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

Studies in Fuzzy Commutative Algebra

The main objective of this thesis was to extend some basic concepts and results in module theory in algebra to the fuzzy setting.The concepts like simple module, semisimple module and exact sequences of R-modules form an important area of study in crisp module theory. In this thesis generalising these concepts to the fuzzy setting we have introduced concepts of ‘simple and semisimple L-modules’ and proved some results which include results analogous to those in crisp case. Also we have defined and studied the concept of ‘exact sequences of L-modules’.Further extending the concepts in crisp theory, we have introduced the fuzzy analogues ‘projective and injective L-modules’. We have proved many results in this context. Further we have defined and explored notion of ‘essential L-submodules of an L-module’. Still there are results in crisp theory related to the topics covered in this thesis which are to be investigated in the fuzzy setting. There are a lot of ideas still left in algebra, related to the theory of modules, such as the ‘injective hull of a module’, ‘tensor product of modules’ etc. for which the fuzzy analogues are not defined and explored.

Studies on Fuzzy Matroitls and Related Topics

The doctoral thesis focuses on the Studies on fuzzy Matroids and related topics.Since the publication of the classical paper on fuzzy sets by L. A. Zadeh in 1965.the theory of fuzzy mathematics has gained more and more recognition from many researchers in a wide range of scientific fields. Among various branches of pure and applied mathematics, convexity was one of the areas where the notion of fuzzy set was applied. Many researchers have been involved in extending the notion of abstract convexity to the broader framework of fuzzy setting. As a result, a number of concepts have been formulated and explored. However. many concepts are yet to be fuzzified. The main objective of this thesis was to extend some basic concepts and results in convexity theory to the fuzzy setting. The concept like matroids, independent structures. classical convex invariants like Helly number, Caratheodoty number, Radon number and Exchange number form an important area of study in crisp convexity theory. In this thesis, we try to generalize some of these concepts to the fuzzy setting. Finally, we have defined different types of fuzzy matroids derived from vector spaces and discussed some of their properties.

A study on semigroup action on fuzzy subsets, inverse fuzzy automata and related topics

This thesis comprises five chapters including the introductory chapter. This includes a brief introduction and basic definitions of fuzzy set theory and its applications, semigroup action on sets, finite semigroup theory, its application in automata theory along with references which are used in this thesis. In the second chapter we defined an S-fuzzy subset of X with the extension of the notion of semigroup action of S on X to semigroup action of S on to a fuzzy subset of X using Zadeh's maximal extension principal and proved some results based on this. We also defined an S-fuzzy morphism between two S-fuzzy subsets of X and they together form a category S FSETX. Some general properties and special objects in this category are studied and finally proved that S SET and S FSET are categorically equivalent. Further we tried to generalize this concept to the action of a fuzzy semigroup on fuzzy subsets. As an application, using the above idea, we convert a _nite state automaton to a finite fuzzy state automaton. A classical automata determine whether a word is accepted by the automaton where as a _nite fuzzy state automaton determine the degree of acceptance of the word by the automaton. 1.5. Summary of the Thesis 17 In the third chapter we de_ne regular and inverse fuzzy automata, its construction, and prove that the corresponding transition monoids are regular and inverse monoids respectively. The languages accepted by an inverse fuzzy automata is an inverse fuzzy language and we give a characterization of an inverse fuzzy language. We study some of its algebraic properties and prove that the collection IFL on an alphabet does not form a variety since it is not closed under inverse homomorphic images. We also prove some results based on the fact that a semigroup is inverse if and only if idempotents commute and every L-class or R-class contains a unique idempotent. Fourth chapter includes a study of the structure of the automorphism group of a deterministic faithful inverse fuzzy automaton and prove that it is equal to a subgroup of the inverse monoid of all one-one partial fuzzy transformations on the state set. In the fifth chapter we define min-weighted and max-weighted power automata study some of its algebraic properties and prove that a fuzzy automaton and the fuzzy power automata associated with it have the same transition monoids. The thesis ends with a conclusion of the work done and the scope of further study.

A study on the performance of flexible pavements on mature soil subgrades

The country has witnessed tremendous increase in the vehicle population and increased axle loading pattern during the last decade, leaving its road network overstressed and leading to premature failure. The type of deterioration present in the pavement should be considered for determining whether it has a functional or structural deficiency, so that appropriate overlay type and design can be developed. Structural failure arises from the conditions that adversely affect the load carrying capability of the pavement structure. Inadequate thickness, cracking, distortion and disintegration cause structural deficiency. Functional deficiency arises when the pavement does not provide a smooth riding surface and comfort to the user. This can be due to poor surface friction and texture, hydro planning and splash from wheel path, rutting and excess surface distortion such as potholes, corrugation, faulting, blow up, settlement, heaves etc. Functional condition determines the level of service provided by the facility to its users at a particular time and also the Vehicle Operating Costs (VOC), thus influencing the national economy. Prediction of the pavement deterioration is helpful to assess the remaining effective service life (RSL) of the pavement structure on the basis of reduction in performance levels, and apply various alternative designs and rehabilitation strategies with a long range funding requirement for pavement preservation. In addition, they can predict the impact of treatment on the condition of the sections. The infrastructure prediction models can thus be classified into four groups, namely primary response models, structural performance models, functional performance models and damage models. The factors affecting the deterioration of the roads are very complex in nature and vary from place to place. Hence there is need to have a thorough study of the deterioration mechanism under varied climatic zones and soil conditions before arriving at a definite strategy of road improvement. Realizing the need for a detailed study involving all types of roads in the state with varying traffic and soil conditions, the present study has been attempted. This study attempts to identify the parameters that affect the performance of roads and to develop performance models suitable to Kerala conditions. A critical review of the various factors that contribute to the pavement performance has been presented based on the data collected from selected road stretches and also from five corporations of Kerala. These roads represent the urban conditions as well as National Highways, State Highways and Major District Roads in the sub urban and rural conditions. This research work is a pursuit towards a study of the road condition of Kerala with respect to varying soil, traffic and climatic conditions, periodic performance evaluation of selected roads of representative types and development of distress prediction models for roads of Kerala. In order to achieve this aim, the study is focused into 2 parts. The first part deals with the study of the pavement condition and subgrade soil properties of urban roads distributed in 5 Corporations of Kerala; namely Thiruvananthapuram, Kollam, Kochi, Thrissur and Kozhikode. From selected 44 roads, 68 homogeneous sections were studied. The data collected on the functional and structural condition of the surface include pavement distress in terms of cracks, potholes, rutting, raveling and pothole patching. The structural strength of the pavement was measured as rebound deflection using Benkelman Beam deflection studies. In order to collect the details of the pavement layers and find out the subgrade soil properties, trial pits were dug and the in-situ field density was found using the Sand Replacement Method. Laboratory investigations were carried out to find out the subgrade soil properties, soil classification, Atterberg limits, Optimum Moisture Content, Field Moisture Content and 4 days soaked CBR. The relative compaction in the field was also determined. The traffic details were also collected by conducting traffic volume count survey and axle load survey. From the data thus collected, the strength of the pavement was calculated which is a function of the layer coefficient and thickness and is represented as Structural Number (SN). This was further related to the CBR value of the soil and the Modified Structural Number (MSN) was found out. The condition of the pavement was represented in terms of the Pavement Condition Index (PCI) which is a function of the distress of the surface at the time of the investigation and calculated in the present study using deduct value method developed by U S Army Corps of Engineers. The influence of subgrade soil type and pavement condition on the relationship between MSN and rebound deflection was studied using appropriate plots for predominant types of soil and for classified value of Pavement Condition Index. The relationship will be helpful for practicing engineers to design the overlay thickness required for the pavement, without conducting the BBD test. Regression analysis using SPSS was done with various trials to find out the best fit relationship between the rebound deflection and CBR, and other soil properties for Gravel, Sand, Silt & Clay fractions. The second part of the study deals with periodic performance evaluation of selected road stretches representing National Highway (NH), State Highway (SH) and Major District Road (MDR), located in different geographical conditions and with varying traffic. 8 road sections divided into 15 homogeneous sections were selected for the study and 6 sets of continuous periodic data were collected. The periodic data collected include the functional and structural condition in terms of distress (pothole, pothole patch, cracks, rutting and raveling), skid resistance using a portable skid resistance pendulum, surface unevenness using Bump Integrator, texture depth using sand patch method and rebound deflection using Benkelman Beam. Baseline data of the study stretches were collected as one time data. Pavement history was obtained as secondary data. Pavement drainage characteristics were collected in terms of camber or cross slope using camber board (slope meter) for the carriage way and shoulders, availability of longitudinal side drain, presence of valley, terrain condition, soil moisture content, water table data, High Flood Level, rainfall data, land use and cross slope of the adjoining land. These data were used for finding out the drainage condition of the study stretches. Traffic studies were conducted, including classified volume count and axle load studies. From the field data thus collected, the progression of each parameter was plotted for all the study roads; and validated for their accuracy. Structural Number (SN) and Modified Structural Number (MSN) were calculated for the study stretches. Progression of the deflection, distress, unevenness, skid resistance and macro texture of the study roads were evaluated. Since the deterioration of the pavement is a complex phenomena contributed by all the above factors, pavement deterioration models were developed as non linear regression models, using SPSS with the periodic data collected for all the above road stretches. General models were developed for cracking progression, raveling progression, pothole progression and roughness progression using SPSS. A model for construction quality was also developed. Calibration of HDM–4 pavement deterioration models for local conditions was done using the data for Cracking, Raveling, Pothole and Roughness. Validation was done using the data collected in 2013. The application of HDM-4 to compare different maintenance and rehabilitation options were studied considering the deterioration parameters like cracking, pothole and raveling. The alternatives considered for analysis were base alternative with crack sealing and patching, overlay with 40 mm BC using ordinary bitumen, overlay with 40 mm BC using Natural Rubber Modified Bitumen and an overlay of Ultra Thin White Topping. Economic analysis of these options was done considering the Life Cycle Cost (LCC). The average speed that can be obtained by applying these options were also compared. The results were in favour of Ultra Thin White Topping over flexible pavements. Hence, Design Charts were also plotted for estimation of maximum wheel load stresses for different slab thickness under different soil conditions. The design charts showed the maximum stress for a particular slab thickness and different soil conditions incorporating different k values. These charts can be handy for a design engineer. Fuzzy rule based models developed for site specific conditions were compared with regression models developed using SPSS. The Riding Comfort Index (RCI) was calculated and correlated with unevenness to develop a relationship. Relationships were developed between Skid Number and Macro Texture of the pavement. The effort made through this research work will be helpful to highway engineers in understanding the behaviour of flexible pavements in Kerala conditions and for arriving at suitable maintenance and rehabilitation strategies. Key Words: Flexible Pavements – Performance Evaluation – Urban Roads – NH – SH and other roads – Performance Models – Deflection – Riding Comfort Index – Skid Resistance – Texture Depth – Unevenness – Ultra Thin White Topping

Studies on Fuzzy Graphs

In this thesis an attempt to develop the properties of basic concepts in fuzzy graphs such as fuzzy bridges, fuzzy cutnodes, fuzzy trees and blocks in fuzzy graphs have been made. The notion of complement of a fuzzy graph is modified and some of its properties are studied. Since the notion of complement has just been initiated, several properties of G and G available for crisp graphs can be studied for fuzzy graphs also. Mainly focused on fuzzy trees defined by Rosenfeld in [10] , several other types of fuzzy trees are defined depending on the acyclicity level of a fuzzy graph. It is observed that there are selfcentered fuzzy trees. Some operations on fuzzy graphs and prove that complement of the union two fuzzy graphs is the join of their complements and complement of the join of two fuzzy graphs is union of their complements. The study of fuzzy graphs made in this thesis is far from being complete. The wide ranging applications of graph theory and the interdisciplinary nature of fuzzy set theory, if properly blended together could pave a way for a substantial growth of fuzzy graph theory.

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.

Study on Fuzzy Ordered FuzzyTopological Spaces

In this study we combine the notions of fuzzy order and fuzzy topology of Chang and define fuzzy ordered fuzzy topological space. Its various properties are analysed. Product, quotient, union and intersection of fuzzy orders are introduced. Besides, fuzzy order preserving maps and various fuzzy completeness are investigated. Finally an attempt is made to study the notion of generalized fuzzy ordered fuzzy topological space by considering fuzzy order defined on a fuzzy subset.

Design And Development Of A Named Entity Based Question Answering System For Malayalam Language

This is a Named Entity Based Question Answering System for Malayalam Language. Although a vast amount of information is available today in digital form, no effective information access mechanism exists to provide humans with convenient information access. Information Retrieval and Question Answering systems are the two mechanisms available now for information access. Information systems typically return a long list of documents in response to a user’s query which are to be skimmed by the user to determine whether they contain an answer. But a Question Answering System allows the user to state his/her information need as a natural language question and receives most appropriate answer in a word or a sentence or a paragraph. This system is based on Named Entity Tagging and Question Classification. Document tagging extracts useful information from the documents which will be used in finding the answer to the question. Question Classification extracts useful information from the question to determine the type of the question and the way in which the question is to be answered. Various Machine Learning methods are used to tag the documents. Rule-Based Approach is used for Question Classification. Malayalam belongs to the Dravidian family of languages and is one of the four major languages of this family. It is one of the 22 Scheduled Languages of India with official language status in the state of Kerala. It is spoken by 40 million people. Malayalam is a morphologically rich agglutinative language and relatively of free word order. Also Malayalam has a productive morphology that allows the creation of complex words which are often highly ambiguous. Document tagging tools such as Parts-of-Speech Tagger, Phrase Chunker, Named Entity Tagger, and Compound Word Splitter are developed as a part of this research work. No such tools were available for Malayalam language. Finite State Transducer, High Order Conditional Random Field, Artificial Immunity System Principles, and Support Vector Machines are the techniques used for the design of these document preprocessing tools. This research work describes how the Named Entity is used to represent the documents. Single sentence questions are used to test the system. Overall Precision and Recall obtained are 88.5% and 85.9% respectively. This work can be extended in several directions. The coverage of non-factoid questions can be increased and also it can be extended to include open domain applications. Reference Resolution and Word Sense Disambiguation techniques are suggested as the future enhancements

Studies on a syntax based approach for translation between structurally different languages and the development of a prototype for Malayalam to English translation

This thesis summarizes the results on the studies on a syntax based approach for translation between Malayalam, one of Dravidian languages and English and also on the development of the major modules in building a prototype machine translation system from Malayalam to English. The development of the system is a pioneering effort in Malayalam language unattempted by previous researchers. The computational models chosen for the system is first of its kind for Malayalam language. An in depth study has been carried out in the design of the computational models and data structures needed for different modules: morphological analyzer , a parser, a syntactic structure transfer module and target language sentence generator required for the prototype system. The generation of list of part of speech tags, chunk tags and the hierarchical dependencies among the chunks required for the translation process also has been done. In the development process, the major goals are: (a) accuracy of translation (b) speed and (c) space. Accuracy-wise, smart tools for handling transfer grammar and translation standards including equivalent words, expressions, phrases and styles in the target language are to be developed. The grammar should be optimized with a view to obtaining a single correct parse and hence a single translated output. Speed-wise, innovative use of corpus analysis, efficient parsing algorithm, design of efficient Data Structure and run-time frequency-based rearrangement of the grammar which substantially reduces the parsing and generation time are required. The space requirement also has to be minimised

Buyer information and brand Choice behavior in markets with asymmetries

This thesis Entitled Buyer information and brand choice behaviour in markets with asymmetries.The period of transition set in by globalization and liberalization has ensued a onsiderable degree of homogeneity with western societies with respect to quantity and quality of goods and services.The study is aimed at finding out how the buyers adapt to the prevalent complex and dynamic market configuration by taking an archetypical situation of information gathering and brand- choice decision of select household consumer durables.The study was based on a set of 301 sample respondents who were either first time purchasers or repeat purchasers for household use, of the items under study in the sample area comprising of rural, urban and semi-urban areas. Data were collected using interview schedule and analysis of the same was done with standard statistical computer programs.Buyer confidence as perceived by buyers with respect to information acquisition and brand-choice represents the felt competence to effectively function in the market.In general, lower levels of education, income and occupation showed lower levels of search. The oldest were also low searchers. The repeat purchasers of the product searched less than the first purchasers. The most important source of information was word of mouth or information from others followed by television advertisements. The least important source of information was billboards, displays and similar forms of advertisements.The second factor is characterized by items representing ‘social attributes’ like, use by many others, use by peers, recommendation by significant others and reputation of the brand. The third factor represents ‘susceptibility to incentives and promotions’.

A Study on the Use of Coconut Oil as Plasticiser in Natural Rubber Compounds

Mechanical properties and thermal degradation characteristics of natural rubber compounds captaining coconut oil were compared with that of a control compound containing naphthenic oil. Cure time was marginally lower in the case of coconut oil mixes, probably due to the presence of free fatty acids. Tensile strength , tear strength, resilience and abrasion resistance were better than the naphthenic oil-based compounds . Compression set and hardness were marginally inferior The coconut oil mixes had a crosslink density comparable to that of the reference compound. Thermal studies showed that the temperature of initiation of degradation was increased by 10°C and the temperature at which the peak rate of degradation occured was increased by 7°C. The peak rate of degradation was compa rable to the control compound.