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.

Water Quality Variation, its Influence on Drinking Water Treatment and Remedial Measures - A Case Study of Peechi reservoir, Thrissur, Kerala

The Kerala Water Authority requested the School of Environmental Studies to carry out investigations on the mechanism of sporadic mobilization of iron and odour in the raw water drawn to the drinking water treatment plant. The currently used treatment process failed to remove iron completely. This led to problems in the filter and complaints of taste and colour due to iron in the finished water. The sporadic nature of the problem itself made the trouble shooting difficult. The problem was looked in from three points of view. 1. Influence of environmental (climatic) conditions on the dynamics of the relevant basin of the reservoir. 2. Influence of the physical dynamics on the physico — chemical quality of water. 3. Identification of cost-effective treatment processes to suit the existing plant. Since the problem emerged only during the post- monsoon to pre-monsoon months, a related problem was investigated, namely, influence of anions on the oxidation of Fe(II) in natural waters by air. This is presented in Part II of the dissertation.