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.

Review of applications of the Cutting Angle methods

The theory of abstract convexity provides us with the necessary tools for building accurate one-sided approximations of functions. Cutting angle methods have recently emerged as a tool for global optimization of families of abstract convex functions. Their applicability have been subsequently extended to other problems, such as scattered data interpolation. This paper reviews three different applications of cutting angle methods, namely global optimization, generation of nonuniform random variates and multivatiate interpolation.

Extended cutting angle method of global optimization

Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.

Bounded lower subdifferentiability optimization techniques : applications

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have "flat parts". We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an algorithm to mathematical programming problems inwhich the objective function is derived from economic systems and location problems are described. Computational results are presented.

Some Problems In Algebra And Topology A Study Of Fuzzy Convexity With Special Reference To Separation Properties

This thesis is a study of abstract fuzzy convexity spaces and fuzzy topology fuzzy convexity spaces No attempt seems to have been made to develop a fuzzy convexity theoryin abstract situations. The purpose of this thesis is to introduce fuzzy convexity theory in abstract situations

Abstract types and distributions in independent private value auctions

In this note, in an independent private values auction framework, I discuss the relationship between the set of types and the distribution of types. I show that any set of types, finite dimensional or not, can be extended to a larger set of types preserving incentive compatibility constraints, expected revenue and bidder’s expected utilities. Thus for example we may convexify a set of types making our model amenable to the large body of theory in economics and mathematics that relies on convexity assumptions. An interesting application of this extension procedure is to show that although revenue equivalence is not valid in general if the set of types is not convex these mechanism have underlying distinct allocation mechanism in the extension. Thus we recover in these situations the revenue equivalence.

Saddle Point and Second Order Optimality in Nondifferentiable Nonlinear Abstract Multiobjective Optimization

This article deals with a vector optimization problem with cone constraints in a Banach space setting. By making use of a real-valued Lagrangian and the concept of generalized subconvex-like functions, weakly efficient solutions are characterized through saddle point type conditions. The results, jointly with the notion of generalized Hessian (introduced in [Cominetti, R., Correa, R.: A generalized second-order derivative in nonsmooth optimization. SIAM J. Control Optim. 28, 789–809 (1990)]), are applied to achieve second order necessary and sufficient optimality conditions (without requiring twice differentiability for the objective and constraining functions) for the particular case when the functionals involved are defined on a general Banach space into finite dimensional ones.

Examining the antecedents and consequences of ritualized fan behavior [Abstract]

One of the features of the sporting industry is the ritualized way in which it is consumed across the world. Fans of every sport have rituals and superstitions to help them enjoy the spectacle, socialize with other like-minded fans, and reduce some of the anxiety of watching their team play. These rituals include dress, barracking styles and pre and post match behaviors. What is not known are the factors that lead fans to engage in ritual behaviors and what relationship rituals have with desirable outcomes such as increased attendance, attitudinal loyalty or satisfaction. Given that some ritual behaviors are clearly undesirable, (e.g., hooliganism), understanding these relationships is important to managers who may be questioning whether rituals should be encouraged. Although ritualized behavior amongst fans is clearly visible, the symbolic and emotional nature of ritual poses challenges to researchers. Most previous ritual research is exploratory and qualitative in nature. This study, however, uses a behavior-based scale to measure fan ritual and relates it to desirable outcomes such as commitment and attendance. Over 2,000 season ticket holders of a football (soccer) team in Australia’s professional A-League competition were surveyed to investigate the antecedents and consequences of fan ritual behavior. Cluster analysis was used to explore the characteristics of respondents, and it revealed that those fans that engage in ritual behavior also differed on many other demographic and attitudinal dimensions. The associations between ritual and psychological commitment, and ritual and attendance are positive and significant. When used in conjunction with other constructs, fan ritual also improves the explanation of attendance behavior. The findings support previous research that found a significant and positive relationship between team identification, involvement and attendance, and extend previous research by finding a significant and positive relationship between rituals and attendance. For sports marketing practitioners, the results indicate the importance of developing and managing consumption rituals tied to game day attendance, with a view to generating uncommon loyalty.

How to progress forward in improving safety outcomes in the work-related driving field : a review of work-related driving research and development of an intervention framework [Extended abstract]

Road crashes are now the most common cause of work-related injury, death and absence in a number of countries. Given the impact of workrelated driving crashes on social and economic aspects of business and the community, workrelated road safety and risk management has received increasing attention in recent years. However, limited academic research has progressed on improving safety within the work-related driving sector. The aim of this paper is to present a review of work-related driving safety research to date, and provide an intervention framework for the future development and implementation of workrelated driving safety intervention strategies.

Identity and disciplinarity : Multi-disciplinary student cohorts in Higher Education [Abstract]

This paper will describe a research project that examines the implications of multidisciplinary student cohorts on teaching and learning within undergraduate and postgraduate units in higher education. Whist students generally specialise in one discipline, it is also common that, at some point during their degree, they will choose to undertake subjects that are outside their specialist area. Students may choose a multidisciplinary learning experience either out of interest or because the subject is seen as complementary to their core discipline. When the lens of identity is applied to the multi-disciplinary cohorts in undergraduate and postgraduate units, it assists in identifying learning needs. The nature of disciplinarity, and the impact it has on students’ academic identity, presents challenges to both students and teachers when they engage in teaching and learning, impacting on curriculum design, assessment practices and teaching delivery strategies (Winberg, 2008). This project aims to identify the barriers that exist to effective teaching and learning in units that have multidisciplinary student cohorts. It will identify the particular needs of students in multidisciplinary student cohorts and determine a teaching and learning model that meets the needs of such cohorts. References Becher, T. & Trowler, P.R. (2001). Academic tribes and territories: Intellectual enquiry and the culture of the discipline. Buckingham, UK: Open University Press. Light, G. & Cox, R. (2001). Learning and teaching in higher education: A reflective professional. Thousand Oaks, CA: Sage. Neumann, R. (2001). Disciplinary differences and university teaching. Studies in Higher Education, 26 (2), 135-46. Neumann, R., Parry, S. & Becher, T. (2002). Teaching and Learning in their disciplinary contexts: A conceptual analysis. Studies in Higher Education, 27(4), 405-417. Taylor, P.G. (1999) Making Sense of Academic Life: Academics, Universities and Change. Buckingham, UK: Open University Press. Winberg, C. (2008). Teaching engineering/engineering teaching: interdisciplinary collaboration and the construction of academic identities. Teaching in Higher Education, 13(3), 353 - 367.

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

Exercise for health : a breast cancer recovery program - quality of life benefits [Conference Abstract]

Introduction: Five-year survival from breast cancer in Australia is 87%. Hence, ensuring a good quality of life (QOL) has become a focal point of cancer research and clinical interest. Exercise during and after treatment has been identified as a potential strategy to optimise QOL of women diagnosed with breast cancer.----- Methods: Exercise for Health is a randomised controlled trial of an eight-month, exercise intervention delivered by Exercise Physiologists. An objective of this study was to assess the impact of the exercise program during and following treatment on QOL. Queensland women diagnosed with unilateral breast cancer in 2006/07 were eligible to participate. Those living in urban-Brisbane (n=194) were allocated to either the face-to-face exercise group, the telephone exercise group, or the usual-care group, and those living in rural Queensland (n=143) were allocated to the telephone exercise group or the usual-care group. QOL, as assessed by the Functional Assessment of Cancer Therapy-Breast (FACT-B+4) questionnaire, was measured at 4-6 weeks (pre-intervention), 6 months (mid-intervention) and 12 months (three months post-intervention) post-surgery.----- Results: Significant (P<0.01) increases in QOL were observed between pre-intervention and three months post-intervention 12 months post-surgery for all women. Women in the exercise groups experienced greater mean positive changes in QOL during this time (+10 points) compared with the usual-care groups (+5 to +7 points) after adjusting for baseline QOL. Although all groups experienced an overall increase in QOL, approximately 20% of urban and rural women in the usual-care groups reported a decline in QOL, compared with 10% of women in the exercise groups.----- Conclusions: This work highlights the potential importance of participating in physical activity to optimise QOL following a diagnosis of breast cancer. Results suggest that the telephone may be an effective medium for delivering exercise counselling to newly diagnosed breast cancer patients.

The prognostic significance of quality of life following breast cancer [Conference Abstract]

Introduction: Evidence suggests a positive association between quality of life (QOL). and overall survival(OS). among metastatic breast cancer (BC). patients, although the relationship in early-stage BC is unclear. This work examines the association between QOL and OS following a diagnosis of early-stage BC. ----- Methods: A population-based sample of Queensland women (n=287). with early-stage, invasive, unilateral BC, were prospectively observed for a median of 6.6 years. QOL was assessed at six and 18 months post-diagnosis using the Functional Assessment of Cancer Therapy, Breast FACT-B+4. questionnaire. Raw scores for the FACT-B+4 scales were computed and individuals were categorised according to whether QOL declined, remained stable or improved over time. OS was measured from the date of diagnosis to the date of death or was censored at the date of last follow-up. Risk ratios (RR) and 95% confidence intervals (CI). for the association between QOL and OS were obtained using Cox proportional hazards survival models adjusted for confounding characteristics. ----- Results: A total of 27 (9.4%). women died during the follow-up period. Three baseline QOL scales (emotional, general and overall QOL) were significantly associated with OS, with RRs ranging between 0.89 95% CI: 0.81, 0.98; P=0.01. and 0.98 (95% CI: 0.96, 0.99; P=0.03),indicating a 2%-11% reduced risk of death for every one unit increase in QOL. When QOL was categorised according to changes between six and 18 months post-diagnosis, analyses showed that for those who experienced declines in functional and physical QOL, risk of death increased by two- (95% CI: 1.43, 12.52; P<0.01) and four-fold (95% CI: 1.15, 7.19; P=0.02), respectively. Conclusions: This work indicates that specific QOL scales at six months post-diagnosis, and changes in certain QOL scales over the subsequent 12-month period (as measured by the FACT-B+4), are associated with overall survival in women with early-stage breast cancer.

Longitudinal patterns of weight in women diagnosed with breast cancer [Conference Abstract]

Introduction: Weight gain is a common concern following breast cancer and has been associated with negative health outcomes. As such, prevention of weight gain is of clinical interest. This work describes weight change between 6- and 18-months following a breast cancer diagnosis and explores the personal, treatment and behavioural characteristics associated with gains in weight. Methods: Body mass index was objectively assessed, at three-monthly intervals, on a population-based sample of women newly diagnosed with unilateral breast cancer (n=185). Changes in BMI between 6- and 18-months post-diagnosis were calculated, with gains of one or more being considered clinically detrimental to future health. Results: Approximately 60% of participants were overweight or obese at 6-months post-diagnosis. While BMI remained relatively stable across the testing period (range=27.3-27.8), 24% of participants experienced clinically relevant gains in BMI (median gains=1.9). Following adjustment for potential confounders, younger age (<45 years; Odds ratio, OR=9.8), being morbidly obese at baseline (OR=4.6) and receiving hormone therapy (OR=4.8) were characteristics associated with an increased odds (p<0.05) of gaining BMI. Other characteristics associated with gains in BMI were more extensive surgery and having a history of smoking, although these relationships were not supported statistically. In contrast, caring for younger children was associated with reduced risk of gaining BMI (OR=0.3, p=0.20). Conclusions: Clinically relevant weight gain between 6- and 18-months post-breast cancer diagnosis is an issue for one in four women, with certain subgroups being particularly susceptible. However, the majority of women diagnosed with breast cancer are overweight or obese and gains in body weight are common. Thus, interventions that address the importance of achieving and sustaining a healthy body weight, delivered to all women with breast cancer, may have greater public health impact than interventions targeting any specific breast cancer subgroup.