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Contents of Volume 20 (2010)

1/2010

• [1] Editorial, 1-2.
• [2] Guest Editorial, 2-5.
• [3] Kreinovich V., Perfilieva I. (USA, Czech Republic): A broad prospective on fuzzy transforms: From gauging accuracy of quantity estimates to gauging accuracy and resolution of measuring physical fields, 7-25.

  Fuzzy transform is a new type of function transforms that has been successfully used in different applications. In this paper, we provide a broad prospective on fuzzy transform. Specifically, we show that fuzzy transform naturally appears when, in addition to measurement uncertainty, we also encounter another type of localization uncertainty: that the measured value may come not only from the desired location x, but also from the nearby locations.

• [4] Kupka J., Tomanová I. (Czech Republic): Some extensions of mining of linguistic associations, 27-44.

  This paper is a contribution to the theoretical foundations of data mining. More precisely, we contribute to a part of data mining allowing us to search for associations among attributes that can be expressed in the form of natural language sentences. The theoretical background and also a method for mining such associations was published recently in [V. Novák et al., Mining pure linguistic associations from numerical data, Int. Journal of Approximate Reasoning 48 (2008), 4 -- 22]. We elaborated other mathematical representations of the model presented in the mentioned paper in order to extend its applicability.

• [5] Bohacik J. (Slovak Republic): Discovering fuzzy rules in databases with linguistic variable elimination, 45-61.

  A group of fuzzy IF-THEN rules is belonging to one of the most popular, most effective, and user-friendliest knowledge representations. For this reason, extraction of these rules is becoming a more-and-more important part of the Data Mining stage in the Knowledge Discovery in Databases Process. In this paper, a direct algorithm for extracting fuzzy IF-THEN rules on the basis of linguistic variable elimination is described. The algorithm is implemented within a designed object-oriented software library Fuzzy Rule Miner. Besides the introduced algorithm, it implements two algorithms for fuzzy rule extraction based on using fuzzy decision trees of ID3 kind. An essential precondition for comparing the implemented algorithms and for verifying the legitimacy of the introduced algorithm is performance of experiments. The goal of experiments is to take in the behavior of algorithms on testing databases from the UCI Repository of Machine Learning Databases and to make comparisons of algorithms with one another. According to the conducted experiments, the introduced algorithm achieves high accuracy levels of discovered knowledge. The paper also contains a classification of rules and a specification of the Fuzzy Rule Discovery in Databases Process.

• [6] Petrík M., Sarkoci P. (Czech Republic, Slovak Republic): Zero-reconstructible triangular norms as universal approximators, 63-67.

  This paper is inspired by recent results [15, 16] which have shown that a multiplicative generator of a strict triangular norm can be reconstructed from the first partial derivatives of the triangular norm on the segment {0} x [0,1]. The strict triangular norms to which this method is applicable have been called zero-reconstructible triangular norms. This paper shows that every continuous triangular norm can be approximated (with an arbitrary precision) by a zero-reconstructible one, and thus substantiates the significance of this subclass of strict triangular norms.

• [7] Jágr V., Komorníková M., Mesiar R. (Slovak Republic): Conditioning stable copulas, 69-79.

  Copulas stable under univariate conditioning are studied. Limit approach to construction of conditioning stable copulas is introduced and illustrated. In the class of Archimedean copulas, Clayton copulas are shown to be the only conditioning stable copulas. Conditioning stable singular copulas are also discussed and examples of non-Archimedean absolutely continuous copulas which are conditioning stable are given.

• [8] Bacigál T., Juráňová M., Mesiar R. (Slovak Republic): On some new constructions of Archimedean copulas and applications to fitting problems, 81-90.

  Several constructions of additive generators of binary Archimedean copulas are introduced and discussed. Extension to general Archimedean copulas is also included. Applications to the fitting of copulas to real data are given and examplified.

• [9] de Andrés R., García-Lapresta J. L. (Spain): An endogenous human resources selection model based on linguistic assessments, 91-111.

  This paper proposes an endogenous human resources selection process by using linguistic information from a competency management perspective. We consider different sets of appraisers taking part in the evaluation process, having a different knowledge about the candidates that are being evaluated. Then, appraisers can express their assessments in different linguistic domains according to their knowledge. The proposed method converts each linguistic label into a fuzzy set on a common domain. Candidates are ranked by using different aggregation operators in order to allow the management team to make a final decision.

• [10] Fuerst K. (Austria): Applying fuzzy models in rating systems, 113-124.

  In the following paper, the use of fuzzy models in qualitative rating systems is analyzed in detail. The author works in an Austrian finance institution. There are at the moment two rating systems in use. The main purpose of such a rating system is to analyze company ratios to calculate a rating score, which is a measure for the financial situation and rigidity of a company. The first one is a solely hard fact rating system based on the Quicktest by Kralicek. The second one uses self-organizing maps and neural networks to calculate a rating classification and also offers the possibility to dispose personal appraisal in the calculation process.

  The following work examines the application spectrum of fuzzy logic and fuzzy models in soft-fact rating systems.

  We show that the use of fuzzy models in rating systems enables visualization of additional knowledge and offers the possibility to enhance the influence of a company's soft fact rating to the overall rating.

• [11] Bebčáková I., Talašová J., Pavlačka O. (Czech Republic): Fuzzification of Choquet integral and its application in multiple criteria decision making, 125-137.

  A common approach in the multiple criteria decision making is to obtain the overall evaluation by aggregating the partial evaluations. For this, a member of a large family of aggregation operators is used. Many of these operators commonly employed in decision making (weighted average, ordered weighted average, minimum, maximum, …) can be used only when criteria are independent. On the other hand, the Choquet integral, a generalization of the aforementioned operators, can be used even when some interactions between criteria occur. We present a fuzzified Choquet integral capable of dealing not only with fuzzy partial evaluations (first level fuzzification), but also with fuzzy weights (second level fuzzification). We also provide an effective way to evaluate the fully fuzzified integral, which allows its straightforward application to decision making problems with inherent uncertainty.

• [12] Galar M., Bustince H., Fernandez J., Sanz J., Beliakov G. (Spain, Australia): Fuzzy entropy from weak fuzzy subsethood measures, 139-158.

  In this paper, we propose a new construction method for fuzzy and weak fuzzy subsethood measures based on the aggregation of implication operators. We study the desired properties of the implication operators in order to construct these measures. We also show the relationship between fuzzy entropy and weak fuzzy subsethood measures constructed by our method.

• [13] Poláková R. (Czech Republic): A variant of competitive differential evolution algorithm with exponential crossover, 159-169.

  The differential evolution (DE) algorithm is a powerful population-based stochastic technique to search for global optimum in the continuous search space. Success of DE algorithm strongly depends on choosing its parameters. The competition in differential evolution was shown to be an efficient instrument to avoid time-consuming process of tuning control parameters. A new variant of competitive DE algorithm, called BEBERAN, was proposed and tested on benchmark functions at four levels of the search space dimension. The BEBERAN was compared with the most promising competitive variant, DEBR18. BEBERAN, in contrast to DEBR18, includes in addition the exponential crossover.