Consensus reaching process (CRP) is a key topic in the area of group decision making (GDM). When the consensus level is not high enough, it becomes necessary to adjust the original opinions of decision makers (DMs). To offer the adjustment reference for DMs, we build the programming models to determine the minimum modification to be carried out from the individual and global perspectives. Meanwhile, all DMs are divided into two subgroups: DMs with acceptable and unacceptable consensus levels. If some DMs with unacceptable consensus level do not accept the relevant modifications, the Nash bargaining game-based programming model is built for the fairness and efficiency of modifications. When some DMs refuse to make any modifications or tend to modify the opinions in their way, with respect to different group consensus situations, we make the minimum hybrid penalty mechanism by the Nash bargaining game-based programming models. For each case, we determine the corresponding optimal modification mechanism in view of the fixed individual total modification and the maximum consensus level. Furthermore, we study the arrangements of weights of DMs according to their cardinal and ordinal consensus contributions. Based on these results, we present a new algorithm and illustrate its application by a numerical example. Moreover, we carry out the sensitivity and comparison analysis. We summarize the conclusions and future research directions in the end. The main originality of the new method includes: the fairness and efficiency of modifications, and the determination of the hybrid penalty mechanism.
The commonly used preference elicitation method in decision making is the one using pairwise comparison between alternatives. In this kind of decision making scenario, an essential issue requiring attention is that of consistency, particularly in decision problems with numerous alternatives. Consistency is usually linked to the transitivity concept, which is modeled in several diverse ways. Given the importance of avoiding conflicting opinions in decision making, in this study, we propose an approach to improve the consistency when reciprocal preference relations are used. On one hand, consistency is modeled in terms of the multiplicative transitivity property. On the other hand, information granularity is used to introduce and develop the concept of interval reciprocal preference relations in which the entries are constructed as intervals in place of single numeric values. This provides the necessary flexibility to improve the consistency. To illustrate and test the performance of the approach that is proposed here, an example is given.
With the increase in the number of optimization objectives, balancing the convergence and diversity in evolutionary multiobjective optimization becomes more intractable. So far, a variety of evolutionary algorithms have been proposed to solve many-objective optimization problems (MaOPs) with more than three objectives. Most of the existing algorithms, however, find difficulties in simultaneously counterpoising convergence and diversity during the whole evolutionary process. To address the issue, this paper proposes to solve MaOPs via multistage evolutionary search. To be specific, a two-stage evolutionary algorithm is developed, where the convergence and diversity are highlighted during different search stages to avoid the interferences between them. The first stage pushes multiple subpopulations with different weight vectors to converge to different areas of the Pareto front. After that, the nondominated solutions coming from each subpopulation are selected for generating a new population for the second stage. Moreover, a new environmental selection strategy is designed for the second stage to balance the convergence and diversity close to the Pareto front. This selection strategy evenly divides each objective dimension into a number of intervals, and then one solution having the best convergence in each interval will be retained. To assess the performance of the proposed algorithm, 48 benchmark functions with 7, 10, and 15 objectives are used to make comparisons with five representative many-objective optimization algorithms.
Foreword by Lotfi Zadeh Preface INTRODUCTION Background. Why fuzzy logic? FUNDAMENTAL CONCEPTS OF FUZZY COMPUTATION Vagueness and uncertainty: Theories of vagueness. Theories of uncertainty. Fuzzy sets: concepts and characterizations: Introduction. Operations on fuzzy sets. Interpretations of fuzzy sets. Fuzzy relations. Characterization of fuzzy sets. Fuzzy measure and integral. Fuzzy mathematical objects. Extension principle. Fuzzy set calculus: Introduction. Membership function elicitation. Fuzzy relational calculus. Fuzzy arithmetic. Possibility theory. Fuzzy reasoning: Introduction. Fuzzy inference. Defuzzification. FUZZY MODELS Fuzzy models. Modeling and simulation: Granule-based models. Logical aspects of fuzzy models. Statistical models. Fuzzy Petri Net model. Model acquisition. Approximation aspects of fuzzy models. HYBRID APPROACHES Introduction: motivation for hybrid approaches. Neuro-fuzzy systems. Fuzzy-evolutionary systems. FUZZY COMPUTATION ENVIRONMENTS Software approaches: Programming languages. Knowledge-based systems. Database management, information retrieval, and decision support systems. Hardware approaches: Desirable features. Adapting existing hardware to fuzzy computation. Analog approaches. Digital approaches. Hybrid (digital-analog) approaches. APPLICATIONS OF FUZZY COMPUTATION Knowledge based systems: Knowledge representation. Inference methods. Control methods. Design methods. Control. Principles of fuzzy controllers. Fuzzy control approaches: General design schemes. Cell maps. Sliding mode control. Predictive control. Hierarchical control. Model-based control. Optimal fuzzy control. Machine learning: Introduction: learning fuzzy concepts. Supervised learning. Reinforcement learning. Data and information management: Fuzzy databases. Information retrieval. Case-based reasoning. Decision making and optimization: Decision-making models. Optimization. Pattern analysis. Computer vision. FUZZY COMPUTATION IN PRACTICE Aerospace: Proximity operations spacecraft controller: a case study in fuzzy logic control. Systems control: DC/DC converters fuzzy control. Fuzzy control in telecommunications. Fuzzy-neural traffic control and forecasting. Systems control. Backlash compensation using fuzzy logic. Neurofuzzy modeling for nonlinear system identification. Nuclear engineering: Application of fuzzy logic control system for nuclear reactor control. Manufacturing: Applications of fuzzy set methodologies in manufacturing. Compensation of friction in mechanical positioning systems. Diagnostics: Possibilistic handling of uncertainty in fault diagnosis. Robotics: Autonomous mobile robot control. Chemical engineering: Chemical engineering application. Water treatment: Water treatment application. Automotive: Improvement of the relationship between driver and vehicle using fuzzy logic. Traffic engineering: Traffic engineering application. Civil engineering: Civil engineering application. Engineering design: A fuzzy sets application to preliminary passenger vehicle structure design. Oil refining: Neuro-fuzzy hybrid control system in petroleum plant. Medicine: CADIAG2: hospital-based computer-assisted differential diagnosis in internal medicine. Neural networks for ECG diagnostic classification. Information science: Case-based reasoning. Information retrieval: a case study of the CASHE: PVS systems. Economics, finance and business. Decision support system for foreign exchange trade (FOREX). Operations research: Scheduling. Fuzzy sets in operation research: forecasting, a case study. Quality design using possibilistic regression and optimization. Inventory control. Time series prediction. FUZZY COMPUTATION RESEARCH Directions for future research. APPENDICES
The paper is concerned with the problem of the explicit granulation of data in presence of some labeled patterns. The granulation process is realized as an organic growth of multi-dimensional hyperboxes guided by a compatibility measure. The organic growth signifies that there are no prior assumptions about the number and shape of the information granules. Instead, only the relative position and size of the patterns in the pattern space determine the progression of the granulation process. The rationale for a specific form of the compatibility measure is explained using some illustrative examples. The inclusion of a small number of labeled patterns in the input data is shown to provide a very effective way of coping with complex decision hyperplanes in multi-dimensional pattern spaces. The method is illustrated using several synthetic data sets as well as the Iris data set that is widely regarded as a reference for the comparison of classification and clustering algorithms
The concept of ensemble learning offers a promising avenue in learning from data streams under complex environments because it better addresses the bias and variance dilemma than its single-model counterpart and features a reconfigurable structure, which is well suited to the given context. While various extensions of ensemble learning for mining nonstationary data streams can be found in the literature, most of them are crafted under static base-classifier and revisit preceding samples in the sliding window for a retraining step. This feature causes computationally prohibitive complexity and is not flexible enough to cope with rapidly changing environments. Their complexities are often demanding because they involve a large collection of offline classifiers due to the absence of structural complexities reduction mechanisms and lack of an online feature selection mechanism. A novel evolving ensemble classifier, namely Parsimonious Ensemble (pENsemble), is proposed in this paper. pENsemble differs from existing architectures in the fact that it is built upon an evolving classifier from data streams, termed Parsimonious Classifier. pENsemble is equipped by an ensemble pruning mechanism, which estimates a localized generalization error of a base classifier. A dynamic online feature selection scenario is integrated into the pENsemble. This method allows for dynamic selection and deselection of input features on the fly. pENsemble adopts a dynamic ensemble structure to output a final classification decision where it features a novel drift detection scenario to grow the ensemble's structure. The efficacy of the pENsemble has been numerically demonstrated through rigorous numerical studies with dynamic and evolving data streams, where it delivers the most encouraging performance in attaining a tradeoff between accuracy and complexity.
Undoubtedly, machine learning (ML) has demonstrated a wealth of far-reaching successes present both at the level of fundamental developments, design methodologies and numerous application areas, quite often encountered in domains requiring a high level of autonomous behavior. Over the passage of time, there are growing challenges of privacy and security, interpretability, explainability, confidence (credibility), and computational sustainability, among others. In this study, we advocate that these quests could be addressed by casting them both conceptually and algorithmically in the unified environment augmented by the principles of granular computing. It is demonstrated that the level of abstraction, delivered by granular computing plays a pivotal role in the interpretation by quantifying the level of credibility of ML constructs. The study also highlights the principles of granular computing and elaborates on its landscape. The original idea of a comprehensive and unified framework of data-knowledge environment of ML is introduced along with a detailed discussion on how data and knowledge are used in a seamless fashion by invoking granular embedding and producing relevant loss functions. Key categories of knowledge-data integration realized at the levels of data and model (involving symbolic/qualitative models and physics-oriented models) and investigated.
Abstract In this paper, we look closely at the issue of contaminated data sets, where apart from legitimate (proper) patterns we encounter erroneous patterns. In a typical scenario, the classification of a contaminated data set is always negatively influenced by garbage patterns (referred to as foreign patterns). Ideally, we would like to remove them from the data set entirely. The paper is devoted to comparison and analysis of three different models capable to perform classification of proper patterns with rejection of foreign patterns. It should be stressed that the studied models are constructed using proper patterns only, and no knowledge about the characteristics of foreign patterns is needed. The methods are illustrated with a case study of handwritten digits recognition, but the proposed approach itself is formulated in a general manner. Therefore, it can be applied to different problems. We have distinguished three structures: global, local, and embedded, all capable to eliminate foreign patterns while performing classification of proper patterns at the same time. A comparison of the proposed models shows that the embedded structure provides the best results but at the cost of a relatively high model complexity. The local architecture provides satisfying results and at the same time is relatively simple.
In the analytic hierarchy process (AHP), the reciprocal matrix is generated based on the pairwise comparisons completed among all the alternatives or attributes under consideration. To ensure reliability and validity of the decision solution, a certain modification of entries of the matrix is usually needed to improve the consistency of the reciprocal matrix. This study aims to present a consistency improvement method by admitting some level of information granularity in the evaluation process. This gives rise to a granular rather than numeric matrix of pairwise comparisons. First, with a given average level of information granularity, we present an optimal granularity model that is characterized by maximal consistency. One can maximize the consistency degree by invoking a process of allocation of information granularity across the corresponding modifications of the reciprocal matrix. Based on the optimal granularity model, an interactive consistency improvement process is presented with the involvement of the decision maker. Then, an adaptive differential evolution algorithm is applied to optimize entries of the modified reciprocal matrix. Detailed experiments along with a thorough comparative analysis are completed to demonstrate the effectiveness of the proposed method.
