A Study Of Frames In The Fuzzy And Intuitionist Fuzzy Contexts

The fuzzy set theory has a wider scope of applicability than classical set theory in solving various problems. Fuzzy set theory in the last three decades as a formal theory which got formalized by generalizing the original ideas and concepts in classical mathematical areas and as a very powerful modeling language, that can cope with a large fraction of uncertainties of real life situations. In Intuitionistic Fuzzy sets a new component degree of non membership in addition to the degree of membership in the case of fuzzy sets with the requirement that their sum be less than or equal to one. The main objective of this thesis is to study frames in Fuzzy and Intuitionistic Fuzzy contexts. The thesis proved some results such as ifµ is a fuzzy subset of a frame F, then µ is a fuzzy frame of F iff each non-empty level subset µt of µ is a subframe of F, the category Fuzzfrm of fuzzy frames has products and the category Fuzzfrm of fuzzy frames is complete. It define a fuzzy-quotient frame of F to be a fuzzy partition of F, that is, a subset of IF and having a frame structure with respect to new operations and study the notion of intuitionistic fuzzy frames and obtain some results and introduce the concept of Intuitionistic fuzzy Quotient frames. Finally it establish the categorical link between frames and intuitionistic fuzzy topologies.

A Study of Morphological Operators with Applications

The present work deals with the A study of morphological opertors with applications. Morphology is now a.necessary tool for engineers involved with imaging applications. Morphological operations have been viewed as filters the properties of which have been well studied (Heijmans, 1994). Another well-known class of non-linear filters is the class of rank order filters (Pitas and Venetsanopoulos, 1990). Soft morphological filters are a combination of morphological and weighted rank order filters (Koskinen, et al., 1991, Kuosmanen and Astola, 1995). They have been introduced to improve the behaviour of traditional morphological filters in noisy environments. The idea was to slightly relax the typical morphological definitions in such a way that a degree of robustness is achieved, while most of the desirable properties of typical morphological operations are maintained. Soft morphological filters are less sensitive to additive noise and to small variations in object shape than typical morphological filters. They can remove positive and negative impulse noise, preserving at the same time small details in images. Currently, Mathematical Morphology allows processing images to enhance fuzzy areas, segment objects, detect edges and analyze structures. The techniques developed for binary images are a major step forward in the application of this theory to gray level images. One of these techniques is based on fuzzy logic and on the theory of fuzzy sets.Fuzzy sets have proved to be strongly advantageous when representing in accuracies, not only regarding the spatial localization of objects in an image but also the membership of a certain pixel to a given class. Such inaccuracies are inherent to real images either because of the presence of indefinite limits between the structures or objects to be segmented within the image due to noisy acquisitions or directly because they are inherent to the image formation methods.

The Aesthetics Of Paul Verlaine And Changampuzha Krishnapillai - A Comparative Perspective

The present study is entitled The Aesthetics of Paul Verlaine and Changampuzha Krishnapillai - a comparative perspective. The purpose of the study is to compare the poetic genius of the French poet Paul Verlaine (1844-1896) and that of the Malayalam poet Changampuzha Krishnapillai (1911-1948), within a descriptive framework. The investigation will hopefully answer the questions- Has Changampuzha been indeed influenced by Verlaine, if so, to what extent? Can the aesthetic appreciation be justified in both poets as illustrated in their works? The comparative methodology of juxtaposing the selected oeuvres of the poets is largely adopted in the study. Since the span of analysis is across national and linguistic borders, the distinguishing as well as exclusive traits of the individual poets will be of much importance in formulating the comparative assumption in this work. The vastly differing geographical, linguistic and cultural milieus of these two poets,-one a national French poet and the other, a regional Indian poet writing in Malayalam prima facie,endow the theme of the dissertation with an innate hue of diversity. Such an ambitious task would naturally entail a renewed research into the dedication of the poets to their muses and their ultimate contributions to poetics. The analysis, while attempting to illuminate from a fresh angle, the amply researched oeuvre of Verlaine and the lesser studied one of Changampuzha, cannot but be aware of the limitations of the task at hand. The present study is the first of its kind on the specific theme of analysis, and is hoped that it would be of relevance since no work has so far been known to have been undertaken on the topic. At a time when the birth centenary celebrations of Changampuzha have just concluded, this study is hoped to assume significance as it would help in isolating the originality of the poet's works, extricating the garb of the French influence. Ultimately, this study aims at creating a wider appreciation of the impact that the French writers have had on Malayalam writers, thus shedding new light on the benign foreign influences that served to enhance the beauty of our cultural heritage