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In practical decision-making problems, the coexistence of several complex situations increases the difficulty for decision makers to make reasonable decision, such as attributes outnumber alternatives, heterogeneous relationships among multiple attributes, and individual risk tendency of decision maker. In view of the advantage of probabilistic linguistic term sets (PLTSs) in presenting qualitative information, a novel decision-making approach with PLTSs is constructed to deal with the above special situations simultaneously. To realize this goal, some basic models have been proposed. First of all, to truly reflect the importance of attributes from the heterogeneous relationships, a weight determination model with generalized Banzhaf values is developed to analyze the interaction between combinations of attributes. Then, for analyzing the individual risk tendency of decision maker, the generalized Banzhaf TODIM method with PLTSs is constructed. Moreover, based on the above research results, the generalized Banzhaf TODIM-QUALIFLEX method with PLTSs is developed to solve decision-making problems where the number of attributes exceeds the number of alternatives, the combinations of attributes are interacted with each other, and decision maker is affected by individual risk propensity. Lastly, smartphones selection through online ratings is a typical case of decision-making problems with the above situations, which is designed to illustrate the performance of the proposed method. And its rationality and advantages are further demonstrated through some comparative analyses with other methods.
The paper consider a fuzzy inference scheme in the truth space that assumes the i-th rule linguistically qualified, that is, it comes with a truth value of the implication. In contrast to the standard version of modus ponens, the entire inference process is completed at the higher conceptual level formed by the mechanisms of fuzzy logic. The reasoning process invokes three phases: inverse linguistic truth qualification; inference based on fuzzy truth values exploiting the notion of fuzzy implication and the solution of an inverse relational equation; inverse linguistic truth qualification. An immediate application of the approach concerns fuzzy logic control.
Discovering and utilizing problem domain knowledge is a promising direction towards improving the efficiency of evolutionary algorithms (EAs) when solving optimization problems. We propose a knowledge‐based variable reduction strategy (VRS) that can be integrated into EAs to solve unconstrained and first‐order derivative optimization functions more efficiently. VRS originates from the knowledge that, in an unconstrained and first‐order derivative optimization function, the optimal solution locates in a local extreme point at which the partial derivative over each variable equals zero. Through this collective of partial derivative equations, some quantitative relations among different variables can be obtained. These variable relations have to be satisfied in the optimal solution. With the use of such relations, VRS could reduce the number of variables and shrink the solution space when using EAs to deal with the optimization function, thus improving the optimizing speed and quality. When we apply VRS to optimization problems, we just need to modify the calculation approach of the objective function. Therefore, practically, it can be integrated with any EA. In this study, VRS is combined with particle swarm optimization variants and tested on several benchmark optimization functions and a real‐world optimization problem. Computational results and comparative study demonstrate the effectiveness of VRS.
Summary form only. Data mining in databases aims to make sense of data by revealing meaningful and easily interpretable relationships. In spite of many existing variations, this research goal permeates the entire area. The domain of data mining is highly heterogeneous embracing a number of well-established information technologies including: statistical pattern recognition, neural networks, machine learning, knowledge-based systems, etc. The synergistic character of data mining is one of its dominant features that makes this pursuit an emerging new area of research and application. By its nature, data mining is very much oriented towards the end-user, thus implying that any results need to be easily interpretable. Granulation of information promotes this interpretability and channels pursuits of data mining, which can be computationally intensive and thus highly prohibitive, towards more efficient and feasible processing of information granules. Finally, an interesting emerging area of data mining involves perception. Data mining often retrieves "perceived data" and the problem is to reconcile this perceived data with the real world. Information granulation can help with this problem.
Regression models are well known and widely used as one of the important models in system modeling. In this paper, we extend the concept of regression models in order to handle hybrid data coming from various sources of data quite often exhibiting diverse levels of quality. The major objective of this study is to develop a convex hull method being regarded as a potential vehicle, which helps reduce the computing time, especially in real-time data analysis as well as an overall computational complexity. We propose an efficient real-time fuzzy switching regression analysis based on the convex hull approach in which a Beneath-Beyond algorithm is employed to design a convex hull. The method addresses situations when we have to deal with heterogeneous data. In the proposed design setting, we emphasize a pivotal role of convex hull approach which is crucial when alleviating limitations of a linear programming manifesting in system modeling.
The study is concerned with an approach to the design of a new category of fuzzy neural networks. The proposed Fuzzy Polynomial Neural Networks (FPNN) with hybrid multi-layer inference architecture is based on fuzzy neural networks (FNN) and polynomial neural networks (PNN) for model identification of complex and nonlinear systems. The one and the other are considered as premise and consequence part of FPNN respectively. Therefore, the proposed FPNN is available effectively for multi-input variables and high-order polynomial according to the combination of FNN and PNN. We introduce two kinds of FPNN architectures, namely the basic and modified architectures depending on the connection points (nodes) of the layer of FNN. Owing to the specific features of two combined architectures, it is possible to consider the nonlinear characteristics of process and to get output performance with superb predictive ability. The availability and feasibility of the FPNN is discussed and illustrated with the aid of two representative numerical examples. The results show that the proposed FPNN can produce a model with higher accuracy and predictive ability than any other method presented previously.
In classical data-driven machine learning methods, massive amounts of labeled data are required to build a high-performance prediction model. However, the amount of labeled data in many real-world applications is insufficient, so establishing a prediction model is impossible. Transfer learning has recently emerged as a solution to this problem. It exploits the knowledge accumulated in auxiliary domains to help construct prediction models in a target domain with inadequate training data. Most existing transfer learning methods solve classification tasks; only a few are devoted to regression problems. In addition, the current methods ignore the inherent phenomenon of information granularity in transfer learning. In this study, granular computing techniques are applied to transfer learning. Three granular fuzzy regression domain adaptation methods to determine the estimated values for a regression target are proposed to address three challenging cases in domain adaptation. The proposed granular fuzzy regression domain adaptation methods change the input and/or output space of the source domain's model using space transformation, so that the fuzzy rules are more compatible with the target data. Experiments on synthetic and real-world datasets validate the effectiveness of the proposed methods.
