Author
Krassimir T. Atanassov
Bio: Krassimir T. Atanassov is an academic researcher from Bulgarian Academy of Sciences. The author has contributed to research in topics: Fuzzy set operations & Fuzzy classification. The author has an hindex of 30, co-authored 324 publications receiving 22238 citations.
Papers published on a yearly basis
Papers
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TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
13,376 citations
01 Jan 1983
TL;DR: In this article, a definition of the concept "intuitionistic fuzzy set" (IFS) is given, the latter being a generalization of the Fuzzy Set and an example is described.
Abstract: A definition of the concept 'intuitionistic fuzzy set' (IFS) is given, the latter being a generalization of the concept 'fuzzy set' and an example is described. Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
2,256 citations
Book•
21 Sep 2019
TL;DR: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced and the majority of the proofs below are analogous to the proofs from Chapter 1.
Abstract: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.
2,255 citations
Book•
19 Oct 1999
TL;DR: The basic definitions and properties of the Intuitionistic Fuzzy Sets (IFSs) are introduced in the book and readers will find discussions on some of the IFS extensions (for example, interval-values IFSs, temporal I FSs and others) and applications.
Abstract: The basic definitions and properties of the Intuitionistic Fuzzy Sets (IFSs) are introduced in the book. The IFSs are substantial extensions of the ordinary fuzzy sets. IFSs are objects having degrees of membership and of non-membership, such that their sum is exactly 1. The most important property of IFS not shared by the fuzzy sets is that modal-like operators can be defined over IFSs. The IFSs have essentially higher describing possibilities than fuzzy sets. In this book, readers will find discussions on some of the IFS extensions (for example, interval-values IFSs, temporal IFSs and others) and applications (e.g. intuitionistic fuzzy expert systems, intuitionistic fuzzy neural networks, intuitionistic fuzzy systems, intuitionistic fuzzy generalized nets, and other).
1,837 citations
TL;DR: Two news operators on intuitionistic fuzzy sets are defined and their basic properties are studied to introduce new results on intuitionism fuzzy sets.
1,238 citations
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Book•
21 Sep 2019
TL;DR: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced and the majority of the proofs below are analogous to the proofs from Chapter 1.
Abstract: In this chapter, the basic definitions and properties of the interval valued intuitionistic fuzzy sets (IVIFSs) will be introduced. We will omit the majority of the proofs below, which are, in general, analogous to the proofs from Chapter 1.
2,255 citations
[...]
TL;DR: It is proved that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set, and it is proved also that the operations proposed are consistent with the ones of intuitionist fuzzy sets when applied to the envelope.
Abstract: Several extensions and generalizations of fuzzy sets have been introduced in the literature, for example, Atanassov's intuitionistic fuzzy sets, type 2 fuzzy sets, and fuzzy multisets. In this paper, we propose hesitant fuzzy sets. Although from a formal point of view, they can be seen as fuzzy multisets, we will show that their interpretation differs from the two existing approaches for fuzzy multisets. Because of this, together with their definition, we also introduce some basic operations. In addition, we also study their relationship with intuitionistic fuzzy sets. We prove that the envelope of the hesitant fuzzy sets is an intuitionistic fuzzy set. We prove also that the operations we propose are consistent with the ones of intuitionistic fuzzy sets when applied to the envelope of the hesitant fuzzy sets. © 2010 Wiley Periodicals, Inc.
2,232 citations
TL;DR: Based on score function and accuracy function, a method is introduced for the comparison between two intuitionistic fuzzy values and some aggregation operators are developed, such as the intuitionism fuzzy weighted averaging operator, intuitionists fuzzy ordered weighted averaging operators, and intuitionistic fuzziness hybrid aggregation operator, for aggregating intuitionist fuzzy values.
Abstract: An intuitionistic fuzzy set, characterized by a membership function and a non-membership function, is a generalization of fuzzy set. In this paper, based on score function and accuracy function, we introduce a method for the comparison between two intuitionistic fuzzy values and then develop some aggregation operators, such as the intuitionistic fuzzy weighted averaging operator, intuitionistic fuzzy ordered weighted averaging operator, and intuitionistic fuzzy hybrid aggregation operator, for aggregating intuitionistic fuzzy values and establish various properties of these operators.
2,131 citations
[...]
TL;DR: The authors define equality of two soft sets, subset and super set of a soft set, complement of asoft set, null soft set and absolute soft set with examples and De Morgan's laws and a number of results are verified in soft set theory.
Abstract: In this paper, the authors study the theory of soft sets initiated by Molodtsov. The authors define equality of two soft sets, subset and super set of a soft set, complement of a soft set, null soft set, and absolute soft set with examples. Soft binary operations like AND, OR and also the operations of union, intersection are defined. De Morgan's laws and a number of results are verified in soft set theory.
2,114 citations