This paper addresses four new distance measures as tools in pattern recognition for intuitionistic fuzzy sets (IFSs). Following the discussion on literature of distance measures, proposed measurement scales and the proof of their properties would be presented. In order to show the reliability of addressed formulations, this paper employs them in a part of medical diagnosis progress in bacillus ...

Although many measures of similarity between intuitionistic fuzzy set (IFS) have been proposed in the literature, some existing similarity measures are not always effective in some cases. A main reason is that existing similarity measures have not or little considered degree of hesitancy in intuitionistic fuzzy set. In this paper, based on this foundation that the degree of hesitancy in intuiti...

The correlation coefficient (Pearson’s r) is one of the most frequently used tools in statistics. In this paper we discuss a correlation coefficient between Atanassov’s intuitionistic fuzzy sets (A-IFSs). We have constructed the coefficient so it provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the prop...

This paper concerns the theory of intuitionistic fuzzy sets according to Atanassov. If triangular norms, especially nonstrict Archimedean ones, are used, we propose a revision and a flexibilizing generalization of some fundamental notions and constructions of that theory. Its application to group decision making is outlined.

In the present paper a generalization of the operator Fα,β de ned by Atanassov in [1] is considered. This operator is de ned over the class of p-intuitionistic fuzzy sets. Its properties are studied and a Theorem analogous to the results obtained in [4] is proved.

The author would like to thank Ioannis K. Vlachos, George D. Sergiadis [1] for providing some comments on the paper “Image thresholding using type II fuzzy sets” [2]. The main subject of the comments deals with the relationship between interval-values fuzzy sets (IVFSs) and the intuitionistic fuzzy sets (IFSs) on one side and the entropy measures introduced on the other side. Apparently, this i...

We propose a new similarity measure for intuitionistic fuzzy sets (cf. Atanassov [1, 2]) and show its usefulness in medical diagnostic reasoning. We point out advantages of this new concept over the method proposed previously (cf. Szmidt and Kacprzyk [23]) where distances were used instead of the proposed similarity measure.

We consider some existing similarity measures for Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short). We show that neither similarity measures treating an A-IF as a simple interval values fuzzy set, nor straightforward generalizations of the similarity measures well-known for the classic fuzzy sets work under reasonable circumstances. Next, expanding upon our previous works, we consider ...

The problem of segmentation is an important research field and often a critical and decisive preprocessing step for many image processing applications. During the past years, the use of colour images instead of gray images is growing fast in many research areas. Moreover, the use of segmentation over colour images is advised when additional colour information conveyed is necessary to further di...

We proposed the theory of multi-fuzzy sets [Sabu and Ramakrishnan (2010a), (2011a)] as an extension of theories of fuzzy sets, L-fuzzy sets [Goguen (1967)] and intuitionistic fuzzy sets [Atanassov (1986)]. Theory of multi-fuzzy sets deals with multi-level fuzziness and multi-dimensional fuzziness. Our previous papers discussed the basic notions of multi-fuzzy sets, multi-fuzzy topology, and mul...