Interval Ranking Research Articles

Melodic interval perception with acoustic and electric hearing in bimodal and single-sided deaf cochlear implant listeners

Two notes sounded sequentially elicit melodic intervals and contours that form the basis of melody. Many previous studies have characterized pitch perception in cochlear implant (CI) users to be poor which may be due to the limited spectro-temporal resolution and/or spectral warping with electric hearing compared to acoustic hearing (AH). Poor pitch perception in CIs has been shown to distort melodic interval perception. To characterize this interval distortion, we recruited CI users with either normal (single sided deafness, SSD) or limited (bimodal) AH in the non-implanted ear. The contralateral AH allowed for a stable reference with which to compare melodic interval perception in the CI ear, within the same listener.Melodic interval perception was compared across acoustic and electric hearing in 9 CI listeners (4 bimodal and 5 SSD). Participants were asked to rank the size of a probe interval presented to the CI ear to a reference interval presented to the contralateral AH ear using a method of constant stimuli. Ipsilateral interval ranking was also measured within the AH ear to ensure that listeners understood the task and that interval ranking was stable and accurate within AH. Stimuli were delivered to the AH ear via headphones and to the CI ear via direct audio input (DAI) to participants’ clinical processors. During testing, a reference and probe interval was presented and participants indicated which was larger. Ten comparisons for each reference-probe combination were presented. Psychometric functions were fit to the data to determine the probe interval size that matched the reference interval.Across all AH reference intervals, the mean matched CI interval was 1.74 times larger than the AH reference. However, there was great inter-subject variability. For some participants, CI interval distortion varied across different reference AH intervals; for others, CI interval distortion was constant. Within the AH ear, ipsilateral interval ranking was accurate, ensuring that participants understood the task. No significant differences in the patterns of results were observed between bimodal and SSD CI users.The present data show that much larger intervals were needed with the CI to match contralateral AH reference intervals. As such, input melodic patterns are likely to be perceived as frequency compressed and/or warped with electric hearing, with less variation among notes in the pattern. The high inter-subject variability in CI interval distortion suggests that CI signal processing should be optimized for individual CI users.

Efficiency intervals, rank intervals and dominance relations of decision-making units with fixed-sum outputs

How to evaluate the performance of decision-making units (DMUs) with fixed-sum outputs is a timely and challenging question in data envelopment analysis (DEA). Two major challenges are (1) how to determine a common equilibrium efficient frontier and (2) how to deal with multiple feasible equilibrium efficient frontiers. This paper first uses a simple dataset to illustrate the possibility of multiple equilibrium efficient frontiers and the corresponding major differences in the DMUs’ efficiencies and rankings resulting from these frontiers. We address these challenges by considering all feasible equilibrium efficient frontiers and develop several models to obtain the corresponding efficiency intervals, ranking intervals and dominance relations for the DMUs with fixed-sum outputs. We illustrate the proposed approach with two numerical examples and show that it gives more informative results than previous DEA approaches. For example, there are interesting dominance relations between DMUs under the fixed-sum outputs; yet these relations do not exist when there are no fixed-sum outputs. In addition, the efficiency ranges and ranking intervals can be narrowed by accounting for policy suggestions such as adjustment constraints of fixed-sum outputs for DMUs.

Prediction of transcriptional signatures in glomeruli of a mouse model of nephropathy using the human Global Prior rank

BackgroundDifferential gene expression is commonly used to provide insight into the molecular mechanisms of disease. Each human or murine cell contains roughly 20000 protein coding genes and 30 to 50% are expected to be significantly expressed. Recent analysis of human transcriptomes studies showed that generic transcriptional signatures commonly occur. The Global Prior ranks human genes based on the likelihood of being differentially expressed regardless of experimental conditions. Given that rodent models are extensively used to infer mechanisms of human disease, we tested whether the predictability of gene expression found in humans applies to a mouse model of renal disease.HypothesisThe human Global Prior rank would predict differential gene expression in the transgenic Tg26 mouse.MethodsTranscriptomes of isolated glomeruli from Tg26 mice and non‐transgenic controls were obtained using Affymetrix microarrays. Differential gene expression between groups was assessed with Limma. The human Global Prior was obtained from GitHub. The differentially expressed genes (DEG) by Limma were extracted and mapped to the Global Prior for exploratory data analysis.ResultsThe Global Prior contained 19171 human genes, while our complete Limma results list contained 19525 mouse genes. There were 15183 human‐mouse orthologues present in both lists. We further subset the overlapping genes according to the following criteria: 1st) a Limma FDR <= 0.05, and 2nd) at least 25% change in Tg26 as compared to control (log2FC < −0.42 or log2FC > 0.32). This process yielded a list of 449 DEG by Limma, with corresponding human orthologues in the Global Prior. We then explored the distribution of the Limma DEG along the Global Prior rank. Roughly 50% of the Limma DEG mapped to the top‐10% Global Prior rank interval, and 70% of the Limma DEG map to the top 20% Global Prior rank, p < 2×10−16, as measured by a Fisher’s exact test using all 15183 common genes as background list. To further characterize the predictive power of the Global Prior we examined the overlap between the top‐20% of the Global Prior (n = 3361 genes) and the Limma DEG list (n = 449 genes). The 312 genes common to both list, represent only a small fraction (9%) of the top‐20% of genes in the Global Prior. This indicate that part of the Global Prior predictive power resides in the large number of genes with 80% or more likelihood of being differentially expressed.ConclusionThe human Global Prior successfully predicted differential gene expression in mouse glomeruli. These data does not mean that the transcriptional responses in the Tg26 kidney are generic. The Global Prior does not predict the outcome of any particular study, instead it ranks commonly used transcriptional responses. Thus, the transcriptional response in Tg26 glomeruli is specific to the model, but not unique to it. Our analysis also highlights the similarities between mouse and human transcriptional responses, and validate the usefulness of experimental animals to model human diseases.Support or Funding InformationDK007470, DK097836, DK108329, DK114908

An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand

Due to the uncertainty of market economy as well as fluctuation of customer’s demand, appropriate modelling of an inventory problem is a challenging task to the researchers/OR practitioners. In order to overcome this type of challenging situation, in this article, using the parametric approach of interval a non-deterministic inventory model for deteriorating items with partially backlogged shortages and interval-valued deterioration rate has been developed. Here, the demand rate is considered to be interval-valued and dependent upon the selling price which is also interval-valued. Also, all the parameters (like ordering cost, holding cost, etc.) except the backlogging parameter have been considered as interval-valued. The corresponding problem has been formulated as a maximization problem with an interval-valued objective. Then, to solve the said problem, we have used different variants of the QPSO algorithm with interval fitness using interval ranking. Then, the computational results have been illustrated with the help of three numerical examples. Finally, the sensitivity of the solution has been analysed with the changes in the values of different parameters associated with the model and a fruitful conclusion has been drawn.

Allocating a fixed cost across decision making units with explicitly considering efficiency rankings

Fixed cost allocation (FCA) is one of the most important applications of the data envelopment analysis (DEA). Numerous studies on this problem have appeared in the literature in the last two decades; however, almost all of them are based on either efficiency invariance or efficiency maximization, both of which focus mainly on efficiency scores. It is notable that the efficiency score is more an intermediate indicator and the corresponding efficiency ranking is actually the main focus. Motivated by this observation, this paper aims to propose a new approach for allocating the fixed cost across decision making units (DMUs) based on efficiency ranking. To this end, the efficiency ranking intervals are explicitly determined by taking allocated costs and feasible weights into account. The results indicate that each DMU can be ranked at any position ranging from the best one to the worst n, and there are fixed cost allocation schemes that can determine the best efficiency ranking of one for each individual DMU simultaneously under a set of common weights. Furthermore, we define a new comprehensive satisfaction degree based on the interval of the upper and lower bounds of the allocated costs. Then, we generate the final allocation scheme using an iterative procedure to maximize the satisfaction degree across all DMUs. Finally, the proposed approach is applied to a classic numerical example from prior literature and an empirical study from the real world to illustrate its usefulness and efficacy.

A Novel Ratio-Based Parallel DEA Approach for Evaluating the Energy and Environmental Performance of Chinese Transportation Sectors

As a high-energy-consumption and high-CO2-emission industry in China, the transportation sector has been under increasing pressure to improve its performance. This paper develops a novel parallel DEA approach to measure Chinese transportation sector’s energy and environmental performance (EEP) over all possible weights, which is to avoid the risk of using the extreme or the most favorable weights in performance evaluation. In our method, the transportation sector is consisted of two parallel subsystems (passenger transportation and freight transportation) with shared inputs and undesirable shared outputs. All possible weights are considered in the EEP evaluation, then the EEP of a transportation sector is represented by a ranking interval. Finally, the proposed approach is applied to the transportation sectors in 30 Chinese provinces. Results show that the best and the worst ranking of most provinces vary greatly. Besides, the EEP of most provinces is hard to dominate others strictly, but the general tendency is the EEP of eastern provinces better than western provinces. Furthermore, the EEP difference of some adjacent provinces with similar features is distinct. These findings are not all the same as previous studies, which verifies the necessity of considering all possible weights in performance evaluation. Therefore, our method provides a new point of view in performance evaluation and can give more robust results for decision makers.

Dominance degrees for intervals and their application in multiple attribute decision-making

Since intervals are used to express decision information in various decision-making problems, it is necessary to give a feasible method to rank them. The most commonly used method is to employ the possibility degree to compare intervals in pairs, then construct a fuzzy preference relation. Generally, the constructed fuzzy preference relation does not keep (additive, multiplicative) consistency. In order to ensure the consistency of decision information, optimization models are constructed by using the logical relationship between the elements of the consistent fuzzy preference relation and their weights. Then, by solving the optimization models, consistent fuzzy preference relations are obtained. The consistent fuzzy preference relations are the proxy of the original inconsistent fuzzy preference relation constructed by the possibility degree. However, such treatment is flawed. The inconsistent fuzzy preference relation generated from the possibility degree can't guarantee the reliability of the result while the proxy consistent fuzzy preference relation would cause bias. To solve this problem, the additive dominance degree and multiplicative dominance degree for intervals are proposed as a result of indirect comparison. The fuzzy preference relations are constructed from the dominance degrees of intervals to ensure the consistency of decision information. In the process of ranking intervals, this can avoid decision-making bias. Furthermore, a new approach to interval multiple attribute decision-making is proposed based on the dominance degrees.

Particle swarm optimization hybridized with genetic algorithm for uncertain integrated process planning and scheduling with interval processing time

Integrated process planning and scheduling (IPPS) is a hot research topic on providing a blueprint of efficient manufacturing system. Most existing IPPS models and methods focus on the static machining shop status. However, in the real-world production, the machining shop status changes dynamically because of external and internal fluctuations. The uncertain IPPS can better model the practical machining shop environment but is rarely researched because of its complexity (including the difficulties of modelling and algorithm design). To deal with the uncertain IPPS problem, this paper presents a new uncertain IPPS model with uncertain processing time represented by the interval number. A new probability and preference-ratio based interval ranking method is proposed for precise interval computation. Particle swarm optimization (PSO) algorithm hybridizing with genetic algorithm (GA) is designed to achieve the good solution. To improve the search capability of the hybrid algorithm, the special genetic operators are adopted corresponding to the characteristics of uncertain IPPS problem. Some strategies are designed to prevent the particles from trapping into a local optimum. Six experiments which are adopted from some famous IPPS benchmark problems have been used to evaluate the performance of the proposed algorithm. The experimental results illustrate that the proposed algorithm has achieved good improvement and is effective for uncertain IPPS problem.

Ranking intervals for two-stage production systems

Traditional Data Envelopment Analysis (DEA) models find the most desirable weights for each Decision Making Unit (DMU) in order to estimate the highest efficiency score as possible. Usually, decision-makers are using these efficiency scores for ranking the DMUs. The main drawback in this process is that the ranking based on weights obtained from the standard DEA models ignore other feasible weights, this is due to the fact that DEA may have multiple solutions for each DMU. To overcome this problem, Salo and Punkka (2011) deemed each DMU as a “Black box” and developed a mix-integer model to obtain the ranking intervals for each DMU over sets of all its feasible weights. In many real-world applications, there are DMUs that have a two-stage production system. In this paper, we extend the Salo and Punkka (2011)’s model to more common and practical applications considering the two-stage production structure. The proposed approach calculates each DMU’s ranking interval for the overall system as well as for each subsystem/sub-stage. An application for non-life insurance companies is given to illustrate the applicability of the proposed approach. A real application in Chinese commercial banks shows how this approach can be used by policy makers.

The schedule of World Cup and its impact on the team

This paper discusses the organization of the World Cup competition, in which through the establishment of a number of scheduling model, the use of analytic hierarchy process and stochastic simulation and other methods to solve this problem and obtain a more reasonable arrangement of the competition. For the arrangement of the Order of the game, first of all, the existing competition is studied. On the premise of the increase in the number of teams and the previous arrangement of the group points, it is considered from the appropriateness of the field, whether the schedule is wonderful, whether the arrangement is simple and whether the ranking is reasonable. 3 new competition competitions are proposed for the improvement of the original competition. Then, the analytic hierarchy process is used to compare and analyze the 3 new competition methods, and the optimal competition method is selected. Finally, under the previously established game, FIFA’s integral algorithm formula is used to analyze and calculate the impact of the results produced under the competition on FIFA rankings. In the application of formula calculation, the stochastic factor is introduced, and the results are simulated by computer, which can get the approximate upward trend of the team in different ranking intervals.

Interval differential evolution with dimension-reduction interval analysis method for uncertain optimization problems

• A new optimization method is proposed to directly solve uncertain problems with interval parameters. • Dimension-reduction interval analysis calculates intervals of objective function and constraints caused by uncertainty. • The satisfaction value of interval possibility degree model utilizes to handle the uncertain constraints. • The interval preferential rule directly realizes the ranking of different design vectors. • The computational accuracy and efficiency of proposed method is verified. A constrained nonlinear interval optimization method under the framework of differential evolution algorithm is developed to solve the uncertain structural optimization problems with interval uncertainties. The proposed method is a direct optimization method based on the interval differential evolution and dimension-reduction interval analysis. The interval preferential rule based on the satisfaction value of interval possibility degree model is used to realize the direct interval ranking of different design vectors. At each evolutionary generation, the outer optimizer by differential evolution optimizer searches for the best solution within the design space. The dimension-reduction interval analysis is employed to calculate the intervals of objective and constraints for each design vector in the inner layer. This operation transforms the original nesting optimization problem into a single loop one which improves the computational efficiency of the proposed method. Finally, the effectiveness of the presented direct method is verified by two numerical examples and an engineering application.

An interval number distance- and ranking-based method for remotely sensed image fuzzy clustering

ABSTRACTFuzzy c-means clustering is an important non-supervised classification method for remote-sensing images and is based on type-1 fuzzy set theory. Type-1 fuzzy sets use singleton values to express the membership grade; therefore, such sets cannot describe the uncertainty of the membership grade. Interval type-2 fuzzy c-means (IT2FCM) clustering and relevant methods are based on interval type-2 fuzzy sets. Real vectors are used to describe the clustering centres, and the average values of the upper and lower membership grades are used to determine the classification of each pixel. Thus, the width information for interval clustering centres and interval membership grades are ignored. The main contribution of this article is to propose an improved IT2FCM* algorithm by adopting interval number distance (IND) and ranking methods, which use the width information of interval clustering centres and interval membership grades, thus distinguishing this method from existing fuzzy clustering methods. Three different IND definitions are tested, and the distance definition proposed by Li shows the best performance. The second contribution of this work is that two fuzzy cluster validity indices, FS- and XB-, are improved using the IND. Three types of multi/hyperspectral remote-sensing data sets are used to test this algorithm, and the experimental results show that the IT2FCM* algorithm based on the IND proposed by Li performs better than the IT2FCM algorithm using four cluster validity indices, the confusion matrix, and the kappa coefficient (κ). Additionally, the improved FS- index has more indicative ability than the original FS- index.

Hybrid reliability analysis and optimization for spacecraft structural system with random and fuzzy parameters

In aerospace engineering, the incomplete environment conditions have been realized to be a significant factor affecting the system safety assessment. Considering the hybrid random and fuzzy uncertainties in system inputs, the paper proposes a novel numerical procedure for reliability analysis and reliability-based optimization. Random parameters are adopted to denote the aleatory uncertainties with sufficient sample information; whereas fuzzy parameters are used to quantify the epistemic uncertainties associated with expert opinions. Using the level-cut operation, fuzzy parameters are converted into interval variables, and a satisfaction degree-based interval ranking strategy is utilized to precisely quantify the interval safety possibility. Then the system safety possibility is calculated by the multiple integral, where cut levels of different fuzzy parameters are treated as independent variables. Subsequently based on the given safety index, a hybrid reliability optimization model is established. To avoid the huge computational burden caused by nested-loop optimization, a modified interval Monte Carlo method (MIMC) is proposed for limit state function evaluation. Eventually, a numerical example about the refractory ceramics tile of spacecraft verifies the feasibility of proposed method for hybrid reliability analysis and optimization design in practical aerospace engineering.

Multi-section-Oriented Robust Algorithm for Unconstrained Global Optimization

We develop a new hybrid method called multi-section-oriented artificial bee colony MSO-ABC algorithm, to solve complex unconstrained optimization problems. The method initially decomposes the search region into finite collection of subregions in which the best interval value of the objective function is found using ABC algorithm. ABC algorithm uses chaotic maps to express parameter adaption to improve the search performance and escape from local optima. Then, interval ranking rule defined with respect to the optimistic decision makers’ point of view is applied to find most promising subregion containing best objective value for further division and non-promising region(s) are discarded. The technique narrows the search region by recursive decomposition and enhances computational effort toward better solution. The process is repeated reducing the search space consecutively. The global/ close to global values are obtained in the form of an interval with negligible width. Validity of MSO-ABC is tested on benchmark functions followed by the non-parametric tests viz., Friedman and Wilcoxon rank test for assessing statistical significance of the proposed method against other well-established optimization methods.

Determining units Ranking with the Best and the Worst Rank of Each unit as well as Interval Ranking.

Determining units Ranking with the Best and the Worst Rank of Each unit as well as Interval Ranking.

Data Envelopment Analysis Based on Choquet Integral

Data envelopment analysis (DEA) is a widely used technique in decision making. The existing DEA models always assume that the inputs (or outputs) of decision-making units (DMUs) are independent with each other. However, there exist positive or negative interactions between inputs (or outputs) of DMUs. To reflect such interactions, Choquet integral is applied to DEA. Self-efficiency models based on Choquet integral are first established, which can obtain more efficiency values than the existing ones. Then, the idea is extended to the cross-efficiency models, including the game cross-efficiency models. The optimal analysis of DEA is further investigated based on regret theory. To estimate the ranking intervals of DMUs, several models are also established. It is founded that the models considering the interactions between inputs (or outputs) can obtain wider ranking intervals.

Mixed Nonprobabilistic Reliability-Based Optimization Method for Heat Transfer System With Fuzzy and Interval Parameters

By combining the nonprobabilistic reliability theory with optimization design approach, this paper proposes a mixed reliability-based optimization method for the heat transfer system design with both fuzzy and interval parameters in material property, external load, and boundary condition. Fuzzy variables are used to represent subjective uncertainties associated with expert opinions; whereas, interval variables are adopted to quantify objective uncertainties with limited information. Based on the level-cut strategy, the mixed uncertain problem is transformed into a pure interval problem first. Then, a modified reliability analysis method using an interval ranking strategy and integral operation is presented to precisely assess the system safety possibility. Subsequently, a mixed reliability-based optimization model with fuzzy and interval parameters is established, which is a nested optimization problem with huge computational cost. A subinterval perturbation method is eventually presented for temperature field prediction, which can replace the inner loop optimization and improve the computational efficiency. A transient heat conduction example about a three-layer thermal structure verifies the superiority of the proposed model and method for mixed reliability analysis and optimization in practical engineering.

Measuring Similarity and Ordering Based on Interval Type-2 Fuzzy Numbers

This paper extends a preference degree to rank interval type-2 fuzzy numbers. A general method to measure the similarity between interval type-2 fuzzy numbers is also introduced. Using some theorems and lemmas, it is proven that the extended similarity measures satisfy many common and desired properties based on the common axiomatic definitions introduced for similarity measures. The main properties of the extended preference degree are studied. In addition, several possible applications of the proposed methods are illustrated by some application examples in pattern recognition and multicriteria group decision making. Moreover, the proposed methods are examined in order to compare them with other existing methods, and the feasibility and effectiveness of the proposed methods are cleared via some lemmas and numerical comparisons.

Novel numerical methods for reliability analysis and optimization in engineering fuzzy heat conduction problem

Engineering fuzzy heat conduction problem with subjective uncertainties in input parameters constitutes a significant challenge. Based on fuzzy and interval theory, this paper presents novel numerical methods to efficiently identify the effect of fuzzy uncertainty on the system reliability analysis and optimization design. Firstly using the interval ranking strategy, the interval safety possibility in the transition state can be precisely quantified, and the eventual fuzzy safety possibility is calculated by integral operation. Then a fuzzy reliability-based optimization model is established with considerable computational cost caused by the two-layer nested loop. In order to improve the computational efficiency, a subinterval perturbation method based on the first-order Taylor series is presented to replace the inner loop. Comparing numerical results with traditional reliability model, two numerical examples are provided to evidence the superiority of proposed model and method for fuzzy reliability analysis and optimization in practical engineering.

Aerodynamic robust optimization of flying wing aircraft based on interval method

PurposeThe purpose of this paper is to propose a robust optimization strategy to deal with the aerodynamic optimization issue, which does not need a large sum of information on the uncertainty of input parameters.Design/methodology/approachInterval numbers were adopted to describe the uncertain input, which only requires bounds and does not necessarily need probability distributions. Based on the method, model outputs were also regarded as intervals. To identify a better solution, an order relation was used to rank interval numbers.FindingsBased on intervals analysis method, the uncertain optimization problem was transformed into nested optimization. The outer optimization was used to optimize the design vector, and inner optimization was used to compute the interval of model outputs. A flying wing aircraft was used as a basis for uncertainty optimization through the suggested optimization strategy, and optimization results demonstrated the validity of the method.Originality/valueIn aircraft conceptual design, the uncertain information of design parameters are often insufficient. Interval number programming method used for uncertainty analysis is effective for aerodynamic robust optimization for aircraft conceptual design.