A Novel Method for Solving the Fully Fuzzy Bilevel Linear Programming Problem

We address a fully fuzzy bilevel linear programming problem in which all the coefficients and variables of both objective functions and constraints are expressed as fuzzy numbers. This paper is to develop a new method to deal with the fully fuzzy bilevel linear programming problem by applying interval programming method. To this end, we first discretize membership grade of fuzzy coefficients and fuzzy decision variables of the problem into a finite number of α-level sets. By using α-level sets of fuzzy numbers, the fully fuzzy bilevel linear programming problem is transformed into an interval bilevel linear programming problem for each α-level set. The main idea to solve the obtained interval bilevel linear programming problem is to convert the problem into two deterministic subproblems which correspond to the lower and upper bounds of the upper level objective function. Based on the Kth-best algorithm, the two subproblems can be solved sequentially. Based on a series of α-level sets, we introduce a linear piecewise trapezoidal fuzzy number to approximate the optimal value of the upper level objective function of the fully fuzzy bilevel linear programming problem. Finally, a numerical example is provided to demonstrate the feasibility of the proposed approach

Angels in the House: Female Images in Victorian Children’s Fantasy

Victorian period witnessed prosperity and popularity of children’s fantasy. Female characters abound in the adult fiction of Victorian literature. But what are they like in works written for children? This thesis attempts to analyze different women images in children’s fantasy. Some writers choose to omit women; some idealize women as the angel in the house; some portray them as powerful and aggressive. These different images of women reflect the social values of the time

Reflected Backward Stochastic Differential Equations Driven by L\'{e}vy Process

In this paper, we deal with a class of reflected backward stochastic differential equations associated to the subdifferential operator of a lower semi-continuous convex function driven by Teugels martingales associated with L\'{e}vy process. We obtain the existence and uniqueness of solutions to these equations by means of the penalization method. As its application, we give a probabilistic interpretation for the solutions of a class of partial differential-integral inclusions.Comment: 14 page

Detection and differentiation of Borrelia burgdorferi sensu lato in ticks collected from sheep and cattle in China

<p>Abstract</p> <p>Background</p> <p>Lyme disease caused by <it>Borrelia burgdorferi </it>sensu lato complex is an important endemic zoonosis whose distribution is closely related to the main ixodid tick vectors. In China, isolated cases of Lyme disease infection of humans have been reported in 29 provinces. Ticks, especially ixodid ticks are abundant and a wide arrange of <it>Borrelia </it>natural reservoirs are present. In this study, we developed a reverse line blot (RLB) to identify <it>Borrelia </it>spp. in ticks collected from sheep and cattle in 7 Provinces covering the main extensive livestock regions in China.</p> <p>Results</p> <p>Four species-specific RLB oligonucleotide probes were deduced from the spacer region between the 5S-23S rRNA gene, along with an oligonucleotide probe which was common to all. The species specific probes were shown to discriminate between four genomic groups of <it>B. burgdorferi </it>sensu lato i.e. <it>B. burgdorferi </it>sensu stricto, <it>B. garinii, B. afzelii</it>, and <it>B. valaisiana</it>, and to bind only to their respective target sequences, with no cross reaction to non target DNA. Furthermore, the RLB could detect between 0.1 pg and 1 pg of <it>Borrelia </it>DNA.</p> <p>A total of 723 tick samples (<it>Haemaphysalis, Boophilus, Rhipicephalus </it>and <it>Dermacentor</it>) from sheep and cattle were examined with RLB, and a subset of 667 corresponding samples were examined with PCR as a comparison. The overall infection rate detected with RLB was higher than that of the PCR test.</p> <p>The infection rate of <it>B. burgdoreri </it>sensu stricto was 40% in south areas; while the <it>B. garinii infection rate </it>was 40% in north areas. The highest detection rates of <it>B. afzelii </it>and <it>B. valaisiana </it>were 28% and 22%, respectively. Mixed infections were also found in 7% of the ticks analyzed, mainly in the North. The proportion of <it>B. garinii </it>genotype in ticks was overall highest at 34% in the whole investigation area.</p> <p>Conclusion</p> <p>In this study, the RLB assay was used to detect <it>B. burgdorferi </it>sensu lato in ticks collected from sheep and cattle in China. The results showed that <it>B. burdorferi senso stricto </it>and <it>B. afzelii </it>were mainly distributed in the South; while <it>B. garinii </it>and <it>B. valaisiana </it>were dominant in the North. <it>Borrelia </it>spirochaetes were detected in <it>Rhipicephalus </it>spp for the first time. It is suggested that the <it>Rhipicephalus </it>spps might play a role in transmitting <it>Borrelia </it>spirochaetes.</p

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method

A novel approach based on preference-based index for interval bilevel linear programming problem

Abstract This paper proposes a new methodology for solving the interval bilevel linear programming problem in which all coefficients of both objective functions and constraints are considered as interval numbers. In order to keep as much uncertainty of the original constraint region as possible, the original problem is first converted into an interval bilevel programming problem with interval coefficients in both objective functions only through normal variation of interval number and chance-constrained programming. With the consideration of different preferences of different decision makers, the concept of the preference level that the interval objective function is preferred to a target interval is defined based on the preference-based index. Then a preference-based deterministic bilevel programming problem is constructed in terms of the preference level and the order relation ⪯ m w $\preceq_{mw}$ . Furthermore, the concept of a preference δ-optimal solution is given. Subsequently, the constructed deterministic nonlinear bilevel problem is solved with the help of estimation of distribution algorithm. Finally, several numerical examples are provided to demonstrate the effectiveness of the proposed approach

Abdominal aortic calcification score can predict all-cause and cardiovascular mortality in maintenance hemodialysis patients

AbstractPurpose Abdominal aortic calcification (AAC) assessed by using standard lateral lumbar radiographs can be graded, and composite summary scores (range, 0–24) have been shown to be highly predictive of subsequent cardiovascular morbidity and mortality in hemodialysis (HD) patients. However, few studies have sought to determine the optimal AAC score cutoff values for the prediction of mortality among HD patients.Methods This retrospective cohort study included 408 hemodialysis patients. AAC severity was quantified by the AAC score, which was measured by lateral lumbar radiography with complete follow-up data from January 2015 to December 2021. We used receiver operating characteristic (ROC) analysis to find the cutoff AAC value for the prediction of mortality. The Kaplan–Meier method was used to analyze all-cause and cardiovascular mortality.Results The cutoff calcification score for the prediction of mortality was 4.5 (sensitivity, 67.3%; specificity, 70.4%). The patients with AAC scores above 4.5 had significantly higher all-cause (log-rank p  4.5 have significantly elevated all-cause and cardiovascular mortality compared with those with an AAC score ≤ 4.5. AAC was a better predictor than cardiac valve calcification for mortality in HD patients