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.

Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Women and political change in kerala since independence

even after 45 years of independence, it is seen that women are still left cum the periphery cnf the political process. Effective and meaningful participation of women in politics remains elusive for most of them. The representation of women in the state legislatures and in both Houses of Parliament has been very marginal. The percentage of women members in the LokSabha to the total membership of the body has never touched a two-digit figure so far. Within these 45 years, India could field only five women as Union Cabinet Ministers. In the case of the various states also, the position of women's participation in political activities is not very different. On the whole, it is seen that in independent India the role played by women in the electoral politics of the country or in the day to day activities of the different political parties is very" ineffective and insignificant. The present study was undertaken to make an assessment of women's involvement in the political process of Kerala since independence. This small state in the southernmost part of India claims ‘that it possesses certain. unique features in its social fabric that makes it different from the rest of the country as far as the place of women in society is concerned.

Performance Improvement of Fuzzy and Neuro Fuzzy Systems: Prediction of Learning Disabilities in School-age Children

Learning Disability (LD) is a classification including several disorders in which a child has difficulty in learning in a typical manner, usually caused by an unknown factor or factors. LD affects about 15% of children enrolled in schools. The prediction of learning disability is a complicated task since the identification of LD from diverse features or signs is a complicated problem. There is no cure for learning disabilities and they are life-long. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. The aim of this paper is to develop a new algorithm for imputing missing values and to determine the significance of the missing value imputation method and dimensionality reduction method in the performance of fuzzy and neuro fuzzy classifiers with specific emphasis on prediction of learning disabilities in school age children. In the basic assessment method for prediction of LD, checklists are generally used and the data cases thus collected fully depends on the mood of children and may have also contain redundant as well as missing values. Therefore, in this study, we are proposing a new algorithm, viz. the correlation based new algorithm for imputing the missing values and Principal Component Analysis (PCA) for reducing the irrelevant attributes. After the study, it is found that, the preprocessing methods applied by us improves the quality of data and thereby increases the accuracy of the classifiers. The system is implemented in Math works Software Mat Lab 7.10. The results obtained from this study have illustrated that the developed missing value imputation method is very good contribution in prediction system and is capable of improving the performance of a classifier.

Community Participation in Ecotourism: An Inclusive Development Option for Kerala

The inferences obtained from the study are presented in coherent area-specific levels so as to understand the ecotourism and its sub-sector areas for the researchers and policy makers about the issues, importances and potentialities of the sector. An analysis of the tourism sector in Kerala has shown tremendous growth both in terms of tourist arrivals and in terms of revenue generation from direct and indirect sources. The foreign tourist visitors in Kerala in 2014 was 9,23,336 which shows 7.60 percent increase from the last year and the domestic tourist visitors were 1,16,95,411 which again shows 7.71 percent increase, is a clear evidence of its potential. In 2014 the industry contributed revenue of 24885.44 crores from direct and indirect sources giving rise to an increase of 12.11 percent from the last year. A dichotomy of tourists and ecotourists shows that tourists in the ecotourism destinations come to 42.6 percent of the total, shows the scope, significance and its potential. Correlation of zone-wise tourist arrivals based on the ecotourism destinations highlights the fact that with only 19 of the 64 destinations that come in the central zone are the most preferred centres (around 54 percent) for the domestic as well as foreign tourists. The north zone encompassing 6 districts with rich biodiversity shows that the tourists‟ arrival patterns exhibit less promising results. Though the north zone has 31 ecotourism destinations of the state receives only 6.19 percent of the foreign visitors. The ecotourism activities in the state are primarily managed by the Eco-Development Committees (EDCs) and the Vana Samrakshana Samithies (VSS) under the Forest Development Agency of Kerala. Social class-wise categorization of membership shows that 13142 families have membership in 190 EDCs with SC (28 percent), ST (33 percent) and other marginalised communities (39 percent). But this in the VSS shows that 400 VSS have 59085 members actively engaged in ecotourism activities and social category of the VSS makes clear that majority are from the other marginalized fringe households with 62 percent where as the participation of SC is 12 percent and ST is 26 percent. An evaluation of the socio-economic and demographic matrix of the community members involved in ecotourism activities brings out region specific differences. About 75.70 percent of the respondents are males and the rest are females. Majority of the respondents (about 60 percent) are in the age group of 20 to 40 years, followed by the age group of 40-50 (20 percent). The average age of respondents in the three zones is between 35 and 37 years. The majority of the respondents are married, a few are unmarried. Average family size is 4-5 members and differences are identified among zones. Average number of adults per household is 3 and child per household is 2. Majority have an education of 10th class and below i.e. about 60 percent of the sample have only basic school education like primary, secondary and high school (i.e. up to SSLC but not passed) level. About 18 percent are SSLC passed, 10 percent are undergraduates whereas 6 percent constitute respondents having qualification of graduation and above. Majority of the „graduates and above‟ are from south and central zone. Inter-zone differences in educational profile are also identified with lesser number of „graduates and above‟ are identified in the north zone compared to the other two zones. Investigating into the income and livelihood options of the respondents gives insight about the prominence of ecotourism as an employment and livelihood option for the community members, as more than 90 percent of the respondents have cited tourism sector as their main employment option. Most (49.30 percent) of respondents get 100 percent income from tourism related activities, followed by 37.30 percent of community members have income between 75-99 percent from tourism whereas the rest (13 percent) have less than 74 percent of their income from tourism and there exists difference between zones and percentage of income. Financial habit shows that about 49.7 percent hold active bank accounts, 61 percent have savings behaviour and 73.8 percent have indebtedness. Analysis about the ownership of house brings to light that 37 percent of respondents live in their own house followed by 25.7 percent in government funded/provided house and 21 percent in their parent‟s house and 3.5 percent in rented house. About 12 percent of the respondents have other kinds of accommodation facilities such as staff quarters, etc. But in the case of north zone majority i.e. 52 percent primarily depend on the government funded house indicating the effectiveness of government housing programme. Standard of living measured in SLI frameworks shows that majority of the respondents have medium SLI values (42.3 percent); the remaining 47.7 percent have low SLI and 10 percent have high SLI. The community members have been benefitted immensely from forest and its resources. Since the ecotourism destinations are located amidst the wildlife settings, majority of them depend on forest for their livelihood. The information on the tourist‟s demographic characteristics like age, sex, educational qualification and annual income show that the age category of domestic and foreign tourists falls below the age group of less than 35 years (about 65 percent), whereas only 16 percent of tourists are aged above 46 years. The age group below 25 years consists of more international tourists (31.3 percent) compared to the proportion of domestic tourists (12.5 percent). Male-female ratio shows that the males constitute 56 percent of the sample and females with 44 percent. The factors determining the impact of ecotourism programmes in the community was evaluated with the aid of a factor analysis with 12 selected statements. The worries and concerns of the community members about the impact of ecotourism on the environment are well understood from this analysis. It can be drawn that environment protection and the role of ecotourism in improving the income and livelihood options of the local communities is the most important factor concerning the community members.