Penalty functions over a cartesian product of lattices

In this work we present the concept of penalty function over a Cartesian product of lattices. To build these mappings, we make use of restricted dissimilarity functions and distances between fuzzy sets. We also present an algorithm that extends the weighted voting method for a fuzzy preference relation.

William Wardell's 1859 St John's College - a rare realisation of Pugin's ideal Catholic College?

William Wardell’s St John’s College, Sydney, considered the grandest and architecturally most distinguished university college in New South Wales, is an exceptional example of 19th century Gothic Revival architecture.  The information board outside the college states that St John’s is ‘a rare realisation of Pugin’s ideal Catholic College’ and further that ‘it demonstrates [Pugin]’s profound influence on the work of Wardell’. This is but a small part of the story. The commission for St John’s College was far more complex.  The correspondence between the architects, William Wardell, Edmund Blacket and others, and St John’s Council indicates that right from the beginning there was a general lack of understanding of Wardell’s original design concept for the building. This has continued to the present day, as evidenced by the information on the board outside St John’s College, in which it is incorrectly assumed that Wardell’s proposal included a quadrangle as featured in Pugin’s ‘ideal College’. This paper, based largely on primary sources, investigates such claims about St John’s, considers William Wardell and the Gothic Revival, examines St John’s College within the University of Sydney – its design and its translation and posits a few conclusions leading to new understandings.

Defining Bonferroni means over lattices

In the face of mass amounts of information and the need for transparent and fair decision processes, aggregation functions are essential for summarizing data and providing overall evaluations. Although families such as weighted means and medians have been well studied, there are still applications for which no existing aggregation functions can capture the decision makers' preferences. Furthermore, extensions of aggregation functions to lattices are often needed to model operations on L-fuzzy sets, interval-valued and intuitionistic fuzzy sets. In such cases, the aggregation properties need to be considered in light of the lattice structure, as otherwise counterintuitive or unreliable behavior may result. The Bonferroni mean has recently received attention in the fuzzy sets and decision making community as it is able to model useful notions such as mandatory requirements. Here, we consider its associated penalty function to extend the generalized Bonferroni mean to lattices. We show that different notions of dissimilarity on lattices can lead to alternative expressions.

Negations generated by bounded lattices t-norms

From the birth of fuzzy sets theory, several extensions have been proposed changing the possible membership values. Since fuzzy connectives such as t-norms and negations have an important role in theoretical as well as applied fuzzy logics, these connectives have been adapted for these generalized frameworks. Perhaps, an extension of fuzzy logic which generalizes the remaining extensions, proposed by Joseph Goguen in 1967, is to consider arbitrary bounded lattices for the values of the membership degrees. In this paper we extend the usual way of constructing fuzzy negations from t-norms for the bounded lattice t-norms and prove some properties of this construction.

The ideal Ileal-Pouch design : a long-term randomized control trial of J- vs W-pouch construction

BACKGROUND: The IPAA has become established as the preferred technique for restoring intestinal continuity postproctocolectomy. The ideal pouch design has not been established. W-pouches may give better functional results owing to increased volume, whereas the J-pouch’s advantage is its straightforward construction. We report short- and long-term results of an randomized control trial designed to establish the ideal pouch.

DESIGN: Ninety-four patients were randomly assigned to J- and W-pouches (49:45) and assessed at 1 and 8.7 years postoperatively. Assessment was questionnaire based and designed to assess pouch function and patient quality of life.

RESULTS: Eighty-five percent of patients were followed up at 1 year, and 68% were followed up at 8.7 years. At 1 year, there was a significant difference in 24-hour bowel movement frequency J- vs W-pouches 7 vs 5(p < 0.001) and in daytime frequency J- vs W-pouches 6 vs 4 (p < 0.001), with no difference in nocturnal function. At 9-year follow-up, function had equilibrated between the 2 groups: 24-hour bowel movement frequency J- vs W-pouches 6.5 vs 6 (p = 0.36), daytime frequency 5.5 vs 5 (p = 0.233), and nocturnal function 1 vs 1 (p = 0.987). Mean operating time of J- and W-pouches was 195 and 215 minutes (p < 0.05). All other parameters, pad usage, urgency, incontinence, and quality of life, did not differ significantly between groups.

CONCLUSION: These data demonstrate that the theoretical functional advantage conferred on the W-pouch by its greater volume exists only in the short term and is of little consequence to patients’ long-term quality of life. This advantage is attenuated as the pouches mature, resulting in no disparity in pouch function. This, combined with the more consistent, efficient, and easily taught construction of the J-pouch, should conclusively establish it as the optimum ileal-pouch design.

Effect of timing of dialysis commencement on clincial outcomes of patients with planned initiation of peritoneal dialysis in the ideal trial

Background: Since the mid-1990s, early dialysis initiation has dramatically increased in many countries. The Initiating Dialysis Early and Late (IDEAL) study demonstrated that, compared with late initiation, planned early initiation of dialysis was associated with comparable clinical outcomes and increased health care costs. Because residual renal function is a key determinant of outcome and is better preserved with peritoneal dialysis (PD), the present pre-specified subgroup analysis of the IDEAL trial examined the effects of early-compared with late-start dialysis on clinical outcomes in patients whose planned therapy at the time of randomization was PD.

Methods: Adults with an estimated glomerular filtration rate (eGFR) of 10 - 15 mL/min/1.73 m2 who planned to be treated with PD were randomly allocated to commence dialysis at an eGFR of 10 - 14 mL/min/1.73 m2 (early start) or 5 - 7 mL/min/1.73 m2 (late start). The primary outcome was all-cause mortality.

Results: Of the 828 IDEAL trial participants, 466 (56%) planned to commence PD and were randomized to early start (n = 233) or late start (n = 233). The median times from randomization to dialysis initiation were, respectively, 2.03 months [interquartile range (IQR):1.67 - 2.30 months] and 7.83 months (IQR: 5.83 - 8.83 months). Death occurred in 102 early-start patients and 96 late-start patients [hazard ratio: 1.04; 95% confidence interval (CI): 0.79 - 1.37]. No differences in composite cardiovascular events, composite infectious deaths, or dialysis-associated complications were observed between the groups. Peritonitis rates were 0.73 episodes (95% CI: 0.65 - 0.82 episodes) per patient-year in the early-start group and 0.69 episodes (95% CI: 0.61 - 0.78 episodes) per patient-year in the late-start group (incidence rate ratio: 1.19; 95% CI: 0.86 - 1.65; p = 0.29). The proportion of patients planning to commence PD who actually initiated dialysis with PD was higher in the early-start group (80% vs 70%, p = 0.01).

Conclusion: Early initiation of dialysis in patients with stage 5 chronic kidney disease who planned to be treated with PD was associated with clinical outcomes comparable to those seen with late dialysis initiation. Compared with early-start patients, late-start patients who had chosen PD as their planned dialysis modality were less likely to commence on PD.

(S,N)-implications on bounded lattices

Since the birth of the fuzzy sets theory several extensions have been proposed. For these extensions, different sets of membership functions were considered. Since fuzzy connectives, such as conjunctions, negations and implications, play an important role in the theory and applications of fuzzy logics, these connectives have also been extended. An extension of fuzzy logic, which generalizes the ones considered up to the present, was proposed by Joseph Goguen in 1967. In this extension, the membership values are drawn from arbitrary bounded lattices. The simplest and best studied class of fuzzy implications is the class of (S,N)-implications, and in this chapter we provide an extension of (S,N)-implications in the context of bounded lattice valued fuzzy logic, and we show that several properties of this class are preserved in this more general framework.

The ‘Australian Girl’ and the domestic ideal in colonial women’s fiction

The vast majority of novels and periodicals read by colonial Australian girls were written and published in Britain. ‘Daughters of the Southern Cross’ were more likely to have access to the Girl’s Own Paper by subscription or to imported fictions that had proven popular with British girl readers than any locally produced depictions of girlhood. From the 1880s, however, Australian authors produced several milestone fictions of girlhood for both adult and juvenile audiences. Rosa Praed's An Australian Heroine (1880) and Catherine Martin’s An Australian Girl (1890)  gave voice to the lived experience of Australia for young women, and their publication in Britain contributed to an emergent reciprocal transpacific flow of literary culture.

Two canonical Australian novels that focus on the maturation of girl protagonists who live on bush homesteads were also published in this period. Ethel Turner’s Seven Little Australians (1894) and Miles Franklin’s My Brilliant Career (1901) feature intelligent girls who are not able to be effectively socialised to embrace domesticity. Turner’s Judy Woolcot is distinct among her six siblings as a plucky girl who instigates trouble, while Franklin’s aspiring writer Sybylla Melvyn is informed that ‘girls are the helplessest, uselessest, troublesomest little creatures in the world.’

The 1890s saw an agricultural depression in Australia that only fuelled the urban perpet-uation of the idealised and nationalistic bushman myth in literary and popular culture. The ubiquity of the myth problematised any attempt to situate women heroically within the nation outside of the home. British fictional imaginings of Australian girls lauded their lack of conformity and physical abilities and often showed them bravely defending the family property with firearms. In contrast, Australian domestic fiction, this chapter argues, is unable to accommodate bracing female heroism, postulating ambiguous outcomes at best for heroines who deviate from the feminine ideal.

Judy’s grandmother describes her ‘restless fire’ as something that ‘would either make a noble, daring, brilliant woman of her’, or ‘would flame up higher and higher and consume her’. Turner does not allow Judy’s unconventionality to prosper. Instead, she is killed by a falling gum tree while saving the life of her brother, leaving the future fulfilment of the domestic ideal to her sister, Meg, whose subsequent story occupies Little Mother Meg (1902). Franklin’s Sybylla expresses her inability to be content with the simple pleasures of keeping a home, and this informs her decision to reject a marriage proposal from a wealthy suitor. The novel’s indeterminate conclusion does not allow fulfilment of Sybylla’s writing aspirations, situating her outside the feminine ideal yet not affirming the merits of her desire to reject married life.

While Sharyn Pearce suggests that Judy’s tragic end follows a narrative pattern that sup-ports the glorification of male heroes and renders ‘over-reaching women’ as ‘noble failures’, the novel might also productively be read within the context of other fictions featuring girl protagonists of the period, such as Praed and Martin's novels. This chapter makes the case that Turner and Franklin’s thwarted heroines critique the containment of Australian girls to the banalities of the home by exposing the negative and uncertain outcomes for those who desire the freedoms and aspirations permitted to boys and men. Unlike British fictions that champion adventurous girls, these Australian fictions critique the continuation of gendered restrictions in the colonies by proposing that girls who desire excitement and independence ‘should have been…boy[s]’ (as Sybylla’s mother remarks).