Identification of transparent, compact, accurate and reliable linguistic fuzzy models

Transparency, accuracy, compactness and reliability all appear to be vital (even though somewhat contradictory) requirements when it comes down to linguistic fuzzy modeling. This paper presents a methodology for simultaneous optimization of these criteria by chaining previously published various algorithms - a heuristic fully automated identification algorithm that is able to extract sufficiently accurate, yet reliable and transparent models from data and two algorithms for subsequent simplification of the model that are able to reduce the number of output parameters as well as the number of fuzzy rules with only a marginal negative effect to the accuracy of the model.     

GP-COACH: Genetic Programming-based learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems

In this paper we propose GP-COACH, a Genetic Programming-based method for the learning of COmpact and ACcurate fuzzy rule-based classification systems for High-dimensional problems. GP-COACH learns disjunctive normal form rules (generated by means of a context-free grammar) coded as one rule per tree. The population constitutes the rule base, so it is a genetic cooperative-competitive learning approach. GP-COACH uses a token competition mechanism to maintain the diversity of the population and this obliges the rules to compete and cooperate among themselves and allows the obtaining of a compact set of fuzzy rules. The results obtained have been validated by the use of non-parametric statistical tests, showing a good performance in terms of accuracy and interpretability.     

Global and well-distributed Pareto frontier by modified normalized normal constraint methods for bicriterion problems

Important efforts have been made in the last years to develop methods for the construction of Pareto frontiers that guarantee uniform distribution and that exclude the non-Pareto and local Pareto points. Nevertheless, these methods are susceptible of improvement or modifications to reach the same level of results more efficiently. This paper presents some of these possibilities, based on two types of techniques: those based on nonlinear optimization and those based on genetic algorithms. The first provides appropriate solutions at reasonable computational cost though they are highly dependent on the initial points and on the presence or absence of local minima. The second technique does not present such dependence although computational cost is higher. Since the construction of the Pareto frontier is usually off-line, that computational cost is not a restrictive factor. Goodness of the improvements proposed in the paper are shown with two bicriterion examples.     

Development of genetic algorithm-based fuzzy rules design for metal cutting data selection

Fuzzy rules optimization is always a problem for a complex fuzzy model. For a simple 2-inputs-1-output fuzzy model, the designer has to select the most optimum set of fuzzy rules from more than 10 000 combinations. The authors have developed fuzzy models for machinability data selection (Int. J. Flexible Autom. Integrated Manuf. 5 (1 and 2) (1997) 79). There are more than 2×10²⁹ possible sets of rules for each model. The situation would be more complicated if there were a further increase in the number of inputs and/or outputs. The fuzzy rules (Turning Handbook of High-Efficiency Metal Cutting, General Electric Co., Detroit) were selected based on trial and error and/or intuition. Genetic optimization has been suggested in this paper to further optimize the fuzzy rules. The development of a Fuzzy Genetic Optimization algorithm is presented and discussed. An object-oriented library to handle fuzzy rules optimization with genetic optimization has been developed. The effect of constraint rules is also presented and discussed. Comparisons between the results from the optimized models and literature are made.     

hGA: Hybrid genetic algorithm in fuzzy rule-based classification systems for high-dimensional problems

The aim of this work is to propose a hybrid heuristic approach (called hGA) based on genetic algorithm (GA) and integer-programming formulation (IPF) to solve high dimensional classification problems in linguistic fuzzy rule-based classification systems. In this algorithm, each chromosome represents a rule for specified class, GA is used for producing several rules for each class, and finally IPF is used for selection of rules from a pool of rules, which are obtained by GA. The proposed algorithm is experimentally evaluated by the use of non-parametric statistical tests on seventeen classification benchmark data sets. Results of the comparative study show that hGA is able to discover accurate and concise classification rules.     

Improving the performance of fuzzy rule-based classification systems with interval-valued fuzzy sets and genetic amplitude tuning

Among the computational intelligence techniques employed to solve classification problems, Fuzzy Rule-Based Classification Systems (FRBCSs) are a popular tool because of their interpretable models based on linguistic variables, which are easier to understand for the experts or end-users.The aim of this paper is to enhance the performance of FRBCSs by extending the Knowledge Base with the application of the concept of Interval-Valued Fuzzy Sets (IVFSs). We consider a post-processing genetic tuning step that adjusts the amplitude of the upper bound of the IVFS to contextualize the fuzzy partitions and to obtain a most accurate solution to the problem.We analyze the goodness of this approach using two basic and well-known fuzzy rule learning algorithms, the Chi et al.’s method and the fuzzy hybrid genetics-based machine learning algorithm. We show the improvement achieved by this model through an extensive empirical study with a large collection of data-sets.     

Hierarchical aggregation of multiple fuzzy controllers for global complex control problems

In this paper, we illustrate a proposed method for control that combines the outputs of several individual controllers to improve global control of complex nonlinear plants. In the first part of this paper, we illustrate the proposed method that consists of two levels, where in the top level a fuzzy system represents a superior control that is designed for adjusting the behavior of the individual fuzzy controllers at the lower level. To test the approach, we consider the problem of flight control because it requires several individual controllers. Also a comparison is performed, where the hierarchical control strategy is compared with a simple control approach using the t student test. In this paper, we show that the proposed method outperforms the conventional fuzzy control approach. In the optimal design of the proposed control architecture a genetic algorithm was also applied to tune the parameters of the fuzzy systems in an optimal fashion.     

基于二叉树型分层的广义混合模糊系统推理规则数的缩减

为避免广义混合模糊系统因输入变量个数的增加而引起规则爆炸现象,应用二叉树型分层方法给出混合推理规则,进而对广义混合模糊系统的输入实施二叉树型分层,从理论上获得了该系统分层后的输入输出表达式和推理规则总数的计算公式.此外,通过实例对该系统分层和不分层的规则总数进行了比较和分析,结果表明分层后广义混合模糊系统可大幅度缩减推理规则总数,并可有效地避免规则爆炸.     

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of different proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable properties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Limitations of existing ranking methods have been studied. Further for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.     

Some new distance measures for type-2 fuzzy sets and distance measure based ranking for group decision making problems

In this paper, we propose some distance measures between type-2 fuzzy sets, and also a new family of utmost distance measures are presented. Several properties of differ- ent proposed distance measures have been introduced. Also, we have introduced a new ranking method for the ordering of type-2 fuzzy sets based on the proposed distance measure. The proposed ranking method satisfies the reasonable prop- erties for the ordering of fuzzy quantities. Some properties such as robustness, order relation have been presented. Lim- itations of existing ranking methods have been studied. Fur- ther for practical use, a new method for selecting the best alternative, for group decision making problems is proposed. This method is illustrated with a numerical example.     

基于聚类和模糊关联规则的中医药对量效分析*

以数据挖掘为技术手段,对方剂中药对的量效关联进行分析,主要工作包括：根据中药方剂中药物剂量分布的一般规律,用聚类方法自动划分药物剂量的模糊区间;基于模糊关联规则的概念,提出药对量效关联规则的挖掘算法;对所提出的算法进行了实现和验证。结果表明,基于聚类和模糊关联规则挖掘的中医药对量效关联分析符合中医药的基本特点,挖掘出的知识具有较高的正确率。     

一种基于充要强度的优化规则发现方法

提出了一种基于信息系统的优化规则的提取方法,主要目的是提取信息系统中具有一定充要性的优化规则。首先,提出了充要强度并讨论了它的性质。其次,由于搜索空间的巨大和遗传算法的全局优化的特性,设计了使用遗传算法进行优化规则搜索的方法。最后,通过实验说明方法的有效性。     

A multi-objective genetic optimization for fast,fuzzy rule-based credit classification with balanced accuracy and interpretability

Credit classification is an important component of critical financial decision making tasks such as credit scoring and bankruptcy prediction. Credit classification methods are usually evaluated in terms of their accuracy, interpretability, and computational efficiency. In this paper, we propose an approach for automatic designing of fuzzy rule-based classifiers (FRBCs) from financial data using multi-objective evolutionary optimization algorithms (MOEOAs). Our method generates, in a single experiment, an optimized collection of solutions (financial FRBCs) characterized by various levels of accuracy-interpretability trade-off. In our approach we address the complexity- and semantics-related interpretability issues, we introduce original genetic operators for the classifier's rule base processing, and we implement our ideas in the context of Non-dominated Sorting Genetic Algorithm II (NSGA-II), i.e., one of the presently most advanced MOEOAs. A significant part of the paper is devoted to an extensive comparative analysis of our approach and 24 alternative methods applied to three standard financial benchmark data sets, i.e., Statlog (Australian Credit Approval), Statlog (German Credit Approval), and Credit Approval (also referred to as Japanese Credit) sets available from the UCI repository of machine learning databases (http://archive.ics.uci.edu/ml). Several performance measures including accuracy, sensitivity, specificity, and some number of interpretability measures are employed in order to evaluate the obtained systems. Our approach significantly outperforms the alternative methods in terms of the interpretability of the obtained financial data classifiers while remaining either competitive or superior in terms of their accuracy and the speed of decision making.     

Optimization of type-2 fuzzy weights in backpropagation learning for neural networks using GAs and PSO

In this paper the optimization of type-2 fuzzy inference systems using genetic algorithms (GAs) and particle swarm optimization (PSO) is presented. The optimized type-2 fuzzy inference systems are used to estimate the type-2 fuzzy weights of backpropagation neural networks. Simulation results and a comparative study among neural networks with type-2 fuzzy weights without optimization of the type-2 fuzzy inference systems, neural networks with optimized type-2 fuzzy weights using genetic algorithms, and neural networks with optimized type-2 fuzzy weights using particle swarm optimization are presented to illustrate the advantages of the bio-inspired methods. The comparative study is based on a benchmark case of prediction, which is the Mackey-Glass time series (for τ = 17) problem.     

A comparison of scheduling algorithms for flexible flow shop problems with unrelated parallel machines,setup times,and dual criteria

This paper considers a flexible flow shop scheduling problem, where at least one production stage is made up of unrelated parallel machines. Moreover, sequence- and machine-dependent setup times are given. The objective is to find a schedule that minimizes a convex sum of makespan and the number of tardy jobs in a static flexible flow shop environment. For this problem, a 0–1 mixed integer program is formulated. The problem is, however, a combinatorial optimization problem which is too difficult to be solved optimally for large problem sizes, and hence heuristics are used to obtain good solutions in a reasonable time. The proposed constructive heuristics for sequencing the jobs start with the generation of the representatives of the operating time for each operation. Then some dispatching rules and flow shop makespan heuristics are developed. To improve the solutions obtained by the constructive algorithms, fast polynomial heuristic improvement algorithms based on shift moves and pairwise interchanges of jobs are applied. In addition, metaheuristics are suggested, namely simulated annealing (SA), tabu search (TS) and genetic algorithms. The basic parameters of each metaheuristic are briefly discussed in this paper. The performance of the heuristics is compared relative to each other on a set of test problems with up to 50 jobs and 20 stages and with an optimal solution for small-size problems. We have found that among the constructive algorithms the insertion-based approach is superior to the others, whereas the proposed SA algorithms are better than TS and genetic algorithms among the iterative metaheuristic algorithms.     

Integration of fuzzy logic, genetic algorithms and neural networks in collaborative parametric design

The solution to a design problem is extracted through the exploitation of the design knowledge in the context of a space of solution alternatives. The design process incorporates a series of decision making and knowledge management issues, which should be often addressed through collaboration among diverse stakeholders. The alternative solutions must usually be shaped under different formalisms and evaluated against commonly accepted objective criteria.The current paper presents an approach that integrates soft-computing techniques in order to facilitate the computer-aided collaboration among designers. CopDeSC (Collaborative parametric Design with Soft-Computing) is the name of the system developed in order to implement this approach whose key features are: (a) the collaborative structuring of design parameter hierarchies, (b) the modeling of the design objectives through fuzzy preferences stated by the designers on certain design parameters, (c) the deployment of genetic algorithms for locating the optimum solution and (d) the utilization of records of elite solutions that are submitted in a neuro-fuzzy approximation in order to produce a simplified problem formulation, suitable for addressing redesign tasks in significantly less computational time.The efficiency of CopDeSC is evaluated in an example case of the parametric design of oscillating conveyor that has been conducted by a group of designers.     

Algorithms for complex interval‐valued q‐rung orthopair fuzzy sets in decision making based on aggregation operators,AHP, and TOPSIS

The interval‐valued q‐rung orthopair fuzzy set (IVq‐ROFS) and complex fuzzy set (CFS) are two generalizations of the fuzzy set (FS) to cope with uncertain information in real decision making problems. The aim of the present work is to develop the concept of complex interval‐valued q‐rung orthopair fuzzy set (CIVq‐ROFS) as a generalization of interval‐valued complex fuzzy set (IVCFS) and q‐rung orthopair fuzzy set (q‐ROFS), which can better express the time‐periodic problems and two‐dimensional information in a single set. In this article not only basic properties of CIVq‐ROFSs are discussed but also averaging aggregation operator (AAO) and geometric aggregation operator (GAO) with some desirable properties and operations on CIVq‐ROFSs are discussed. The proposed operations are the extension of the operations of IVq‐ROFS, q‐ROFS, interval‐valued Pythagorean fuzzy, Pythagorean fuzzy (PF), interval‐valued intuitionistic fuzzy, intuitionistic fuzzy, complex q‐ROFS, complex PF, and complex intuitionistic fuzzy theories. Further, the Analytic hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) method are also examine based on CIVq‐ROFS to explore the reliability and proficiency of the work. Moreover, we discussed the advantages of CIVq‐ROFS and showed that the concepts of IVCFS and q‐ROFS are the special cases of CIVq‐ROFS. Moreover, the flexibility of proposed averaging aggregation operator and geometric aggregation operator in a multi‐attribute decision making (MADM) problem are also discussed. Finally, a comparative study of CIVq‐ROFSs with pre‐existing work is discussed in detail.     

Ant colony optimization approach to a fuzzy goal programming model for a machine tool selection and operation allocation problem in an FMS

Due to the global competition in manufacturing environment, firms are forced to consider increasing the quality and responsiveness to customization, while decreasing costs. The evolution of flexible manufacturing systems (FMSs) offers great potential for increasing flexibility and changing the basis of competition by ensuring both cost effective and customized manufacturing at the same time. Some of the important planning problems that need realistic modelling and quicker solution especially in automated manufacturing systems have assumed greater significance in the recent past. The language used by the industrial workers is fuzzy in nature, which results in failure of the models considering deterministic situations. The situation in the real life shop floor demands to adopt fuzzy-based multi-objective goals to express the target set by the management. This paper presents a fuzzy goal programming approach to model the machine tool selection and operation allocation problem of FMS. An ant colony optimization (ACO)-based approach is applied to optimize the model and the results of the computational experiments are reported.     

A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertainty measures are compared based on real survey data and then the most suitable ranking method, similarity measure and uncertainty measure that can be used in the computing with words paradigm are suggested. The results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.