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Abstract Consistency is related with reasonableness. This paper proposes a graphical method to visualize and rectify different inconsistencies for fuzzy reciprocal preference relations (FPRs), and the consistency includes the ordinal and cardinal consistencies. Ordinal inconsistency implies cardinal inconsistency, but not vice versa, and cardinal consistency of FPRs includes additive consistency and multiplicative consistency. Therefore, there are four types of inconsistencies, includes: (1) the additive inconsistency; (2) the multiplicative inconsistency; (3) the ordinal and additive inconsistencies, and (4) the ordinal and multiplicative inconsistencies. First, Gower plots are proposed to visualize the ordinal and cardinal inconsistencies on a two-dimensional plane. Then, some optimization models are formulated to rectify the four different types of inconsistences, respectively. Some examples are illustrated to show how the models work, and comparisons with the existing methods are also offered to show the advantages of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract: The analysis of data complexity is a proper framework to characterize the tackled classification problem and to identify domains of competence of classifiers. As a practical outcome of this framework, the proposed data complexity measures may facilitate the choice of a classifier for a given problem. The aim of this paper is to study the behaviour of a fuzzy rule based classification system and its relationship to data complexity. We use as a case of study the fuzzy hybrid genetic based machine learning method presented in [H. Ishibuchi, T. Yamamoto, T. Nakashima, Hybridization of fuzzy GBML approaches for pattern classification problems, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics 35 (2) (2005) 359–365]. We examine several metrics of data complexity over a wide range of data sets built from real data and try to extract behaviour patterns from the results. We obtain rules which describe both good or bad behaviours of the fuzzy rule based classification system. These rules use values of data complexity metrics in their antecedents, so we try to predict the behaviour of the method from the data set complexity metrics prior to its application. Therefore, we can establish the domains of competence of this fuzzy rule based classification system. [Copyright &y& Elsevier]

Abstract Ranking fuzzy numbers plays an important role in the decision process. Several strategies can be found in the abundant literature existing on this topic, which can be basically classified into two main groups: approaches based on the so-called ranking indices and based on fuzzy binary relations. Ranking indices are functions from fuzzy numbers to real values. These defuzzification methods are critiqued by its implicit information loss which leads to results that might not be consistent with human intuition in certain cases. In a fuzzy context, approaches based on binary relations can be considered more suitable solutions. Following this strategy, this paper introduces a new technique for ranking fuzzy numbers which is applicable to the whole set of fuzzy numbers. It is proved that many desired properties (in particular, we give several new properties) are satisfied and numerical examples show reasonable results. The developed technique is very easy to compute and interpret in practice, and it overcomes certain shortcomings that appear when applying other more complex algorithms. In the case of triangular or trapezoidal fuzzy numbers, the procedure is particularly simple and intuitive. Finally, a real-life example involving data of Chinese Economy is also carried out. [ABSTRACT FROM AUTHOR]

We introduce and study aggregation functions based on extremal values, namely extended (l , u) -aggregation functions whose outputs only depend on a fixed number l of extremal lower input values and a fixed number u of extremal upper input values, independently of the arity of the input n -tuples (n ≥ l + u). We discuss several general properties of (l , u) -aggregation functions and we study special (l , u) -aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study (l , u) -aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as (l , u) -ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too. [ABSTRACT FROM AUTHOR]

Agricultural products have experienced sudden changes in prices in recent years as a result of volumes of production and demand at the international level. Volatility is a key element in understanding the difficulties that the market may have. However, the traditional formula for volatility only considers historical information and does not consider decision makers' knowledge and skills. To improve this approach and obtain more accurate results consistent with the reality of the market, the ordered weighted averaging (OWA) operator is used. These new approaches are the OWA-Volatility, Induced OWA-Volatility, Heavy OWA-Volatility, Probabilistic OWA-Volatility, Induced Probabilistic OWA-Volatility and Induced Heavy OWA-Volatility. In addition, some particular cases are presented in which the aggregation process is only applied to one part of the formula or quasi-arithmetic means are used. An example of volatility calculations for corn prices in 2017 is presented. [ABSTRACT FROM AUTHOR]

Classification with big data has become one of the latest trends when talking about learning from the available information. The data growth in the last years has rocketed the interest in effectively acquiring knowledge to analyze and predict trends. The variety and veracity that are related to big data introduce a degree of uncertainty that has to be handled in addition to the volume and velocity requirements. This data usually also presents what is known as the problem of classification with imbalanced datasets, a class distribution where the most important concepts to be learned are presented by a negligible number of examples in relation to the number of examples from the other classes. In order to adequately deal with imbalanced big data we propose the Chi-FRBCS-BigDataCS algorithm, a fuzzy rule based classification system that is able to deal with the uncertainly that is introduced in large volumes of data without disregarding the learning in the underrepresented class. The method uses the MapReduce framework to distribute the computational operations of the fuzzy model while it includes cost-sensitive learning techniques in its design to address the imbalance that is present in the data. The good performance of this approach is supported by the experimental analysis that is carried out over twenty-four imbalanced big data cases of study. The results obtained show that the proposal is able to handle these problems obtaining competitive results both in the classification performance of the model and the time needed for the computation. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with multi-class classification for linguistic fuzzy rule based classification systems. The idea is to decompose the original data-set into binary classification problems using the pairwise learning approach (confronting all pair of classes), and to obtain an independent fuzzy system for each one of them. Along the inference process, each fuzzy rule based classification system generates an association degree for both of its corresponding classes and these values are encoded into a fuzzy preference relation. Our analysis is focused on the final step that returns the predicted class-label. Specifically, we propose to manage the fuzzy preference relation using a non-dominance criterion on the different alternatives, contrasting the behaviour of this model with both the classical weighted voting scheme and a decision rule that combines the fuzzy relations of preference, conflict and ignorance by means of a voting strategy. Our experimental study is carried out using two different linguistic fuzzy rule learning methods for which we show that the non-dominance criterion is a good alternative in comparison with the previously mentioned aggregation mechanisms. This empirical analysis is supported through the corresponding statistical analysis using non-parametrical tests. [ABSTRACT FROM AUTHOR]

Abstract: Different studies have proposed methods for mining fuzzy association rules from quantitative data, where the membership functions were assumed to be known in advance. However, it is not an easy task to know a priori the most appropriate fuzzy sets that cover the domains of quantitative attributes for mining fuzzy association rules. This paper thus presents a new fuzzy data-mining algorithm for extracting both fuzzy association rules and membership functions by means of a genetic learning of the membership functions and a basic method for mining fuzzy association rules. It is based on the 2-tuples linguistic representation model allowing us to adjust the context associated to the linguistic term membership functions. Experimental results show the effectiveness of the framework. [Copyright &y& Elsevier]

Abstract: In the field of classification problems, we often encounter classes with a very different percentage of patterns between them, classes with a high pattern percentage and classes with a low pattern percentage. These problems receive the name of “classification problems with imbalanced data-sets”. In this paper we study the behaviour of fuzzy rule based classification systems in the framework of imbalanced data-sets, focusing on the synergy with the preprocessing mechanisms of instances and the configuration of fuzzy rule based classification systems. We will analyse the necessity of applying a preprocessing step to deal with the problem of imbalanced data-sets. Regarding the components of the fuzzy rule base classification system, we are interested in the granularity of the fuzzy partitions, the use of distinct conjunction operators, the application of some approaches to compute the rule weights and the use of different fuzzy reasoning methods. [Copyright &y& Elsevier]