Interval Ranking Research Articles

Melodic interval perception by normal-hearing listeners and cochlear implant users.

The perception of melodic intervals (sequential pitch differences) is essential to music perception. This study tested melodic interval perception in normal-hearing (NH) listeners and cochlear implant (CI) users. Melodic interval ranking was tested using an adaptive procedure. CI users had slightly higher interval ranking thresholds than NH listeners. Both groups' interval ranking thresholds, although not affected by root note, significantly increased with standard interval size and were higher for descending intervals than for ascending intervals. The pitch direction effect may be due to a procedural artifact or a difference in central processing. In another test, familiar melodies were played with all the intervals scaled by a single factor. Subjects rated how in tune the melodies were and adjusted the scaling factor until the melodies sounded the most in tune. CI users had lower final interval ratings and less change in interval rating as a function of scaling factor than NH listeners. For CI users, the root-mean-square error of the final scaling factors and the width of the interval rating function were significantly correlated with the average ranking threshold for ascending rather than descending intervals, suggesting that CI users may have focused on ascending intervals when rating and adjusting the melodies.

Scale Dependence and Ranking Intervals in Additive Value Models Under Incomplete Preference Information

A multiattribute additive value function that has been built from a complete specification of the decision maker's (DM's) preferences gives scale-independent decision recommendations, which do not depend on how the value function is normalized. In this paper, we show that if the preference specification is incomplete, many widely employed decision rules for comparing alternatives give scale-dependent decision recommendations in which the relative ranking of alternatives depends not only on the DM's preferences but also on the normalization of the value function. But because normalization does not involve preference statements, the recommendations should be scale independent so that they do not depend on the chosen normalization. To provide such recommendations, we propose ranking intervals, which show how a given alternative compares with all other alternatives for all value functions that are consistent with the stated preference information. These intervals can be computed from mixed integer linear optimization problems that are constrained by inequalities implied by the DM's preference statements. We illustrate the use of ranking intervals by analyzing university rankings and discuss their uses in project portfolio selection.

Professionalism in Service Marketing: The Role of Standards and Ethics: A Study of the Nigeria Institute of Public Relations

The level and rate of growth in public relations practice in Nigeria though encouraging, the developmental striveis slow. The later accounts for the retarded growth rate of professionalism status attainment in the practice ofpublic relations in Nigeria. This work therefore considered the role and relevance of standards in the practice ofpublic relations, built on ethics and ethical values; as basic requirements for professionalism. It appraised thepractice of public relations vis-à-vis other practices such as law and medicine and x-rayed the constraints toprofessionalism in public relations. The impact of public relations practitioners’ characters/traits, work habitsand membership enlistments requirements were assessed as factors that influence the quality of members’(service) output. Equally evaluated are the influences of non-universality and inconsistency characteristics ofethics and non-culpability of ethical breach on the practice of public relations. The work in addition, consideredthe role of confidentiality, integrity and objectivity in public relations practice and assessed the NIPRdisciplinary management procedure given the institute’s code of practice. Adequate analytical and statisticaltools including Likert ranking scale and the ordinal and interval ranking scales, were employed in internal andexternal factor influence appraisals and solutions among others. In the midst of constraints were recommendedas strive strategies to the attainment of professionalism in the practice of public relations in Nigeria. Inclusive ofthese are unified method of fees determination for practitioners, pre and post accreditation of membership,review of codes of practice for universality, improvement in the method and procedure of dispute managementamong others.

An interval valued solid transportation problem with budget constraint in different interval approaches

In this paper we investigate on solid transportation problem with interval environment. In this manuscript we develop STP under interval unit transportation cost, availability, requirement, conveyances capacity etc. Also, separately from source, demand and capacity constraints, an additional constraint on the total budget at each destination is imposed. We employ two different approaches (Hu and Wang's Approach and Mahato and Bhunia's Approach) based on interval ranking. After converting the interval transportation models into its crisp equivalent we apply the Weighted Tchebycheff method to solve. The models are illustrated with numerical examples and solved using the LINGO.13 optimization software.

Interval positroid varieties and a deformation of the ring of symmetric functions

Define the <b>interval rank</b> $r_[i,j] : Gr_k(\mathbb C^n) →\mathbb{N}$ of a k-plane V as the dimension of the orthogonal projection $π _[i,j](V)$ of V to the $(j-i+1)$-dimensional subspace that uses the coordinates $i,i+1,\ldots,j$. By measuring all these ranks, we define the <b>interval rank stratification</b> of the Grassmannian $Gr_k(\mathbb C^n)$. It is finer than the Schubert and Richardson stratifications, and coarser than the positroid stratification studied by Lusztig, Postnikov, and others, so we call the closures of these strata <b>interval positroid varieties</b>. We connect Vakil's "geometric Littlewood-Richardson rule", in which he computed the homology classes of Richardson varieties (Schubert varieties intersected with opposite Schubert varieties), to Erdős-Ko-Rado shifting, and show that all of Vakil's varieties are interval positroid varieties. We build on his work in three ways: (1) we extend it to arbitrary interval positroid varieties, (2) we use it to compute in equivariant K-theory, not just homology, and (3) we simplify Vakil's (2+1)-dimensional "checker games" to 2-dimensional diagrams we call "IP pipe dreams". The ring Symm of symmetric functions and its basis of Schur functions is well-known to be very closely related to the ring $\bigoplus_a,b H_*(Gr_a(\mathbb{C}^{(a+b)})$ and its basis of Schubert classes. We extend the latter ring to equivariant K-theory (with respect to a circle action on each $\mathbb{C}^{(a+b)}$, and compute the structure constants of this two-parameter deformation of Symm using the interval positroid technology above.

Uncertain constrained optimization by interval-oriented algorithm

This paper deals with an interval-oriented approach to solve general interval constrained optimization problems. Generally, this type of problems has infinitely many compromise solutions. The aim of this approach is to obtain one of such solutions with higher accuracy and lower computational cost. The proposed algorithm is nothing but a different kind of branch and bound algorithm with multi-section division criterion of the search region (or box). In the proposed technique, the prescribed/accepted region is divided into several distinct subregions and in each feasible subregion the interval objective function value is computed. Then the subregion containing the best objective value is found by applying a specific interval ranking rule defined with respect to the pessimistic decision makers’ point of view. The process is continued until the interval width for each variable in the accepted subregion is negligible. Finally, the algorithm converges to a compromise solution in interval form. To illustrate the method and also to test the efficiency as well as the effectiveness of the proposed algorithm, we have solved some numerical examples.

Fuzzy Evaluation Based on Interval-Valued in the Application of Driver Traffic Behavior

The paper discusses the definition of interval number and basic algorithm. It also described the problem of interval ranking and introduced interval-valued fuzzy comprehensive evaluation model. The model is more suitable for evaluation of many factors, weight distribution than the uniform case.Interval-valued fuzzy comprehensive evaluation model to judge the field of driver traffic safety behavior. According to literature reviews to establish the evaluation index system and set .Then determine the weight of different factors and required basic data by the expert scoring. Finally, the results of the evaluation model is excellent.The application examples explain that the method can effectively reduce the loss of information which with good results.

Evaluating the Performance of the Emergency Medical Services Index

Background: In 2006 Emergency Medical Services Index (EMSI), which summarizes the performance of regional emergency medical services system, was developed. This study assesses the performance of the EMSI to help determine whether EMSI can be used as evaluation tool. Methods: To build a composite score of the EMSI from predefined 24 indicators, 3 normalized values were calculated for each indicator, the normalized values of each indicator were weighted using 4 weighting methods, and the weighted values were aggregated into the final composite score using 2 aggregation schemes. The performance of EMSI was evaluated using 3 criteria: discrimination, construct validity, and sensitivity. Discrimination was the proportion of regions that did not include the overall median rank in the 5th to 95th percentiles rank interval, which was calculated from Monte Carlo simulation. Construct validity was a correlation among the alternative EMSIs. Sensitivity of EMSIs was evaluated by total shift of quartile membership and changes of 5th to 95th percentile intervals. Results: The total discrimination performance of the EMSI was 50.0%. Correlation coefficients between EMSIs using standardized values and those using rescaled values ranged from 0.621 to 0.997. Variation of the quartile membership of regions ranged from 0.0% to 75.0%. The total change in the 5th to 95th percentile intervals ranged from -19 to +17 places. Conclusion: The results suggested that the EMSI could be used as a tool for evaluating quality of regional EMS system and for identifying the areas for quality improvement.

Weekly momentum by return interval ranking

Existing research does not find significant momentum profits in many emerging markets including China. We propose an alternative momentum strategy which groups stocks into return intervals rather than percentiles. We apply the method to the China A-share market and find economically significant momentum profits in weekly returns, but not in monthly returns. The weekly momentum lasts for about 1year. More than half of the profit is realized in the first 3weeks. We apply the method to other Asian equity markets and find significant weekly momentum in Hong Kong, Taiwan, Korea, Thailand, and Indonesia. These findings suggest that momentum may exist in different formats in different markets. Existence of momentum in a closed equity market like China supports momentum is pervasive in short-term stock returns.

Fuzzy multiple attributes group decision-making based on ranking interval type-2 fuzzy sets

In this paper, we present a new method to deal with fuzzy multiple attributes group decision-making problems based on ranking interval type-2 fuzzy sets. First, we propose a new method for ranking interval type-2 fuzzy sets. Then, we propose a new method for fuzzy multiple attributes group decision-making based on the proposed ranking method of interval type-2 fuzzy sets. We also use some examples to illustrate the fuzzy multiple attributes group decision-making process of the proposed method. The proposed method is simpler than the methods presented in Chen and Lee (2010a, 2010b) for fuzzy multiple attributes group decision-making based on interval type-2 fuzzy sets. It provides us with a useful way for dealing with fuzzy multiple attributes group decision-making problems based on interval type-2 fuzzy sets.

Ranking Intervals and Dominance Relations for Ratio-Based Efficiency Analysis

We develop comparative results for ratio-based efficiency analysis (REA) based on the decision-making units' (DMUs') relative efficiencies over sets of feasible weights that characterize preferences for input and output variables. Specifically, we determine (i) ranking intervals, which indicate the best and worst efficiency rankings that a DMU can attain relative to other DMUs; (ii) dominance relations, which show what other DMUs a given DMU dominates in pairwise efficiency comparisons; and (iii) efficiency bounds, which show how much more efficient a given DMU can be relative to some other DMU or a subset of other DMUs. Unlike conventional efficiency scores, these results are insensitive to outlier DMUs. They also show how the DMUs' efficiency ratios relate to each other for all feasible weights, rather than for those weights only for which the data envelopment analysis (DEA) efficiency score of some DMU is maximized. We illustrate the usefulness of these results by revisiting reported DEA studies and by describing a recent case study on the efficiency comparison of university departments. This paper was accepted by Teck-Hua Ho, decision analysis.

Management Insights

Management Insights

Acceptable consistency analysis of interval reciprocal comparison matrices

When a decision maker expresses his/her opinions by means of an interval reciprocal comparison matrix, the study of consistency becomes a very important aspect in decision making in order to avoid a misleading solution. In the present paper, an acceptably consistent interval reciprocal comparison matrix is defined, which can be reduced to an acceptably consistent crisp reciprocal comparison matrix when the intervals become exact numbers. An interval reciprocal comparison matrix with unacceptable consistency can be easily adjusted such that the revised matrix possesses acceptable consistency. Utilizing a convex combination method, a family of crisp reciprocal comparison matrices with acceptable consistency can be obtained, whose weights are further found to exhibit a style of convex combination, and aggregated to obtain interval weights from an acceptably consistent interval reciprocal comparison matrix. A novel, simple yet effective formula of possibility degree is presented to rank interval weights. Numerical results are calculated to show the quality and quantity of the proposed approaches and compare with other existing procedures.

When Talk Ain't Cheap - Costly Information Transmission in Continuous Time

This paper formulates a continuous time information transmission model in which an altruistic sender privately observes a stochastic state variable, and incurs a communication cost when she sends a message. We study three issues associated with this costly information transmission: 1) The sender's optimal strategy involves sending discrete messages; 2) With pre-fixed ranking intervals, the sender optimally sets a tolerance band around the cutoff point of each interval; 3) The optimal announcement frequency is characterized. We also propose to use this model to study the tradeoff between rating accuracy and stability.

Interval oriented multi-section techniques for global optimization

This paper deals with two different optimization techniques to solve the bound-constrained nonlinear optimization problems based on division criteria of a prescribed search region, finite interval arithmetic and interval ranking in the context of a decision maker’s point of view. In the proposed techniques, two different division criteria are introduced where the accepted region is divided into several distinct subregions and in each subregion, the objective function is computed in the form of an interval using interval arithmetic and the subregion containing the best objective value is found by interval ranking. The process is continued until the interval width for each variable in the accepted subregion is negligible. In this way, the global optimal or close to global optimal values of decision variables and the objective function can easily be obtained in the form of an interval with negligible widths. Both the techniques are applied on several benchmark functions and are compared with the existing analytical and heuristic methods.

Ranking of DMUs on interval data by DEA

The paper considers the problem ranking interval data in data envelopment analysis (IDEA), different of the other methods. In this approach, we use the statistical concepts. The end DEA models are modified and for illustration a numerical example is proposed.

A preference aggregation method through the estimation of utility intervals

In this paper, a preference aggregation method is developed for ranking alternative courses of actions by combining preference rankings of alternatives given on individual criteria or by individual decision makers. In the method, preference rankings are viewed as constraints on alternative utilities, which are normalized, and linear programming models are constructed to estimate utility intervals, which are weighted and averaged to generate an aggregated utility interval. A simple yet pragmatic interval ranking method is used to compare and/or rank alternatives. The final ranking is generated as the most likely ranking with certain degrees of belief. Three numerical examples are examined to illustrate the potential applications of the proposed method. Scope and purpose The aggregation of preference rankings has wide applications in group decision making, social choice, committee election and voting systems. The purpose of this paper is to develop a preference aggregation method through the estimation of utility intervals, in which preference rankings are associated with utility intervals that are estimated using linear programming models and aggregated using the simple additive weighting method.

Inversion Coding

The Burrows–Wheeler Compression (BWC) described by Burrows and Wheeler has received considerable attention. An essential part of BWC schemes is the Move-to-Front coder (recency ranking). In this paper we introduce a different coding (ranking) scheme, the inversion coder. We prove the information theoretic relationship between interval ranks and canonical sorting permutations. We also introduce a faster and more memory efficient-algorithm for inversion ranks. Finally, we explore the relationship between inversion ranks and recency ranks and show that inversion coding is superior to interval ranking as well as recency ranking.

Tracing the Origin of Unburned Carbon in Fly Ashes from Coal Blends

This study shows the utility of optical microscopy to trace the origin of unburned carbon in fly ashes from coal blends. Coal blends currently burned in four power groups in Spain have been investigated. Mill samples were separated into size fractions, and petrographic analysis were performed to assess the extent of blend components segregation as a function of different coal grindability. Strong segregation was observed when coals from a wide rank interval were ground together. In this case, anthracite particles accumulated in the largest size fractions, high and medium volatile bituminous coals accumulated in the smallest ones, and semianthracites accumulated in the intermediate size fractions. No clear segregation trend was observed for anthracites ground together with an inertinite-rich semianthracite. Chars from single coals were prepared in a drop tube furnace operated at 1300 °C under 5% oxygen in a nitrogen atmosphere. Petrographic analysis of chars were based on the optical texture and developmen...

Solving the full rank interval least squares problem

We propose some results based on QR factorization using interval Householder transformations to bound the solutions of full rank least squares problems ‖ A·x− b‖ with A and b both varying within given compact intervals.