Generalization Of Rough Set Theory Research Articles

Near Krasner hyperrings on nearness approximation space

Krasner hyperrings are a generalization of rings. Indeed, in a Krasner hyperring the addition is a hyperoperation, while the multiplication is an ordinary operation. On the other hand, a generalization of rough set theory is the near set theory. Now, in this paper we are interested in combining these concepts. We study and investigate the notion of near Krasner hyperrings on a nearness approximation space. Also, we define near subhyperring, near hyperideal, near homomorphism and prove some results and present several examples in this respect.

Plastic Surgery Facial Image Correspondence: A Near Set Approach

article introduces perceptual resemblance of plastic surgery facial images using near sets. Near sets are disjoint sets that resemble each other. Near sets facilitate measurement of similarity between objects (digital images) based on features values (obtained by probe functions) that describe the objects. Resemblance between disjoint sets occurs whenever there are observable similarities between the objects in the sets. Each list of feature values defines an object's description. Objects that are perceived as similar based on their descriptions are grouped together. These groups of similar objects can provide information and reveal patterns about objects of interest in the disjoint sets. The practical application of near set theory on the pre and post plastic surgery facial images to extract resemblance between them was introduced in this article. Facial plastic surgery can be reconstructive to correct facial feature anomalies or cosmetic to improve the appearance. Both corrective as well as cosmetic surgeries alter the original facial information to a great extent thereby posing a great challenge for face recognition algorithms. The main aim of this article is to measure the degree of resemblance of facial images before and after plastic surgery. Blepharoplasty (Eyelid surgery) and Rhinoplasty (Nose surgery) is being considered for this research work due to the maximum number of individuals and easy to differentiate faces before and after plastic surgery .tHD ,tNM and tHM is being used to measure the degree of resemblances between plastic surgery images. tHD measure shows around 100% nearness as compared to tNM and tHM for all features . These measures can also be used in increasing the efficiency of any face recognition system containing plastic surgery images. rejection of genuine users or acceptance of impostors. To this challenge yet much literature is not available. Very few researchers till now have contributed in this field. In (3) authors have shown the comparative study of different face recognition algorithms for plastic surgery. Based on the experimentation carried out by authors it has been concluded that face recognition algorithms such as PCA, FDA, GF, LLA, LBP and GNN have shown recognition rate not more than 40% for local plastic surgery. Moreover, for global surgery it was merely up to 10%. Among all the algorithms, geometrical feature based approach has proven to a great extent comparatively for local plastic surgery. This article introduces perceptual resemblance of plastic surgery facial images using near sets . Near sets were introduced by James Peters in 2006(10) and formally defined in 2007(11) and elaborated in (12). Near sets result from a generalization of rough set theory. One set X is near another set Y to the extent that the description of at least one of the objects in X matches the description of at least one of the objects in Y. The hallmark of near set theory is object description and the classification of objects by means of features (13). Rough sets were introduced by Zdzislaw Pawlak during the early 1980s (14)(15) and provide a basis for perception of objects viewed on the level of classes rather than the level of individual objects. A fundamental basis for near set as well as rough set theory is the approximation of one set by another set considered in the context of approximation spaces. It was observed by Ewa Orlowska in 1982 that approximation spaces serve as a formal counterpart of perception, or observation

New topological approach of rough set generalizations

In this paper, we introduce a generalization of rough set theory using topological structures generated by any binary general relation. The class of all after-composed sets and the class of all fore-composed sets defined here are used to generate two topological spaces. These topologies are used to approximate sets topologically. Lower and upper approximations are defined topologically and some of their properties are studied using these topologies. Also, membership, equality, inclusion relations and power set notions in the generalized approximation space are studied. Many differences are shown between notions of ordinary set theory and notions of rough set theory. These notions introduced in this work are good future work to knowledge discovery and data mining.

α-RST: a generalization of rough set theory

The paper presents a transition from the crisp rough set theory to a fuzzy one, called Alpha Rough Set Theory or, in short, α-RST. All basic concepts or rough set theory are extended, i.e., information system, indiscernibility, dependency, reduction, core, definability, approximations and boundary. The resulted theory takes into account fuzzy data and allows the approximation of fuzzy concepts. Besides, the control of knowledge granularity is natural in α-RST which is based on a parameterized indiscernibility relation. α-RST is developed to recognize non-deterministic relationships using notions as α-dependency, α-reduct and so forth. On the other hand, we introduce a notion of relative dependency as an alternative of the absolute definibility presented in rough set theory. The extension α-RST leads naturally to the new concept of alpha rough sets which represents sets with fuzzy non-empty boundaries.