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.

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.

A Sensation Model for Color Images’ Cognition

2013 ◽  
Vol 303-306 ◽  
pp. 1489-1493
Author(s):  
Zhong Sheng Li ◽  
Tong Cheng Huang ◽  
Niu Li ◽  
Ze Su Cai
Keyword(s):  
Image Processing ◽  
Computational Intelligence ◽  
High Speed ◽  
Granular Computing ◽  
Color Image ◽  
Color Images ◽  
Color Image Processing ◽  
New Concepts ◽  
Single Attribute ◽  
Human Thinking

It’s a new idea to make computers be able to obtain “sensations” from a color image through some unsupervised ways. To let the idea come into true, a granule-based model, based on granular computing(GrC) which is a new way to simulate human thinking to help solve complicated problems in the field of computational intelligence, is proposed for color image processing. First, this paper deems data a hypercube, defines two new concepts, attribute granules(AtG) and connected granules(CoG), and presents the definitions of the granule-based model. Then, in order to fulfill the granule-based model, this paper designs a single attribute analyser(SAA), defines some theorems and lemmas related to decomposition, and describes the processing of extracting all attibute granules. Experimental results on over 300 color images show that the proposed analyser is accurate, robust, high-speed, and able to provide computers with “sensations”.

Intuitionistic Fuzzy Image Processing

2011 ◽  
pp. 967-974 ◽  
Author(s):  
Ioannis K. Vlachos ◽  
George D. Sergiadis
Keyword(s):  
Image Processing ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy ◽  
Alternative Approach ◽  
Human Decision ◽  
Nature Of Information ◽  
Flexible Framework ◽  
Image Pixels ◽  
Fuzzy Techniques ◽  
Fuzzy Image

Since its genesis, fuzzy sets (FSs) theory (Zadeh, 1965) provided a flexible framework for handling the indeterminacy characterizing real-world systems, arising mainly from the imprecise and/or imperfect nature of information. Moreover, fuzzy logic set the foundations for dealing with reasoning under imprecision and offered the means for developing a context that reflects aspects of human decision-making. Images, on the other hand, are susceptible of bearing ambiguities, mostly associated with pixel values. This observation was early identified by Prewitt (1970), who stated that “a pictorial object is a fuzzy set which is specified by some membership function defined on all picture points”, thus acknowledging the fact that “some of its uncertainty is due to degradation, but some of it is inherent”. A decade later, Pal & King (1980) (1981) (1982) introduced a systematic approach to fuzzy image processing, by modelling image pixels using FSs expressing their corresponding degrees of brightness. A detailed study of fuzzy techniques for image processing and pattern recognition can be found in Bezdek et al and Chi et al (Bezdek, Keller, Krisnapuram, & Pal, 1999) (Chi, Yan, & Pham, 1996). However, FSs themselves suffer from the requirement of precisely assigning degrees of membership to the elements of a set. This constraint raises some of the flexibility of FSs theory to cope with data characterized by uncertainty. This observation led researchers to seek more efficient ways to express and model imprecision, thus giving birth to higher-order extensions of FSs theory. This article aims at outlining an alternative approach to digital image processing using the apparatus of Atanassov’s intuitionistic fuzzy sets (A-IFSs), a simple, yet efficient, generalization of FSs. We describe heuristic and analytic methods for analyzing/synthesizing images to/from their intuitionistic fuzzy components and discuss the particular properties of each stage of the process. Finally, we describe various applications of the intuitionistic fuzzy image processing (IFIP) framework from diverse imaging domains and provide the reader with open issues to be resolved and future lines of research to be followed.

A Novel Approach of Edge Detection Based on Vector Morphology

2014 ◽  
Vol 511-512 ◽  
pp. 545-549
Author(s):  
Qiang Chen
Keyword(s):  
Image Processing ◽  
Edge Detection ◽  
Color Image ◽  
Detection Algorithm ◽  
Difficult Problem ◽  
Color Images ◽  
Edge Detection Algorithm ◽  
Morphological Gradient ◽  
Novel Approach ◽  
Image Edges

Edge detection of color image is a difficult problem in image processing. Although a lot of corresponding to methods have been proposed, however, none of them can effectively detect image edges while suppressing noises. In this paper, a novel edge detection algorithm of color images based on mathematical morphology is proposed. Through designing a new anti-noise morphological gradient operators, we can obtain better edge detection results. The proposed gradient operators are applied to detect edge for three components of a color image. An then, the final edge can be obtained by fusing the three edge results. Experimental results show that the feasibility and effectiveness of the proposed algorithm. Moreover, the proposed algorithm has better effect of preserving the edge details and better robustness to noises than traditional methods.

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.

Sign in / Sign up

Export Citation Format

Share Document