A note on double lacunary statistical $$\sigma$$-convergence of fuzzy numbers

Quite recently, Sava? (Appl Math Lett 21:134–141, 2008), defined the lacunary statistical analogue for double sequence \(X=\{X_{k,l}\}\) of fuzzy numbers as follows: a double sequence \(X=\{X_{k,l}\}\) is said to be lacunary P-statistically convergent to \(X_{0}\) provided that for each \(\epsilon >0\)

$ P-\lim_{r,s}\frac{1}{h_{r,s}}\left | \{(k,l)\in I_{r,s}: d(X_{k,l },X_0)\geq \epsilon\}\right|= 0. $

In this paper we introduce and study double lacunary \(\sigma\)-statistical convergence for sequence of fuzzy numbers and also we get some inclusion theorems.

     

A K-nearest neighbours method based on imprecise probabilities

K-nearest neighbours algorithms are among the most popular existing classification methods, due to their simplicity and good performances. Over the years, several extensions of the initial method have been proposed. In this paper, we propose a K-nearest neighbours approach that uses the theory of imprecise probabilities, and more specifically lower previsions. We show that the proposed approach has several assets: it can handle uncertain data in a very generic way, and decision rules developed within this theory allow us to deal with conflicting information between neighbours or with the absence of close neighbour to the instance to classify. We show that results of the basic k-NN and weighted k-NN methods can be retrieved by the proposed approach. We end with some experiments on the classical data sets.     

Missing data imputation for fuzzy rule-based classification systems

Fuzzy rule-based classification systems (FRBCSs) are known due to their ability to treat with low quality data and obtain good results in these scenarios. However, their application in problems with missing data are uncommon while in real-life data, information is frequently incomplete in data mining, caused by the presence of missing values in attributes. Several schemes have been studied to overcome the drawbacks produced by missing values in data mining tasks; one of the most well known is based on preprocessing, formerly known as imputation. In this work, we focus on FRBCSs considering 14 different approaches to missing attribute values treatment that are presented and analyzed. The analysis involves three different methods, in which we distinguish between Mamdani and TSK models. From the obtained results, the convenience of using imputation methods for FRBCSs with missing values is stated. The analysis suggests that each type behaves differently while the use of determined missing values imputation methods could improve the accuracy obtained for these methods. Thus, the use of particular imputation methods conditioned to the type of FRBCSs is required.     

Learning-enhanced differential evolution for numerical optimization

Differential evolution (DE) is a simple and powerful population-based search algorithm, successfully used in various scientific and engineering fields. However, DE is not free from the problems of stagnation and premature convergence. Hence, designing more effective search strategies to enhance the performance of DE is one of the most salient and active topics. This paper proposes a new method, called learning-enhanced DE (LeDE) that promotes individuals to exchange information systematically. Distinct from the existing DE variants, LeDE adopts a novel learning strategy, namely clustering-based learning strategy (CLS). In CLS, there are two levels of learning strategies, intra-cluster learning strategy and inter-cluster learning strategy. They are adopted for exchanging information within the same cluster and between different clusters, respectively. Experimental studies over 23 benchmark functions show that LeDE significantly outperforms the conventional DE. Compared with other clustering-based DE algorithms, LeDE can obtain better solutions. In addition, LeDE is also shown to be significantly better than or at least comparable to several state-of-art DE variants as well as some other evolutionary algorithms.     

Residuated bilattices

We introduce a new product bilattice construction that generalizes the well-known one for interlaced bilattices and others that were developed more recently, allowing to obtain a bilattice with two residuated pairs as a certain kind of power of an arbitrary residuated lattice. We prove that the class of bilattices thus obtained is a variety, give a finite axiomatization for it and characterize the congruences of its members in terms of those of their lattice factors. Finally, we show how to employ our product construction to define first-order definable classes of bilattices corresponding to any first-order definable subclass of residuated lattices.     

Consensus reaching models of linguistic preference relations based on distance functions

In group decision making (GDM) using linguistic preference relations to obtain the maximum degree of agreement, it is desirable to develop a consensus process prior to the selection process. This paper proposes two consensus models with linguistic information to support the GDM consensus reaching process. Two different distance functions between linguistic preference relations are introduced to measure both individual consistency and group consensus. Based on these measures, the consensus reaching models are developed. The two models presented have the same concept that the expert whose preference is farthest from the group preference needs to update their opinion according to the group preference relation. In addition, the convergence of the models is proved. After achieving the predefined consensus level, each expert’s consistency indexes are still acceptable under the condition that the initial preference relations are of satisfactory consistency. Finally, an example is given to show the effectiveness of the models and to verify the theoretical results.     

SVM-based ontology matching approach

There are a lot of heterogeneous ontologies in semantic web, and the task of ontology mapping is to find their semantic relationship. There are integrated methods that only simply combine the similarity values which are used in current multi-strategy ontology mapping. The semantic information is not included in them and a lot of manual intervention is also needed, so it leads to that some factual mapping relations are missed. Addressing this issue, the work presented in this paper puts forward an ontology matching approach, which uses multi-strategy mapping technique to carry on similarity iterative computation and explores both linguistic and structural similarity. Our approach takes different similarities into one whole, as a similarity cube. By cutting operation, similarity vectors are obtained, which form the similarity space, and by this way, mapping discovery can be converted into binary classification. Support vector machine (SVM) has good generalization ability and can obtain best compromise between complexity of model and learning capability when solving small samples and the nonlinear problem. Because of the said reason, we employ SVM in our approach. For making full use of the information of ontology, our implementation and experimental results used a common dataset to demonstrate the effectiveness of the mapping approach. It ensures the recall ration while improving the quality of mapping results.     

Comparative study on economic contribution rate of education of China and foreign countries based on soft computing method

Economic contribution rate of education (ECRE) is the key factor of education economics. This article selected China, South Korea, United States and other countries for a total of 15 samples, and put the data of the same period under the framework of soft computing, to simulate the production chain of “education–potential human capital–actual human capital–economic growth”. The basic idea is: Firstly, 15 countries are softly categorized according to the level of science and technology (S&T) progress. Secondly, potential human capital and actual human capital establish the internal correlation (fuzzy mapping) in the same classification, and we conceptualize actual human capital as one production factor, joined with the other two production factors, fixed asset and land, to set up the fuzzy mapping to economic growth., and then calculate economic contribution rate of education of China and foreign by two fuzzy mapping of them. Thirdly, this paper analyzes the present state and differences in the development of education between China and foreign according to different ECRE, and offers proposals for promoting the education in China.     

Birman–Wenzl–Murakami algebra, topological parameter and Berry phase

In this paper, a 3?×?3-matrix representation of Birman?CWenzl?CMurakami (BWM) algebra has been presented. Based on which, unitary matrices A(??, ?? ₁, ?? ₂) and B(??, ?? ₁, ?? ₂) are generated via Yang?CBaxterization approach. A Hamiltonian is constructed from the unitary B(??, ??) matrix. Then we study Berry phase of the Yang?CBaxter system, and obtain the relationship between topological parameter and Berry phase.     

An efficient initialization approach of Q-learning for mobile robots

This article demonstrates that Q-learning can be accelerated by appropriately specifying initial Q-values using dynamic wave expansion neural network. In our method, the neural network has the same topography as robot work space. Each neuron corresponds to a certain discrete state. Every neuron of the network will reach an equilibrium state according to the initial environment information. The activity of the special neuron denotes the maximum cumulative reward by following the optimal policy from the corresponding state when the network is stable. Then the initial Q-values are defined as the immediate reward plus the maximum cumulative reward by following the optimal policy beginning at the succeeding state. In this way, we create a mapping between the known environment information and the initial values of Q-table based on neural network. The prior knowledge can be incorporated into the learning system, and give robots a better learning foundation. Results of experiments in a grid world problem show that neural network-based Q-learning enables a robot to acquire an optimal policy with better learning performance compared to conventional Q-learning and potential field-based Qlearning.