Immune Algorithm for Optimization of Membership Function in Fuzzy Models

This paper presents fuzzy models which rules were extracted from numerical data using clonal selection, subtractive, fuzzy C-means, Gustafson–Kessel clustering algorithms, implemented in the MATLAB code. These algorithms were used for the identification of parameters in the fuzzy model Sugeno-type. There are two testing examples: Trip data and DWP data set from the multi-detector sensor. Fuzzy model of the fire risk index was built based on the laboratory data measurements. The results are shown in tables and graphs.

In this paper, we present a scheme to improve immune cloning selection algorithm. The improved algorithm, which is referred to as adaptive cloning selection algorithm (ACSA), is proposed and then applied to function optimization. At first, we present adaptive gene mutation which decides mutation probability of each code point (locus) based on the quality of antibodies and the number of evolution iterations. Secondly, we present an iteratively increasing method from one locus to the all ones, which can be used in function optimization. Then, the cloning selection process of evolution is divided into two-stages. The first step is to increase locus of antibodies. In the other one, the Baldwin effect learning operator is employed. And finally, an experiment is carried out to verify the theoretical analyses on several testing functions.

Error measures for fuzzy linear regression: Monte Carlo simulation approach

We introduce an optimization of fuzzy set-fuzzy systems based on IG (Information Granules). The proposed fuzzy model implements system structure and parameter identification by means of IG and GAs. The concept of information granulation was coped with to enhance the abilities of structural optimization of the fuzzy model. Granulation of information realized with C-Means clustering helps determine the initial parameters of the fuzzy model such as the initial apexes of the membership functions in the premise part and the initial values of polynomial functions in the consequence part of the fuzzy rules. The initial parameters are adjusted effectively with the help of the GAs and the standard least square method. To optimally identify the structure and the parameters of the fuzzy model we exploit GAs with successive tuning method to simultaneously search the structure and the parameters within one individual. We also consider the variant generation-based evolution to adjust the rate of identification of the structure and the parameters in successive tuning method. The proposed model is evaluated with the performance of the conventional fuzzy model.

This paper proposed an a fuzzy inference rule model for decision support to maximize the safe asset management of railway systems by utilizing data information on the climate environmental risks of railway facilities. The state monitoring sensor information of the railway operation line and the operation agency operation handling information were fused, and real-time climate data information was used. Climate condition digital information used anemometer, avalanche, visibility, and earthquake information, while radar, 3D camera, and ultrasonic sensor information were used for information mounted on the train. As a digital intelligence convergence algorithm, a fuzzy inference rule model that processes multiple generation environmental data was proposed. The implemented fuzzy inference rule model can be applied to the train operation management system and can be applied as an asset management and operation management decision-making algorithm of railway facilities.

Identification of interpretable and accurate fuzzy classifiers and function estimators with hybrid methods

Fuzzy systems are widely used in most fields of science and engineering, mainly because the models they produce are robust, accurate, easy to evaluate and capture real-world uncertainty better than do the classical alternatives. We propose a new methodology for structure and parameter tuning of Takagi–Sugeno–Kang fuzzy models using several optimization techniques. The output parameters are determined analytically, by finding the minimum of the root-mean-square error (RMSE) for a properly defined error function. The membership functions are simplified by considering symmetry and equispacing, to reduce the optimization problem of finding their parameters, and allow it to be carried out using the numerical method of gradient descent. Both algorithms are fast enough to finally implement a strategy based on the hill climbing approach to finding the optimal structure (number and type of membership functions) of the fuzzy system. The effectiveness of the proposed strategy is shown by comparing its performance, using four case studies found in current relevant works, to the popular adaptive network-based fuzzy inference system (ANFIS), and to other recently published strategies based on evolutionary fuzzy models. In terms of the RMSE, performance was at least 28% better in all case studies.

This chapter presents two novel approaches for the identification of Takagi-Sugeno fuzzy models with time variant and time invariant features. The mixed fuzzy clustering (MFC) algorithm is used for determining the parameters of Takagi-Sugeno fuzzy models (FMs) in two different ways: (1) MFC FM, where the antecedent fuzzy sets are determined based on the partition matrix generated by the mixed fuzzy clustering algorithm; (2) FCM–UMFC FM, where the input features are transformed using MFC and the antecedent fuzzy sets are derived using fuzzy c-means (FCM). The fuzzy modeling approaches are tested on four health care applications for the classification of critically ill patients: administration of vasopressors in pancreatitis and pneumonia patients, mortality in septic shock and early readmissions. Both approaches increase the performance of Takagi-Sugeno based on FCM, in all datasets. In particular, the best performer, FCM–UMFC FM, achieves notable improvements in the four datasets.

Living in the era of deluge demands for an increase in the application and development of machine learning methods, both in basic and applied research. Among these methods, in the last decades fuzzy inference systems carved out their own niche as (light) grey box models, which are considered more interpretable and transparent than other commonly employed methods, such as artificial neural networks. Although commercially distributed alternatives are available, software able to assist practitioners and researchers in each step of the estimation of a fuzzy model from data are still limited in scope and applicability. This is especially true when looking at software developed in Python, a programming language that quickly gained popularity among data scientists and it is often considered their language of choice. To fill this gap, we introduce pyFUME, a Python library for automatically estimating fuzzy models from data. pyFUME contains a set of classes and methods to estimate the antecedent sets and the consequent parameters of a Takagi-Sugeno fuzzy model from data, and then create an executable fuzzy model exploiting the Simpful library. pyFUME can be beneficial to practitioners, thanks to its pre-implemented and user-friendly pipelines, but also to researchers that want to fine-tune each step of the estimation process.

This paper is concerned with the problem of constructing a fuzzy model from numerical data through a self-organizing counter propagation network (SOCPN). Two self-organizing algorithms, unsupervised USOCPN and supervised SSOCPN, are introduced. SOCPN can be employed in two ways. It can be used as a knowledge extractor by which a set of rules are generated from the available numerical data set. The generated rule-base is then utilized by a fuzzy reasoning model. It can also be used as an online adaptive fuzzy model in which the rule-base in terms of connection weights is updated successively in response to the incoming measured data. The simulation results on some well studied examples are given.

Research on multiobjective optimization (MO) becomes one of the hot points of intelligent computation. Compared with evolutionary algorithm, the artificial immune system used for solving MO problems (MOPs) has shown many good performances in improving the convergence speed and maintaining the diversity of the antibody population. However, the simple clonal selection computation has some difficulties in handling some more complex MOPs. In this paper, the simple clonal selection strategy is improved and a novel immune clonal algorithm (NICA) is proposed. The improvements in NICA are mainly focus on four aspects. 1) Antibodies in the antibody population are divided into dominated ones and nondominated ones, which is suitable for the characteristic of one multiobjective optimization problem has a series Pareto-optimal solutions. 2) The entire cloning is adopted instead of different antibodies having different clonal rate. 3) The clonal selection is based on the Pareto-dominance and one antibody is selected or not depending on whether it is a nondominated one, which is different from the traditional clonal selection manner. 4) The antibody population updating operation after the clonal selection is adopted, which makes antibody population under a certain size and guarantees the convergence of the algorithm. The influences of the main parameters are analyzed empirically. Compared with the existed algorithms, simulation results on MOPs and constrained MOPs show that NICA in most problems is able to And much better spread of solutions and better convergence near the true Pareto-optimal front.

In this dissertation, three different evolutionary algorithms are proposed by hybridizing the Taguchi method, chaos disturbance method, multilevel immune algorithm (MIA), clonal selection algorithm (CLONALG), and artificial bee colony algorithm (ABC). Including multi-level immune algorithm and clonal selection algorithm is derived by the immune algorithm. These algorithms are thus called HTCMIABC, HTCABC, and HCABC. The HTCMIABC comprises two main different phases. We use the MIA as the recognition phase to balance local and global search and accelerate the search speed to enhance the evolutionary phase. Second, the evolutionary phase is built on the ABC and chaos disturbance operation to have the capabilities of exploration and exploitation. Moreover, the Taguchi method and crossover operation are inserted between the recognition phase and evolutionary phase for the recombination and diversification of several antibodies to improve the searching ability. In the HTCABC, the chaos search algorithm and adaptive bound method are adopted to improve the ABC performance. Then, the Taguchi method and crossover operation are incorporated into the chaos artificial bee colony (CABC) to accelerate the search capacity. Moreover, the natural phenomenon of the elite strategy is adopted and the recruitment of new scout bees is used for HTCABC, which can maintain the diversity of the population, and escape from local optima. Additionally, there is no complex parameter setting in the algorithm design. In the HCABC, the mutation mechanism of the CLONALG by using the advantages of ABC can improve the capabilities of exploration and exploitation. Finally, the HTCMIABC algorithm is examined by parameter identification of nonlinear chaotic system. Simulation results show that the HTCMIABC is more efficient than some typical existing algorithms. The HTCABC algorithm is examined by using a set of benchmarks and the proposed approach is also applied to solve the parameter identification of a chaotic system. Simulation results show that the HTCABC is more efficient than some existing algorithms reported in the literature. In addition, the simulation results also demonstrate that HCABC can effectively achieve the best PID-like fuzzy controller structure and parameters.

Aiming at the lack of relevant research on relationship constraints between facilities in the corridor allocation problem (CAP). In this paper, fixed position constraints and ordering constraints are considered in CAP, and the logistics cost is minimized. Considering that the existing search technology is complicated and time-consuming in dealing with such constrained CAP (cCAP), and immune clone selection algorithm with variable neighborhood operation (ICSAVNS) is provided for solving this problem. Two approaches to initial solution generation are designed to improve the quality of the initial population. A variable neighborhood search operator is embedded to improve the accuracy of the local search. A threshold is set in the mutation operation of the ICSAVNS to achieve population expansion better. A double index of sequences consisting of affinity values and constrained facility index values is used to select and reselect, achieving population compression in the clonal selection part. Finally, by exactly solving the model, the rationality of the model is verified. The hybrid clone selection algorithm is used to solve the cCAP and cbCAP benchmark instances of different sizes, and compared with the state-of-the-art optimization algorithms. The results show that the proposed algorithm exhibits better performance.

A novel adaptive evolving Takagi-Sugeno (T-S) model identification method is investigated and integrated in a control architecture to control of nonlinear processes is investigated. The proposed system identification approach consists of two main steps: antecedent T-S fuzzy model parameters identification and consequent parameters identification. First, a new unsupervised fuzzy clustering algorithm (NUFCA) is introduced to combine the K-nearest neighbor and fuzzy C-means methods into a fuzzy modeling method for partitioning of the input-output data and identifying the antecedent parameters of the fuzzy system. Then, a recursive procedure using a particle swarm optimization (PSO) algorithm is exploited to construct an online fuzzy model identification and adaptive control methodology. For better demonstration of the robustness and efficiency of the proposed methodology, it is applied to the identification of a model for the estimation of the flour concentration in the effluent of a real-world wastewater treatment plant (WWTP), and identification and control, using a generalized predictive controller (GPC), of a real experimental setup composed of two coupled DC motors. The results show that the developed evolving T-S fuzzy model methodology can identify nonlinear systems satisfactorily and can be successfully used for a prediction model of the process for the GPC.

Small and medium-sized manufacturing enterprises have the characteristics of large numbers and small scales. Problems such as backward manufacturing technology, lack of talents, small amount of information resources, and insufficient product research and development capabilities have severely restricted the development of enterprises. The backward manufacturing design model cannot adapt to the development trend of modern manufacturing informatization. This paper proposes and designs a fuzzy inference model and fuzzy inference engine algorithm with threshold. In order to describe the numerical multiple input and multiple output variables in the industrial manufacturing design industry, the relevant experience is used to make numerical reasoning decisions. Applying fuzzy sets and fuzzy theory to the expert system, a fuzzy rule model containing the membership function information and thresholds of the corresponding fuzzy sets is proposed and established, and a fuzzy reasoning system suitable for numerical and uncertain reasoning decisions is constructed. The improved grey relational analysis method is used to decompose and evaluate the exponential mathematical quantitative process of manufacturing enterprises. Based on the fuzzy Decision Analytic Network Process (DANP) method to calculate the relative weight of the influencing factors in the evaluation system, the evaluation index of the enterprise is obtained. Starting from the industrial manufacturing design process, this article constructs a relatively comprehensive and reasonable enterprise exponential mathematical quantitative process decomposition evaluation system. Considering that there are complex interactions between the various influencing factors in the system, the fuzzy Decision Making Trial and Evaluation Laboratory (DEMATEL) method is selected to process the direct impact matrix of the evaluation system, and the causal relationship between the indicators is obtained. The fuzzy exponential gray correlation method is used to evaluate the quantitative process of industrial manufacturing design, avoiding the shortcomings of traditional methods that only consider ideal values.