shown in expression 8.7) in [SFH95] a single coefficient is considered for the output. In [CV93] rules with fuzzy inputs and fuzzy outputs (like those in expression 8.6) are used. In [Thr91], GAs are used to modify the decision table of an FLC, which is applied to control a system with two input and one output variables. A chromosome is formed from the decision table by going row wise and coding each output fuzzy set as an integer in 0, 1, n, where n is the number of ....

Thrift P. (1991) Fuzzy logic synthesis with genetic algorithms. In Proceedings 4th. International Conference on Genetic Algorithms, pages 509-- 513. Morgan Kaufmann.

....optimum searching ability of evolutionary algorithms to synthesize and optimize a fuzzy system, The author was sponsored in part by SGSThomson Microelectronics such as a fuzzy rule set or a neuro fuzzy network. This combination has already been investigated by several authors (see for example [4, 12, 6, 7, 3]) and has given quite promising results. Evolutionary algorithms are relatively easy to implement and in general their performance tends to be rather satisfactory in comparison with the small amount of knowledge about the problem they need in order to work; however, typically they would require ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo, CA, 1991. Morgan Kaufmann.

....variables need three coefficients to obtain the output value (as shown in expression 2) In [25] the consequents are constants needing a single coefficient for each consequent. Rules with fuzzy inputs and fuzzy outputs (like those in expression 1) are used in [4] Evolving decision tables. In [27], GAs are used to modify the decision table of an FLC, which is applied to control a system with one output and two input variables. A chromosome is obtained from the decision table by going row wise and coding each output fuzzy set as an integer in 0, 1, n, where n is the number of ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In Proceedings 4th. International Conference on Genetic Algorithms, pages 509--513. Morgan Kaufmann, 1991.

....scattered and loosely interconnected computing resources. 2 EVOLUTIONARY TUNING OF SOFTWARE COMPONENTS Investigation on using EAs to tune software components, let al..one FSCs, is relatively recent. The first attempts aimed to the synthesis and optimization of FSCs were applied to control [6, 16, 8, 5, 15]. Another area in which research is active is data mining, where EAs are used to optimize database queries against completeness and relevance of the results they are able to retrieve [11] A representative overview of current state of the art in the field of evolutionary tuning of fuzzy systems is ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms, San Mateo, CA, 1991. Morgan Kaufmann.

....majority of the approaches belonging to this group are based on learning the consequents of the fuzzy control rules included in the FLC RB. In this way, many of these genetic processes encode the complete system decision table in the chromosomes. There are different methods developing this task [Bon93, HT94, Kar91a, KB93, Thr91] but in many cases the only difference existing among them is the cappability of learning the number of rules forming the RB. This characteristic is presented when there exist a possible alelle representing the absence of consequent for a rule with a concrete antecedent, that is, the absence of ....

....altough the first of them do not encode the complete decision table as we are going to see in the following. The remaining ones commented are able to learn the number of fuzzy rules. In this subsection we are going to study three different approaches. The methods selected were proposed by Thrift [Thr91], Karr [Kar91a] and Bonarini [Bon93] This last one constitutes an original approach for learning FLC RB and differs a lot from the others belonging to this family as we are going to see in the following. The RB derivation method proposed by Thrift This method, as many others belonging to these ....

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Thrift P. (1991) Fuzzy logic synthesis with genetic algorithms. In Proc. Fourth International Conference on Genetic Algorithms (ICGA'91), pages 509-- 513.

....were possible, a string of length 3n represents every possible rule set for the FLC. Once an acceptable rule set was learned with a GA, the selection of high performance membership functions with the rule set is carried out using the above described tuning process. The method proposed by Thrift [Thr91] The method proposed by Thrift is similar to the above proposed by Karr, except that Thrift introduced a new possible value for the consequent of rules, the label . The symbol indicates that there is no fuzzy set entry at a position that it appears. A chromosome is formed from the decision ....

Thrift, P., Fuzzy Logic Synthesis with Genetic Algorithms. Proc. of the Fourth Int. Conf. on Genetic Algorithms. Morgan Kaufmann, 1991, 509-513.

....which determines the degree of dependency with the number of iterations. This property causes this operator to make an uniform search in the initial space when t is small, and a very local one in later stages. The mutation operator selected for C 1 is similar to the one proposed by Thrift in [21]. When a mutation on a gene belonging to the first part of the chromosome is going to be performed, a local modification is developed by changing the current linguistic term to the inmediately preceding or subsequent one (the decision is made at random) When the label to be changed is the first ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms. Proceedings of Fourth International Conference on Genetic Algorithms (1991) 509-513.

....trapezoidal functions are employed. These functions are parameterized with one to four coefficients and each of these coefficients will constitute a gene of the chromosome for the GA. This gene may be a binary code (representing the coefficient) 2, 3, 4] or a real number (the coefficient) 5] In [6], GAs are used to modify the decision table of a FLC, which is applied to control a system with two input and one output variables. A chromosome is formed from the decision table by going rowwise and coding each output fuzzy set as an integer in 0, 1, n, where n is the number of MF defined ....

Thrift P., "Fuzzy Logic Synthesis with Genetic Algorithms ", Proceedings 4th. International Conference on Genetic Algorithms, pp 509-513. Morgan Kaufmann, 1991.

.... Fuzzy Systems There are different aspects on the design of FS and FLCS, as for instance, how to get the set of fuzzy control rules, to decide the number of fuzzy rules, to decide the shape of the membership functions, to tune the fuzzy rules base, etc, in which GA have been successfully applied [Bon93, Cas93, Gey92, 93, Gon93, Her93a, c, Kar91a, b ,c, Kro93, Lee93a, Nom92, Sur93, Tak93, Thr91, Val91a, b]. As it is known, the problem of managing a fuzzy rules base (adquisition, learning, tuning) is of utmost importance in the development of fuzzy systems. In a general learning process we can distinguish different components: 1. A generation method of desirable fuzzy rules able to include the ....

Thrift, P., Fuzzy Logic Synthesis with Genetic Algorithms. Proc. of the Fourth Int. Conf. on Genetic Algorithms, San Diego, 1991, 509-513.

....of a FC could be represented by means of a list of rules, a relational matrix or a decision table. Those systems that work with a decision table (or a relational matrix) based representation will generate a genetic code (chromosome) of fixed length and position de pendent meaning. An example is [2] applying a FC to control a system with two input and one output variables. A chromosome is obtained from its decision table by going rowwise and coding each output fuzzy set as an integer in 0, 1, n, where n is the number of membership functions defined for the output variable of the FLC. ....

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In Proceedings 4th. International Conference on Genetic Algorithms, pages 509-- 513. Morgan Kaufmann, 1991.

....and for f 3 (x; y) 100 generations with 50 individuals. We use 21 samples for the function 1, 2 and 121 samples for the function 3. They are selected evenly in the intervals [0,1] of the input domains. The bits for p are decoded in the following way. p = 0:5 2:5(8p[0] 4p[1] 2p[2] p[3]) 16 We should give p the value greater then 0.5, otherwise the fuzzy sets could not cover all input domains. Table 1. The results for f 1 Table 2. The results for f 2 Run Nfs1 Cost Sum err 1 6 8.40183 0.953839 2 6 8.81053 1.41373 3 6 8.34589 0.985277 4 6 8.34589 0.985277 5 6 8.54158 1.0529 Run ....

P. Thrift, Fuzzy Logic Synthesis with Genetic Algorithms, Proceedings of the 4th International Conference on Genetic Algorithm, pp.509-513, 1991.

....operators are going to be considered: Mutation: Two different operators are used, each one of them acting on a different chromosome part. A short description of them is given below: ffl Mutation on C 1 : The mutation operator selected for C 1 is similar to the one proposed by Thrift in [44]. When a mutation on a gene belonging to the first part of the chromosome is going to be performed, a local modification is developed by changing the current primary fuzzy set to the inmediately preceding or subsequent one (the decision is made at random) When the primary fuzzy set to be changed ....

....(WM) method [45] in the first stage, and defining the Data Base by means of the descriptive genetic tuning process presented in [11, 17] in the second, D2. a two stage GFRBS based on obtaining a complete Knowledge Base by deriving the Rule Base by means of the Thrift s genetic learning process [44] in the first stage, and defining the Data Base by means of the same descriptive genetic tuning process used above, and D3. the three stage descriptive GFRBS design method proposed in [11, 17] On the other hand, when working with the approximate one, the three following multi stage GFRBSs are ....

P. Thrift, Fuzzy logic synthesis with genetic algorithms. Proceedings of Fourth International Conference on Genetic Algorithms (ICGA'91) (1991) 509-513.

....the case of unconstrained free semantics, the same mutation operator designed for this case is used for C 2 . Thus, Michalewicz s non uniform mutation operator is employed. Genetic Fuzzy Identification Process 23 The mutation operator selected for C 1 is similar to the one proposed by Thrift in [36]. When mutation for the C 1 part of the chromosome is going to be performed, a local modification is developed by changing the current linguistic value to one of its neighboring linguistic values (the decision is made at random) When the linguistic value to be changed is the first or last one in ....

Thrift, P. (1991): Fuzzy Logic Synthesis with Genetic Algorithms. Proc. Fourth International Conference on Genetic Algorithms, 509-513.

No context found.

P. Thrift. Fuzzy logic synthesis with genetic algorithms. In Proc. Fourth International Conference on Genetic Algorithms (ICGA'91), pages 509--513, San Diego, USA, 1991. Morgan Kaufmann.

No context found.

Thrift P. (1991), Fuzzy logic synthesis with genetic algorithms, Proc. of Fourth International Conference on Genetic Algorithms (ICGA'91), 509-513.

No context found.

P. Thrift, "Fuzzy logic synthesis with genetic algorithms," in R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms (Morgan Kaufmann, San Mateo, CA, 1991).

No context found.

Thrift P., 1991. Fuzzy logic synthesis with genetic algorithms. Proc. of the 4th Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 509--513.

No context found.

Thrift P., 1991. Fuzzy logic synthesis with genetic algorithms. Proc. of the 4th Int. Conf. on Genetic Algorithms, Morgan Kaufmann, San Mateo, CA, 509--513.

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