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.

Speech Analysis using Modern Techniques of Nonlinear Dynamics

Medical fields requires fast, simple and noninvasive methods of diagnostic techniques. Several methods are available and possible because of the growth of technology that provides the necessary means of collecting and processing signals. The present thesis details the work done in the field of voice signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this thesis is to characterize complexities of pathological voice from healthy signals and to differentiate stuttering signals from healthy signals. Efficiency of various acoustic as well as non linear time series methods are analysed. Three groups of samples are used, one from healthy individuals, subjects with vocal pathologies and stuttering subjects. Individual vowels/ and a continuous speech data for the utterance of the sentence "iruvarum changatimaranu" the meaning in English is "Both are good friends" from Malayalam language are recorded using a microphone . The recorded audio are converted to digital signals and are subjected to analysis.Acoustic perturbation methods like fundamental frequency (FO), jitter, shimmer, Zero Crossing Rate(ZCR) were carried out and non linear measures like maximum lyapunov exponent(Lamda max), correlation dimension (D2), Kolmogorov exponent(K2), and a new measure of entropy viz., Permutation entropy (PE) are evaluated for all three groups of the subjects. Permutation Entropy is a nonlinear complexity measure which can efficiently distinguish regular and complex nature of any signal and extract information about the change in dynamics of the process by indicating sudden change in its value. The results shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Permutation entropy is well suited due to its sensitivity to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. Pathological groups have higher entropy values compared to the normal group. The stuttering signals have lower entropy values compared to the normal signals.PE is effective in charaterising the level of improvement after two weeks of speech therapy in the case of stuttering subjects. PE is also effective in characterizing the dynamical difference between healthy and pathological subjects. This suggests that PE can improve and complement the recent voice analysis methods available for clinicians. The work establishes the application of the simple, inexpensive and fast algorithm of PE for diagnosis in vocal disorders and stuttering subjects.

Finite Element Analysis of Warship Structures

Warships are generally sleek, slender with V shaped sections and block coefficient below 0.5, compared to fuller forms and higher values for commercial ships. They normally operate in the higher Froude number regime, and the hydrodynamic design is primarily aimed at achieving higher speeds with the minimum power. Therefore the structural design and analysis methods are different from those for commercial ships. Certain design guidelines have been given in documents like Naval Engineering Standards and one of the new developments in this regard is the introduction of classification society rules for the design of warships.The marine environment imposes subjective and objective uncertainties on ship structure. The uncertainties in loads, material properties etc.,. make reliable predictions of ship structural response a difficult task. Strength, stiffness and durability criteria for warship structures can be established by investigations on elastic analysis, ultimate strength analysis and reliability analysis. For analysis of complicated warship structures, special means and valid approximations are required.Preliminary structural design of a frigate size ship has been carried out . A finite element model of the hold model, representative of the complexities in the geometric configuration has been created using the finite element software NISA. Two other models representing the geometry to a limited extent also have been created —- one with two transverse frames and the attached plating alongwith the longitudinal members and the other representing the plating and longitudinal stiffeners between two transverse frames. Linear static analysis of the three models have been carried out and each one with three different boundary conditions. The structural responses have been checked for deflections and stresses against the permissible values. The structure has been found adequate in all the cases. The stresses and deflections predicted by the frame model are comparable with those of the hold model. But no such comparison has been realized for the interstiffener plating model with the other two models.Progressive collapse analyses of the models have been conducted for the three boundary conditions, considering geometric nonlinearity and then combined geometric and material nonlinearity for the hold and the frame models. von Mises — lllyushin yield criteria with elastic-perfectly plastic stress-strain curve has been chosen. ln each case, P-Delta curves have been generated and the ultimate load causing failure (ultimate load factor) has been identified as a multiple of the design load specified by NES.Reliability analysis of the hull module under combined geometric and material nonlinearities have been conducted. The Young's Modulus and the shell thickness have been chosen as the variables. Randomly generated values have been used in the analysis. First Order Second Moment has been used to predict the reliability index and thereafter, the probability of failure. The values have been compared against standard values published in literature.

Geodynamics of the Andaman - Sumatra - Java Trench - Arc System Based on Gravity and Seismotectonic Study

This work aims to study the variation in subduction zone geometry along and across the arc and the fault pattern within the subducting plate. Depth of penetration as well as the dip of the Benioff zone varies considerably along the arc which corresponds to the curvature of the fold- thrust belt which varies from concave to convex in different sectors of the arc. The entire arc is divided into 27 segments and depth sections thus prepared are utilized to investigate the average dip of the Benioff zone in the different parts of the entire arc, penetration depth of the subducting lithosphere, the subduction zone geometry underlying the trench, the arctrench gap, etc.The study also describes how different seismogenic sources are identified in the region, estimation of moment release rate and deformation pattern. The region is divided into broad seismogenic belts. Based on these previous studies and seismicity Pattern, we identified several broad distinct seismogenic belts/sources. These are l) the Outer arc region consisting of Andaman-Nicobar islands 2) the back-arc Andaman Sea 3)The Sumatran fault zone(SFZ)4)Java onshore region termed as Jave Fault Zone(JFZ)5)Sumatran fore arc silver plate consisting of Mentawai fault(MFZ)6) The offshore java fore arc region 7)The Sunda Strait region.As the Seismicity is variable,it is difficult to demarcate individual seismogenic sources.Hence, we employed a moving window method having a window length of 3—4° and with 50% overlapping starting from one end to the other. We succeeded in defining 4 sources each in the Andaman fore arc and Back arc region, 9 such sources (moving windows) in the Sumatran Fault zone (SFZ), 9 sources in the offshore SFZ region and 7 sources in the offshore Java region. Because of the low seismicity along JFZ, it is separated into three seismogenic sources namely West Java, Central Java and East Java. The Sunda strait is considered as a single seismogenic source.The deformation rates for each of the seismogenic zones have been computed. A detailed error analysis of velocity tensors using Monte—Carlo simulation method has been carried out in order to obtain uncertainties. The eigen values and the respective eigen vectors of the velocity tensor are computed to analyze the actual deformation pattem for different zones. The results obtained have been discussed in the light of regional tectonics, and their implications in terms of geodynamics have been enumerated.ln the light of recent major earthquakes (26th December 2004 and 28th March 2005 events) and the ongoing seismic activity, we have recalculated the variation in the crustal deformation rates prior and after these earthquakes in Andaman—Sumatra region including the data up to 2005 and the significant results has been presented.ln this chapter, the down going lithosphere along the subduction zone is modeled using the free air gravity data by taking into consideration the thickness of the crustal layer, the thickness of the subducting slab, sediment thickness, presence of volcanism, the proximity of the continental crust etc. Here a systematic and detailed gravity interpretation constrained by seismicity and seismic data in the Andaman arc and the Andaman Sea region in order to delineate the crustal structure and density heterogeneities a Io nagnd across the arc and its correlation with the seismogenic behaviour is presented.