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.     

Environmental-aware virtual data center network

Cloud computing services have recently become a ubiquitous service delivery model, covering a wide range of applications from personal file sharing to being an enterprise data warehouse. Building green data center networks providing cloud computing services is an emerging trend in the Information and Communication Technology (ICT) industry, because of Global Warming and the potential GHG emissions resulting from cloud services. As one of the first worldwide initiatives provisioning ICT services entirely based on renewable energy such as solar, wind and hydroelectricity across Canada and around the world, the GreenStar Network (GSN) was developed to dynamically transport user services to be processed in data centers built in proximity to green energy sources, reducing Greenhouse Gas (GHG) emissions of ICT equipments. Regarding the current approach, which focuses mainly in reducing energy consumption at the micro-level through energy efficiency improvements, the overall energy consumption will eventually increase due to the growing demand from new services and users, resulting in an increase in GHG emissions. Based on the cooperation between Mantychore FP7 and the GSN, our approach is, therefore, much broader and more appropriate because it focuses on GHG emission reductions at the macro-level. This article presents some outcomes of our implementation of such a network model, which spans multiple green nodes in Canada, Europe and the USA. The network provides cloud computing services based on dynamic provision of network slices through relocation of virtual data centers.     

A hybrid online-product recommendation system: Combining implicit rating-based collaborative filtering and sequential pattern analysis

Many online shopping malls in which explicit rating information is not available still have difficulty in providing recommendation services using collaborative filtering (CF) techniques for their users. Applying temporal purchase patterns derived from sequential pattern analysis (SPA) for recommendation services also often makes users unhappy with the inaccurate and biased results obtained by not considering individual preferences. The objective of this research is twofold. One is to derive implicit ratings so that CF can be applied to online transaction data even when no explicit rating information is available, and the other is to integrate CF and SPA for improving recommendation quality. Based on the results of several experiments that we conducted to compare the performance between ours and others, we contend that implicit rating can successfully replace explicit rating in CF and that the hybrid approach of CF and SPA is better than the individual ones.     

Systematic robustness analysis of least squares mobile robot velocity estimation using a regular polygonal optical mouse array

This paper presents the robust velocity estimation of an omnidirectional mobile robot using a regular polygonal array of optical mice that are installed at the bottom of a mobile robot. First, the velocity kinematics from a mobile robot to an array of optical mice is derived, from which the least squares estimation of the mobile robot velocity is obtained as the simple average of the optical mouse velocity readings. Second, it is shown that a redundant number of optical mice contributes to the robustness of the least squares mobile robot velocity estimation against both measurement noises and partial malfunction of optical mice. Third, the sensitivity analysis of the least squares mobile robot velocity estimation to imprecise installation of optical mice is made, from which a practical method of optical mouse position calibration is devised. Finally, some experimental results using commercial optical mice are given to demonstrate the validity and performance of the proposed mobile robot velocity estimation. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Automated synthesis of multiple analog circuits using evolutionary computation for redundancy-based fault-tolerance

Analog circuits are one of the most important parts of modern electronic systems and the failure of electronic hardware presents a critical threat to the completion of modern aircraft, spacecraft, and robot missions. Compared to digital circuits, designing fault-tolerant analog circuits is a difficult and knowledge-intensive task. A simple but powerful method for robustness is a redundancy approach to use multiple circuits instead of single one. For example, if component failures occur, other redundant components can replace the functions of broken parts and the system can still work. However, there are several research issues to make the redundant system automatically. In this paper, we used evolutionary computation to generate multiple analog circuits automatically and then we combined the solutions to generate robust outputs. Evolutionary computation is a natural way to produce multiple redundant solutions because it is a population-based search. Experimental results on the evolution of the low-pass, high-pass and band-stop filters show that the combination of multiple evolved analog circuits produces results that are more robust than those of the best single circuit.