Uncertainty is present in every process of computer vision, therefore fuzzy techniques have been widely use in almost any of the processes. Extensions of fuzzy se- ts are not as specic as their counter-parts of fuzzy se- ts, but this lack of specicity makes them more realistic for some applications. Their advantage is that they allow us to express our uncertainty in identifying a particular membership function. This uncertainty is involved when extensions of fuzzysets are processed, making results of the processing less specic but more reliable. Many au- thors based on this advantage proposed dierent imageprocessing algorithms using extensions of fuzzysets. This work presents a valuable review for the interested reader of the recent works using extensions of fuzzysets in imageprocessing. The chapter is divided as follows: rst we re- call the basics of the extensions of fuzzysets, i.e. Type-2 fuzzysets, Interval-valued fuzzysets and Atanassov's In- tuitionistic fuzzysets. In sequent sections we review the methods proposed for noise removal (section 3), image en- hancement (section 4), edge detection (section 5) and seg- mentation (section 6). There exist other image segmenta- tion tasks such as video de-interlacing, stereo matching or object representation that are not described in this work.
Abstract: GPU architectures offer a significant opportunity for faster morphological imageprocessing, and the NVIDIA CUDA architecture offers a relatively inexpensive and powerful framework for performing these operations. However, the generic morphological erosion and dilation operation in the CUDA NPP library is relatively naive, and performance scales expensively with increasing structuring element size. The objective of this work is to produce a freely available GPU capability for morphological operations so that fast GPU processing can be readily available to those in the morphological imageprocessing community. Open-source extensions to CUDA (hereafter referred to as LTU-CUDA) have been produced for erosion and dilation using a number of structuring elements for both 8 bit and 32 bit images. Support for 32 bit image data is a specific objective of the work in order to facilitate fast processing of image data from 3D range sensors with high depth precision. Furthermore, the implementation specifically al-lows scalability of image size and structuring element size for processing of large imagesets. Images up to 4096 by 4096 pixels with 32 bit precision were tested. This scalability has been achieved by forgoing the use of shared memory in CUDA multiprocessors. The vHGW algorithm for erosion and dilation independent of structuring element size has been implemented for horizontal, vertical, and 45 degree line structuring elements with significant performance improvements over NPP. However, memory handling limitations hinder performance in the vertical line case providing results not independent of structuring element size and posing an interesting challenge for further optimization. This performance limitation is mitigated for larger structuring elements using an optimised transpose function, which is not default in NPP, and applying the horizontal structuring element. LTU-CUDA is an ongoing project and the code is freely available at https://github.com/ VictorD/LTU-CUDA.
Defuzzification is the process of calculating the fuzzy model sets and corresponding membership degrees through a precise numerical value, hence, in a crisp logic results . Defuzzification is usually utilized in a fuzzy control systems . In accordance with that, a set of rules is required to transform various variables into a fuzzy result. The results are to be described accordingly to the terms of membership function in the set of fuzzy logic . Figure 14 shows the rule viewer of the bell pepper and chili pepper classifier. Based on the simulation, it has been verified that at 1.07e+04 area, 116 equivalent diameter, 503 perimeters, and 58.6 roundness, the output response is 0.321 which is closer to 0. Therefore, the sample is a Chili pepper.
Imageprocessing, a technology that allows people to manipulate and analyze data in the form of digital images, is quickly becoming a basic tool for survival in the information age. Fuzzy logic represents a good mathematical framework to deal with uncertainty of information. Fuzzyimageprocessing is the collection of all approaches that understand, represent and process the images, their segments and features as fuzzysets. The representation and processing depend on the selected fuzzy technique and on the problem to be solved. This research problem deals with Fuzzy Knowledge Base (FKB) utilized in an edge detection algorithm based on the fuzzy paradigm. The proposed method calculates fuzzy measure ‘edginess’ at each pixel of the image using masks of different sizes. Then the edge strengths calculated using these masks are used to form a fuzzy knowledge base which in turn is used to decide whether a given pixel belongs to an edge or not. When calculating the above mentioned fuzzy measures, the algorithm takes into account both step like edges and ‘line edges’ in the image being processed.
Fuzzy classifiers are one application of fuzzy theory. Expert knowledge is used and can be expressed in a very natural way using linguistic variables , which are described by fuzzysets Now the expert knowledge for this variables can be formulated as a rules like IF feature A low AND feature B medium AND feature C medium AND feature D medium THEN Class = class 4 The rules can be combined in a table (1) calls rule base and linguistic variables shown in figure (1).
Image fusion plays an efficient role in the field of imageprocessing. According to the traditional definition, ‘image fusion is the combination of two or several images into a single one that is more informative in compared with input images’. In medical science, remote sensing, robotics or these types of sector only single image is not enough to represent appropriate information. In this case, image fusion provides better solution to capture highest relevant information from source images. Similarly, the combination of high resolution panchromatic (PAN) image with low spatial resolution multispectral (MS) image provides high spatial resolution fused image.
Various imageprocessing techniques are generally utilized in Medical field for Smart Healthcare Systems. Among the techniques, picture combination is quickly expanding its hugeness in the combination of medicinal pictures X-ray, CT, MRI, MRA, and PET, SPECT pictures. Over the previous decade, gigantic research has been done in preparing and examination of medicinal information for analysis reason. Intertwining of CT and MRI pictures, MR and PET images, MR and SPECT images provide rich data valuable for effective diagnosis since the CT image gives the details of thick structures like bones and implants with little distortion, but cannot identify physiological changes, while the MRI gives typical and pathological soft tissues information. PET images provide help to evaluate functions of Organs and Tissues. SPECT images provide help in diagnosis of stress fractures in the spine, the blood deprived
In order not to be misled by the local maximum of the non-maximum suppression algorithm, we use a Hysteresis lter, which sets the points to white once they are above the upper threshold and sets them to black when they are under the lower threshold and the grade in between two thresholds can be dened; here, we choose them equal to one. The power of the canny edge detector lies in these two algorithms, but one of the most important things is choosing the best threshold for the real edge, where a threshold set to high can miss important information, while a threshold set to low will falsely identify irrelevant information as important. It is dicult to give a generic threshold that works well on all images. No tried and tested approach to this problem yet exists. In this study, we propose an algorithm for determining the thresholds as follows.
Numerous additional membership values can be calculated. For instance a membership value can be calculated by recursively fitting the time series with straight lines. Suppose a segment of data is fit with a line, and an quality of fit for the data is calculated (such as ρ squared). If the qual- ity indicator is too low, the best fit line is bisected and new fits are calculated for the two new sets of data. Fits are calculated until the quality indicator is good enough or there are to few points in the fit. A local best fit confidence can then be calculated by how far a point is from the fit. Another similar membership value can be calculated from the lag plot, and the atmospheric lag cluster. Specifically the number of sigma a point is from the best fit line can be calculated given the variance in the atmo- spheric lag cluster data. A lag cluster nsigma confidence can then be calculated using an appro- priate membership function such as e x .
 Zang Zhenliang, Classifications of HX-Groups and their chains of normal subgroups, Italian Journal of Pure and Applied Mathematics, Vol. 5, (1999).  Zhang Baojie, Li Hongxing, HX-type Chaotic (hyperchaotic) System Based on Fuzzy Inference Modeling, accepted by Italian Journal of Pure and Applied Mathematics, (2016)
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects. Although any type of object can be collected into a set, set theory is applied most often to objects that are relevant to mathematics. The language of set theory can be used in the definitions of nearly all mathematical objects. Set theory as a foundation for mathematicians accepts that theorems in these areas can be derived from the relevant definitions and the axioms of set theory .
The objective of this paper is to study the codes arising from Fuzzysets and Soft sets.Properties of fuzzy linear codes and fuzzy cyclic codes are discussed by means of fuzzy linear space. P-fuzzysets are considered as mapping from an arbitrary non- empty set S into a partially ordered set P which determines a binary block code V of length n . At last, the codes developed by using soft sets,called soft codes(soft linear codes) are discussed with examples. AMS Mathematics Subject Classification(2010) : 03E72, 06D72,11T71.
Imageprocessing is a form of signal processing for which the input is an image and the output of imageprocessing may be either an image or a set of characteristics or parameters related to the image. Most image-processing techniques treat the image as a two-dimensional signal. Imageprocessing is computer imaging where application involves a human being in the visual loop. In other words the image are to be examined and are acted upon by people. The major topics within the field of imageprocessing include: Image restoration, Image enhancement, Image compression etc.
Intuitionistic fuzzy starshaped sets (i.f.s.) is a generalized model of fuzzy starshaped set. By the definition of i.f.s., the intuitionistic fuzzy general starshaped sets (i.f.g.s.), intuitionistic fuzzy quasi-starshaped sets (i.f.q-s.) and intuitionistic fuzzy pseudo-starshaped sets (i.f.p-s.) are proposed and the relationships among them are studied. The equivalent discrimination conditions of i.f.q-s. and i.f.p-s. are presented on the basis of their properties which are meaningful for the research of the generalized fuzzy starshaped sets. Moreover, the invariance of the two given fuzzysets under the translation transformation and linear reversible transforma- tion are discussed.
ABSTRACT: As we probably aware exceptionally well that India's 75% lives in the towns and for the most part subject to the agribusiness and cultivation. Generally agriculturists are uneducated. They can't identify the malady of plants and farming by human eye. To identify the ailment they takes encourage the specialists. It is exorbitant system. To decrease the cost and for the better outcomes we are utilizing the mechanized strategies, which will be exceptionally useful for the farmers. The obligation of controlling and dealing with the plant development from beginning period to develop collect stage includes observing and recognizable proof of plant sicknesses, controlled water system and controlled utilization of manures and pesticides .Digital imageprocessing is quick, solid and exact system for recognition of infections likewise different calculations can be utilized for distinguishing proof and characterization of leaf ailments in plant. This paper presents procedures utilized by various authors to recognize illness, for example, clustering technique, colour feature image examination strategy, classifier and simulated neural system for order of maladies. The principle focal point of our work is on the investigation of various leaf infection identification strategies and furthermore gives a review of various picture handling methods.
 Kandil A., Biproximities and fuzzy bitopological spaces, Simon Steven 63(1989) ,45-66. Kovar, M.,(2000).On 3-Topological version of Thet-Reularity. Internat.J.Matj,Sci. ,23(6),393-398.  Levine N.(1963). semi open sets and semi –continuity in topological spaces, Amer. Math., 70,36- 41.
Levine  introduced the idea of semi-open sets and semi-continuity in topological space and Mashhour et al.  introduced the concept of pre-open sets and pre continuity in a topological space. Maheshwari and Prasad  introduced semi-open sets in bitopological spaces. Jelic  generalized the idea of pre-open sets and pre continuity in bitopological space.
Although alternatives and sets not included in the minimal dominant set were defined as unstable, their “instability” is being of different degree. Since MD (i) is the minimal dominant set in A\D (i-1) , one can measure the difference in stability of all points in A, not only those in MD, by defining similar systems of point-classes and set-classes for all MD (i) , not only for the minimal domi- nant set. As a result the system of dominant sets and systems of point-classes and set-classes represent respectively macro-scale structure and micro-scale substructure of a universal set. Since the classes do not intersect, and their hi- erarchies cover the whole set A, for any tournament each alternative will be characterized by three numbers k, l, m, as belonging 1) to a minimal dominant set of k’th degree MD (k) , 2) to a class of l-stable points SP (l) and 3) to a class of minimal m-stable sets SS (m) in MD (k) . That is for tournaments, the hierarchy of dominant sets and respective hierarchies of classes of k-stable points and classes of minimal k-stable sets create a system of reference based on the prin-
2) Concentration on memberships in set theoretic and algebraic operations of L2FS and T2FS- As stated above while defining union, intersection on T2FS a emphasis is given on primary membership function. i.e. while defining these operations, extension principle  is used ones and the purpose for doing this is its ease to write a computer program. While in defining operations on level II fuzzy set we need extension principle twice for each computation.
The DIARETDB0 dataset consists of 130 colour fundus images of which 20 are normal and the remaining 110 contain signs of diabetic retinopathy, such as hard exu- dates, soft exudates, microaneurysms, haemorrhages and neovascularisation. The original images, which are of size 1500 9 1152 in PNG format, are captured with 50° field- of-view digital fundus cameras with unknown camera settings . In addition to the DIARETDB0, there is another dataset developed by the Machine Vision and Pattern Recognition Research Group, at Lappeenranta University of Technology, Finland, which is DIARETDB1, with 89 colour fundus images, combining 84 images that contain at least mild non-proliferative signs (microa- neurysms) of diabetic retinopathy and five normal images . The MESSIDOR database is another dataset produced by the research funded by the French Ministry of Research and Defence to facilitate studies on diabetic retinopathy diagnosis . It consists of 1200 colour fundus images, captured using a colour video 3CCD camera on a Topcon TRC NW6 non-mydriatic retinography with a 45° field of view. The images acquired by three ophthalmologic departments have three different sizes: 1440 9 960, 2240 9 1488 and 2304 9 1536 pixels and also 8 bits colour plane . Another database with retinal images is from the DRIVE project , which offers retinal colour images and results of automatic segmentation of blood vessels. The set of 40 images, where 33 do not show any sign of diabetic retinopathy and seven show signs of mild early diabetic retinopathy, were captured using a Canon CR5 non-mydriatic 3CCD camera with a 45° field of view, 8 bits per colour plane and of size 768 by 584 pixels . The STARE project by Dr. Michael Goldbaum at the University of California, San Diego is funded by the U.S. National Institutes of Health produced another database with retinal colour images . The set of 400 raw images with the list of the diagnosis codes and the diagnosis for each image can be obtained from the STARE database. Blood vessel segmentation work involves 40 of these ima- ges , while 80 images are used for optic nerve detection . The DRIVE and STARE dataset are excellent data- bases of retinal vessel pixel segmentations; however, they do not include width measurements. Thus, the REVIEW  dataset is presented to fill this gap. The dataset includes