Feature selection, as one of the essential dimensionality reduction techniques, hasbecome one popular yet challenging area in the field, such as data mining andmachine learning. Unlike feature extraction (such as principle component analysis andnon-negative matrix factorization), preserving the entire information but losing thefeature relevance. Data processing in feature selection will lose information, leading tothe need to develop lightweight, efficient, and practical methods that preserve the datainformation as much as possible while performing dimensional reduction. In this paper,we propose a rankability-based feature selection method. The rankability concept wasproposed in 2019, similar to the entropy concept, and has not been studied widely yet.The proposed method is lightweight in terms of complexity, which requires no iterativeoptimization or auxiliary estimator tools.We experimented with sixteen datasets and compared our results with four otheralgorithms. The results show that our rankability-based feature selection methodoutperforms the fuzzy entropy-based method on five datasets in eight, and the averageaccuracy increased by 0.1482, 0.1078, and 0.1157, respectively. Then, in the varieddimension-reducing experiments, the proposed method shows superiority on fourdatasets out of eight and is competitive with others on two datasets out of eight.

In this article, we return to the problem of the derivation of a conclusion on the basis of fuzzy IF–THEN rules. The so-called Mamdani method is well elaborated and widely applied. In this article, we present an alternative to it. The fuzzy IF–THEN rules are here interpreted as genuine linguistic sentences consisting of the so-called evaluating linguistic expressions. Sets of fuzzy IF–THEN rules are called linguistic descriptions. Linguistic expressions derived on the basis of an observation in a concrete context are called perceptions. Together with the linguistic description, they can be used in logical deduction, which we will call a perception-based logical deduction. We focus on semantics only and confine ourselves to one specific model. If the perception-based deduction is repeated and the result interpreted in an appropriate model, we obtain a piecewise continuous and monotonous function. Though the method has already proved to work well in many applications, the nonsmoothness of the output may sometimes lead to problems. We propose in this article a method for how the resulting function can be made smooth so that the output preserves its good properties. The idea consists of postprocessing the output using a special fuzzy approximation method called F-transform. © 2004 Wiley Periodicals, Inc. Int J Int Syst 19: 1007–1031, 2004.

There are two main fuzzy system methodologies for translating expert rules into a logical formula: In Mamdani's methodology, we get a DNF formula (disjunction of conjunctions), and in a methodology which uses logical implications, we get, in effect, a CNF formula (conjunction of disjunctions). For both methodologies, universal approximation results have been proven which produce, for each approximated function f(x), two different approximating relations RDNF(x, y) and RCNF(x, y). Since, in fuzzy logic, there is a known relation FCNF(x) ≤ FDNF(x) between CNF and DNF forms of a propositional formula F, it is reasonable to expect that we would be able to prove the existence of approximations for which a similar relation RCNF(x, y) ≤ RDNF(x, y) holds. Such existence is proved in our paper. © 2002 Wiley Periodicals, Inc.

In this paper we report an application of fuzzy arithmetic to the reduction of geographical data sets. The proposed technique builds a “summary” of the data within a given subregion in the form of a suitable fuzzy real number. The membership function of this number is obtained with a procedure that resembles the mountain function method introduced by Yager and Filev [IEEE Trans Syst. Man, Cybern Aug. 1994, 24(8), 1279–1284]. The proposed approach is computationally efficient, theoretically sound, and quite robust in terms of experimental noise. In addition, it does not require any statistical assumption about the distribution of the data. The summarization technique reported has been successfully used in modeling a real terrain from collections of sparse elevation data on a terrain. Comparisons with similar approaches are also reported. ©1999 John Wiley & Sons, Inc.