OWA operators in regression problems

We consider an application of fuzzy logic connectives to statistical regression. We replace the standard least squares, least absolute deviation, and maximum likelihood criteria with an ordered weighted averaging (OWA) function of the residuals. Depending on the choice of the weights, we obtain the standard regression problems, high-breakdown robust methods (least median, least trimmed squares, and trimmed likelihood methods), as well as new formulations. We present various approaches to numerical solution of such regression problems. OWA-based regression is particularly useful in the presence of outliers, and we illustrate the performance of the new methods on several instances of linear regression problems with multiple outliers.<br /

Operations on Concavoconvex Type-2 Fuzzy Sets

Concavoconvex fuzzy set is the result of the com-bination of the concepts of convex and concave fuzzy sets. This paper investigates concavoconvex type-2 fuzzy sets. Basic operations, union, intersection and complement on concavoconvex type-2 fuzzy sets us-ing min and product t-norm and max t-conorm are studied and some of their algebraic properties are explored

A contribution to the ranking and description of classifications

This thesis presents a novel and complete fuzzy multi-criteria decision making (MCDM) methodology. This methodology is specifically designed for selecting classifications in the framework of unsupervised learning systems. The main results obtained are twofold. On the one hand, the definition of fuzzy criteria to be used to assess the suitability of a set of given classifications and, on the other hand, the design and development of a natural language generation (NLG) system to qualitatively describe them. Unsupervised learning systems often produce a large number of possible classifications. In order to select the most suitable one, a set of criteria is usually defined and applied sequentially to assess and filter the obtained classifications. This is done, in general, by using a true-false decision in the application of each criterion. This approach could result in classifications being discarded and not taken into account when they marginally fail to meet one particular criterion even though they meet other criteria with a high score. An alternative solution to this sequential approach has been introduced in this thesis. It consists of evaluating the degree up to which each fuzzy criterion is met by each classification and, only after this, aggregating for each classification the individual assessments. This overall value reflects the degree up to which the set of criteria is globally satisfied by each classification. Five fuzzy criteria are defined and analysed to be used collectively to evaluate classifications. The corresponding single evaluations are then proposed to be aggregated into a collective one by means of an Ordered Weighted Averaging (OWA) operator guided by a fuzzy linguistic quantifier, which is used to implement the concept of fuzzy majority in the selection process. In addition, a NLG system to qualitatively describe the most important characteristics of the best classification is designed and developed in order to fully understand the chosen classification. Finally, this new methodology is applied to a real business problem in a marketing context. The main purpose of this application is to show how the proposed methodology can help marketing experts in the design of specific-oriented marketing strategies by means of an automatic and interpretable segmentation system

Entanglement in continuous variable systems: Recent advances and current perspectives

We review the theory of continuous-variable entanglement with special emphasis on foundational aspects, conceptual structures, and mathematical methods. Much attention is devoted to the discussion of separability criteria and entanglement properties of Gaussian states, for their great practical relevance in applications to quantum optics and quantum information, as well as for the very clean framework that they allow for the study of the structure of nonlocal correlations. We give a self-contained introduction to phase-space and symplectic methods in the study of Gaussian states of infinite-dimensional bosonic systems. We review the most important results on the separability and distillability of Gaussian states and discuss the main properties of bipartite entanglement. These include the extremal entanglement, minimal and maximal, of two-mode mixed Gaussian states, the ordering of two-mode Gaussian states according to different measures of entanglement, the unitary (reversible) localization, and the scaling of bipartite entanglement in multimode Gaussian states. We then discuss recent advances in the understanding of entanglement sharing in multimode Gaussian states, including the proof of the monogamy inequality of distributed entanglement for all Gaussian states, and its consequences for the characterization of multipartite entanglement. We finally review recent advances and discuss possible perspectives on the qualification and quantification of entanglement in non Gaussian states, a field of research that is to a large extent yet to be explored.Comment: 61 pages, 7 figures, 3 tables; Published as Topical Review in J. Phys. A, Special Issue on Quantum Information, Communication, Computation and Cryptography (v3: few typos corrected

Ranking and selection of unsupervised learning marketing segmentation

This research paper has been partially conducted during a three-months visiting period by German Sanchez-Hernandez to the Centre for Computational Intelligence (CCI).NOTICE: this is the author’s version of a work that was accepted for publication in . Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Knowledge-Based Systems, 44, pp. 20–33 http://dx.doi.org/10.1016/j.knosys.2013.01.012This paper addresses the problem of choosing the most appropriate classification from a given set of classifications of a set of patterns. This is a relevant topic on unsupervised systems and clustering analysis because different classifications can in general be obtained from the same data set. The provided methodology is based on five fuzzy criteria which are aggregated using an Ordered Weighted Averaging (OWA) operator. To this end, a novel multi-criteria decision making (MCDM) system is defined, which assesses the degree up to which each criterion is met by all classifications. The corresponding single evaluations are then proposed to be aggregated into a collective one by means of an OWA operator guided by a fuzzy linguistic quantifier, which is used to implement the concept of fuzzy majority in the selection process. This new methodology is applied to a real marketing case based on a business to business (B2B) environment to help marketing experts during the segmentation process. As a result, a segmentation containing three segments consisting of 35, 98 and 127 points of sale respectively is selected to be the most suitable to endorse marketing strategies of the firm. Finally, an analysis of the managerial implications of the proposed methodology solution is provided.This work is supported by the SENSORIAL Research Project (TIN2010-20966- C02-01, 02), funded by the Spanish Ministry of Science and Information Technology

BENCHMARKING CLASSIFIERS - HOW WELL DOES A GOWA-VARIANT OF THE SIMILARITY CLASSIFIER DO IN COMPARISON WITH SELECTED CLASSIFIERS?

Digital data is ubiquitous in nearly all modern businesses. Organizations have more data available, in various formats, than ever before. Machine learning algorithms and predictive analytics utilize the knowledge contained in that data, in order to help the business related decision-making. This study explores predictive analytics by comparing different classification methods – the main interest being in the Generalize Ordered Weighted Average (GOWA)-variant of the similarity classifier. The target for this research is to find out how what is the GOWA-variant of the similarity classifier and how well it performs compared to other selected classifiers. This study also tries to investigate whether the GOWA-variant of the similarity classifier is a sufficient method to be used in the busi-ness related decision-making. Four different classical classifiers were selected as reference classifiers on the basis of their common usage in machine learning research, and on their availability in the Sta-tistics and Machine Learning Toolbox in MATLAB. Three different data sets from UCI Machine Learning repository were used for benchmarking the classifiers. The benchmarking process uses fitness function instead of pure classification accuracy to determine the performance of the classifiers. Fitness function combines several measurement criteria into a one common value. With one data set, the GOWA-variant of the similarity classifier per-formed the best. One of the data sets contains credit card client data. It was more complex than the other two data sets and contains clearly business related data. The GOWA-variant performed also well with this data set. Therefore it can be claimed that the GOWA-variant of the similarity classifi-er is a viable option to be used also for solving business related problems

Computer Aided Verification

The open access two-volume set LNCS 12224 and 12225 constitutes the refereed proceedings of the 32st International Conference on Computer Aided Verification, CAV 2020, held in Los Angeles, CA, USA, in July 2020.* The 43 full papers presented together with 18 tool papers and 4 case studies, were carefully reviewed and selected from 240 submissions. The papers were organized in the following topical sections: Part I: AI verification; blockchain and Security; Concurrency; hardware verification and decision procedures; and hybrid and dynamic systems. Part II: model checking; software verification; stochastic systems; and synthesis. *The conference was held virtually due to the COVID-19 pandemic