Eulalia Szmidt

We present a novel classifier based on Atanassov's intuitionistic fuzzy sets (IFSs, for short). Using benchmark data from UCI Machine Learning Repository, we demonstrate that the proposed classifier achieves very good results.

The k-NN (k-Nearest Neighbor) classifier is one of the commonly used classifiers. We present a modification of this classifier based on Atanassov's intuitionistic fuzzy sets (IFSs, for short). We show, using benchmark data from UCI Machine Learning Repository, that the classifier we propose achieves very good results.

We use the natural properties of intuitionistic fuzzy sets (IFSs for short) to represent the pros, cons, and lack of knowledge concerning different options/alternatives, aiding in decision making, particularly in group decision making. We present a novel approach. We do not compare options/alternatives in pairs, we do not use distances. The approach is transparent and easily understandable for decision makers. The novel method points out the best option by ranking them.

Atanassov’s intuitionistic fuzzy sets (IFSs) are a very convenient tool for describing alternatives/options while making decisions because they make it possible to naturally represent the pros, cons, and hesitation. The IFSs have attracted a significant interest and have been applied in various fields. Of course, their use poses some challenges. One of the main challenges is the ranking of alternatives/options described by the intuitionistic fuzzy sets, to be called for brevity the intuitionistic fuzzy alternatives. This is a crucial issue, notably for the applications, for instance, in decision making. We first present in detail and analyze the benefits of a method we introduced previously (cf. Szmidt and Kacprzyk [1]). For this method, we augment the original assumptions with an additional assumption, which is justified and inherently reasonable. As a result, we obtain formulas which are better justified than those previously used as they explicitly consider the arguments in favor (pro), against (con), and hesitance. Since the intuitionistic fuzzy alternatives can not be linearly ranked, then the additional assumptions during the ranking process are necessary. We address these issues and analyze examples to clarify our new approach. We examine some other methods discussed in the literature and analyze their results, and show that the new assumptions reconcile some misconceptions raised by those other papers.

Dimension reduction of the models, i.e., pointing out only the necessary number of input variables (attributes, features) is an important task enabling the efficient performance of different algorithms. This paper is a continuation of our previous works on a new method of selection of the attributes in the models making use of Atanassov's intuitionistic fuzzy sets. We consider classification problems trying to point out the reduced number of the attributes and still obtain satisfactory results. We investigate the previously proposed method in more details comparing its performance with a well-known method of extraction parameters, namely Principal Component Analysis (PCA), and with a well-known method of selecting the attributes in which the so-called Gain Ratio is used. We illustrate our considerations using benchmark data from UCI Machine Learning Repository.

One of the essential formulas of the classical mathematical logic is (A → B) → ((¬A → B) → B). In the present paper, its intuitionistic fuzzy interpretation is introduced, and lists of all defined intuitionistic fuzzy implications that satisfy it as a tautology and an intuitionistic fuzzy tautology are given.

In this paper, we continue our considerations concerning the ranking of intuitionistic fuzzy alternatives (options, variants, ...). We complete our previous considerations by showing in another way why the method proposed by us gives proper results. We stress when the method should be applied and emphasize its transparency.