Four Operations over Extended Intuitionistic Fuzzy Index Matrices and Some of Their Applications

2020 ◽  
pp. 27-39
Author(s):  
Krassimir Atanassov ◽  
Veselina Bureva
Keyword(s):  
Intuitionistic Fuzzy ◽  
Fuzzy Index

Correlation in Interval-Valued Atanassov’s Intuitionistic Fuzzy Sets — Conjugate and Negation Operators

2017 ◽  
Vol 25 (05) ◽  
pp. 787-819 ◽  
Author(s):  
Renata Hax Sander Reiser ◽  
Benjamin Bedregal
Keyword(s):  
Fuzzy Logic ◽  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
Conjugate Functions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Index ◽  
Intuitionistic Fuzzy Logic ◽  
Interval Valued ◽  
Atanassov’S Intuitionistic Fuzzy Sets

This paper studies the conjugate functions related to main connectives of the Intervalvalued Atanassov’s Intuitionistic Fuzzy Logic. The relationships among automorphism classes are formalized by the ϕ-representability theorem, passing from automorphisms to interval-valued intuitionistic automorphisms, also visiting other two ones, intuitionistic automorphisms and interval-valued automorphisms. Additionally, the ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation can be obtained either from an interval-valued fuzzy negation or from an Atanassov’s intuitionistic fuzzy negation, including a discussion presenting such reverse constructions. The ϕ-conjugate of an interval-valued Atanassov’s intuitionistic fuzzy negation not only preserves the main properties of its corresponding fuzzy negation but also of two other ones, the intuitionistic fuzzy negation and interval-valued fuzzy negation. Moreover, an extension of the intuitionistic fuzzy index as well as the correlation coefficient is discussed in terms of fuzzy negations, by considering the Atanassov’s Intuitionistic Fuzzy Logic.

Interval Version of Generalized Atanassov’s Intuitionistic Fuzzy Index

2018 ◽  
pp. 217-229
Author(s):  
Lidiane Costa ◽  
Mônica Matzenauer ◽  
Adenauer Yamin ◽  
Renata Reiser ◽  
Benjamín Bedregal
Keyword(s):  
Intuitionistic Fuzzy ◽  
Fuzzy Index

GENERALIZED ATANASSOV'S INTUITIONISTIC FUZZY INDEX: CONSTRUCTION OF ATANASSOV'S FUZZY ENTROPY FROM FUZZY IMPLICATION OPERATORS

2011 ◽  
Vol 19 (01) ◽  
pp. 51-69 ◽  
Author(s):  
HUMBERTO BUSTINCE ◽  
EDURNE BARRENECHEA ◽  
MIGUEL PAGOLA ◽  
JAVIER FERNANDEZ ◽  
CARLOS GUERRA ◽  
...  
Keyword(s):  
Construction Method ◽  
Fuzzy Entropy ◽  
Index Construction ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Implication ◽  
Aggregation Functions ◽  
Intuitionistic Fuzzy Entropy ◽  
Fuzzy Index

In this paper we introduce the concept of Generalized Atanassov's Intuitionistic Fuzzy Index. We characterize it in terms of fuzzy implication operators and propose a construction method with order automorphisms. Finally, we obtain, by means of special aggregation functions applied to the generalized Atanassov's intuitionistic fuzzy index, the Atanassov's intuitionistic fuzzy entropy given by Burillo and Bustince.

scholarly journals Level Operators over Intuitionistic Fuzzy Index Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 366
Author(s):  
Krassimir Atanassov ◽  
Peter Vassilev ◽  
Olympia Roeva
Keyword(s):  
Standard Case ◽  
Partial Case ◽  
Basic Properties ◽  
Intuitionistic Fuzzy ◽  
Matrix Operations ◽  
Index Matrix ◽  
Fuzzy Index

The index matrix (IM) is an extension of the ordinary matrix with indexed rows and columns. Over IMs’ standard matrix operations are defined and a lot of other ones that do not exist in the standard case. Intuitionistic fuzzy IMs (IFIMs) are modification of the IMs, when their elements are intuitionistic fuzzy pairs (IFPs). Extended IFIMs are IFIMs whose indices of the rows and columns are evaluated by IFPs. Different operations, relations and operators over IFIMs, and some specific ones, are defined for EIFIMs. In the paper, twelve new level operators are defined for EIFIMs and in the partial case, over IFIMs. The proposed level operators fall into two groups: operators that change the values of the EIFIM elements and operators that change the IFPs associated to the indices of the rows and columns. The basic properties of the operators are studied.

scholarly journals Intuitionistic fuzzy index matrix representation of color images

2020 ◽  
Vol 26 (4) ◽  
pp. 64-70
Author(s):  
R. K. Nivendhaa ◽  
◽  
R. Parvathi ◽  
Keyword(s):  
Image Processing ◽  
Fuzzy Sets ◽  
Color Image ◽  
Matrix Representation ◽  
Color Images ◽  
Intuitionistic Fuzzy ◽  
Index Matrix ◽  
Rgb Images ◽  
Fuzzy Index

It is usual in image processing that binary (black & white) and gray images are represented by crisp sets and fuzzy sets respectively. In this paper, an attempt has been made to represent a color image (RGB) using intuitionistic fuzzy index matrices. The objective of this representation is to apply mathematical operators on intuitionistic fuzzy index matrices in processing RGB images.

scholarly journals Generalized Atanassov’s Intuitionistic Fuzzy Index and Conjugate with S-implications

2017 ◽  
Author(s):  
Rosana Zanotelli ◽  
Lidiane Da Silva ◽  
Miriam Born ◽  
Renata Reiser ◽  
Adenauer Yamin
Keyword(s):  
Intuitionistic Fuzzy ◽  
Fuzzy Index
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