Unsymmetrical basic uncertain information with some decision-making methods

Motivated by a specific decision-making situation, this work proposes the concept and definition of unsymmetrical basic uncertain information which is a further generalization of basic uncertain information and can model uncertainties in some new decision-making situations. We show that unsymmetrical basic uncertain information in some sense can model linguistic hedges such as 'at least' and 'at most'. Formative weighted arithmetic means and induced aggregations are defined for the proposed concept. Rules-based decision making and semi-copula based integral for this concept with some numerical examples are also presented.The paper is supported by National Natural Science Foundation of China with grant nos. 72171182 and 71801175, Grant APVV-18-0052, Grant PID2019-108392GBI00, financed by MCIN/AEI/10.13039/501100011033

iAggregator: Multidimensional Relevance Aggregation Based on a Fuzzy Operator

International audienceRecently, an increasing number of information retrieval studies have triggered a resurgence of interest in redefining the algorithmic estimation of relevance, which implies a shift from topical to multidimensional relevance assessment. A key underlying aspect that emerged when addressing this concept is the aggregation of the relevance assessments related to each of the considered dimensions. The most commonly adopted forms of aggregation are based on classical weighted means and linear combination schemes to address this issue. Although some initiatives were recently proposed, none was concerned with considering the inherent dependencies and interactions existing among the relevance criteria, as is the case in many real-life applications. In this article, we present a new fuzzy-based operator, called iAggregator, for multidimensional relevance aggregation. Its main originality, beyond its ability to model interactions between different relevance criteria, lies in its generalization of many classical aggregation functions. To validate our proposal, we apply our operator within a tweet search task. Experiments using a standard benchmark, namely, Text REtrieval Conference Microblog,1 emphasize the relevance of our contribution when compared with traditional aggregation schemes. In addition, it outperforms state-of-the-art aggregation operators such as the Scoring and the And prioritized operators as well as some representative learning-to-rank algorithms

A construction method of Atanassov’s intuitionistic fuzzy sets for image processing

In this work we introduce a new construction method of Atanassov\u27s intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency

Compact versus noncompact LP formulations for minimizing convex Choquet integrals

AbstractWe address here the problem of minimizing Choquet Integrals (also known as “Lovász Extensions”) over solution sets which can be either polyhedra or (mixed) integer sets. Typical applications of such problems concern the search of compromise solutions in multicriteria optimization. We focus here on the case where the Choquet Integrals to be minimized are convex, implying that the set functions (or “capacities”) underlying the Choquet Integrals considered are submodular. We first describe an approach based on a large scale LP formulation, and show how it can be handled via the so-called column-generation technique. We next investigate alternatives based on compact LP formulations, i.e. featuring a polynomial number of variables and constraints. Various potentially useful special cases corresponding to well-identified subclasses of underlying set functions are considered: quadratic and cubic submodular functions, and a more general class including set functions which, up to a sign, correspond to capacities which are both (k+1)−additive and k-monotone for k≥3. Computational experiments carried out on series of test instances, including transportation problems and knapsack problems, clearly confirm the superiority of compact formulations. As far as we know, these results represent the first systematic way of practically solving Choquet minimization problems on solution sets of significantly large dimensions

Medical diagnosis of cardiovascular diseases using an interval-valued fuzzy rule-based classification system

Objective: To develop a classifier that tackles the problem of determining the risk of a patient of suffering from a cardiovascular disease within the next ten years. The system has to provide both a diagnosis and an interpretable model explaining the decision. In this way, doctors are able to analyse the usefulness of the information given by the system. Methods: Linguistic fuzzy rule-based classification systems are used, since they provide a good classification rate and a highly interpretable model. More specifically, a new methodology to combine fuzzy rule-based classification systems with interval-valued fuzzy sets is proposed, which is composed of three steps: 1) the modelling of the linguistic labels of the classifier using interval-valued fuzzy sets; 2) the use of the Kα operator in the inference process and 3) the application of a genetic tuning to find the best ignorance degree that each interval-valued fuzzy set represents as well as the best value for the parameter α of the Kα operator in each rule. Results: The suitability of the new proposal to deal with this medical diagnosis classification problem is shown by comparing its performance with respect to the one provided by two classical fuzzy classifiers and a previous interval-valued fuzzy rule-based classification system. The performance of the new method is statistically better than the ones obtained with the methods considered in the comparison. The new proposal enhances both the total number of correctly diagnosed patients, around 3% with respect the classical fuzzy classifiers and around 1% versus the previous interval-valued fuzzy classifier, and the classifier ability to correctly differentiate patients of the different risk categories. Conclusion: The proposed methodology is a suitable tool to face the medical diagnosis of cardiovascular diseases, since it obtains a good classification rate and it also provides an interpretable model that can be easily understood by the doctors.This work was partially supported by the Spanish Ministry of Science and Technology under project TIN2010-15055 and the Research Services of the Universidad Pública de Navarra

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

Journal of Telecommunications and Information Technology, 2009, nr 3

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