An Application of Interval Arithmetic for Solving Fully Fuzzy Linear Systems with Trapezoidal Fuzzy Numbers

We present a method for solving fully fuzzy linear systems using interval aspects of fuzzy numbers. This new method uses a decomposition technique to convert a fully fuzzy linear system into two types of decomposition in the form of interval matrices. It finds the solution of a fully fuzzy linear system by using interval operations. This new method uses interval arithmetic and two new interval operations ⊖ and ⊘. These new operations, which are inverses of basic interval operations + and ×, will be presented in the middle of this paper. Some numerical examples are given to illustrate the ability of proposed methods.

Enhancing outpatient appointment scheduling system performance when patient no-show percent and lateness rates are high

Purpose High lateness and no-show percentages pose great challenges on the patient scheduling process. Usually this is addressed by optimizing the time between patients in the scheduling process and the percent of extra patients scheduled to account for absent patients. However, since the patient no-show and lateness is highly stochastic we might end up with many patients showing up on time which leads to crowded clinics and high waiting times. The clinic might end up as well with low utilization of the doctor time. The purpose of this paper is to study the effect of scheduled overload percentages and the patient interval on the waiting time, overtime, and the utilization. Design/methodology/approach Actual data collection and statistical modeling are used to model the distribution for common dentist procedures. Simulation and validation are used to model the treatment process. Then algorithm development is used to model and generate the patient arrival process. The simulation is run for various values of basic interval scheduled time between arrivals for the patients. Further, 3D graphical illustration for the objectives is prepared for the analysis. Findings This work initially reports on the statistical distribution for the common procedures in dentist clinics. This can be used for developing a scheduling system and for validating the scheduling algorithms developed. This work also suggest a model for generating patient arrivals in simulation. It was found that the overtime increases excessively when coupling both high basic interval and high overloading percentage. It was also found that: to obtain low overtime we must reduce the basic interval. Waiting time increases when reducing the basic scheduled appointment interval and increase the scheduled overload percentage. Also doctors’ utilization is increased when the basic interval is reduced. Research limitations/implications This work was done at a local clinic and this might limit the value of the modeled procedure times. Practical implications This work presents a statistical model for the various procedures and a detailed technique to model the operations of the clinics and the patient arrival time which might assist researches and developers in developing their own model. This work presents a procedure for troubleshooting scheduling problems in outpatient clinics. For example, a clinic suffering from high patient waiting time is directly instructed to slightly increase their basic scheduled interval between patients or slightly reduce the overloading percentage. Social implications This work is targeting an extremely important constituent of the health-care system which is the outpatient clinics. It is also targeting multiple objectives namely waiting times, utilization overtime, which in turn is related to the economics and doctor utilization. Originality/value This work presents a detailed modeling procedure for the outpatient clinics under high lateness and no-show and addresses the modeling procedure for the patient arrivals. This 3D graphical charting for the objectives includes a study of the multiple objectives that are of high concern to outpatient clinic scheduling interested parties in one paper.

N-Reciprocity Property for Interval-Valued Fuzzy Relations with an Application to Group Decision Making Problems in Social Networks

In this paper we study interval-valued fuzzy relations. We consider preference relations, i.e. a triplet consisting of strict preference, indifference and incomparability which are defined with the use of a fuzzy negation. We analyze the preservation of the fuzzy negation based reciprocity property of interval-valued fuzzy relations by aggregation functions and by some basic interval-valued fuzzy relations. We use diverse representa-tions of aggregation functions. We also consider the connection between N-reciprocal relations and transitivity properties. We provide a numerical example where the final alternative is chosen with the use of generalized voting method, where admissible linear orders for intervals are applied.

Beat-to-beat control of human optokinetic nystagmus slow phase durations

This study provides the first clear evidence that the generation of optokinetic nystagmus fast phases (FPs) is a decision process that is influenced by performance of a concurrent disjunctive reaction time task (DRT). Ten subjects performed an auditory DRT during constant velocity optokinetic stimulation. Eye movements were measured in three dimensions with a magnetic search coil. Slow phase (SP) durations were defined as the interval between FPs. There were three main findings. Firstly, human optokinetic nystagmus SP durations are consistent with a model of a Gaussian basic interval generator (a type of biological clock), such that FPs can be triggered randomly at the end of a clock cycle (mean duration: 200–250 ms). Kolmogorov-Smirnov tests could not reject the modeled cumulative distribution for any data trials. Secondly, the FP need not be triggered at the end of a clock cycle, so that individual SP durations represent single or multiple clock cycles. Thirdly, the probability of generating a FP at the end of each interval generator cycle decreases significantly during performance of a DRT. These findings indicate that the alternation between SPs and FPs of optokinetic nystagmus is not purely reflexive. Rather, the triggering of the next FP is postponed more frequently if a recently presented DRT trial is pending action when the timing cycle expires. Hence, optokinetic nystagmus FPs show dual-task interference in a manner usually attributed to voluntary movements, including saccades. NEW & NOTEWORTHY This study provides the first clear evidence that the generation of optokinetic nystagmus (OKN) fast phases is a decision process that is influenced by performance of a concurrent disjunctive reaction time task (DRT). The slow phase (SP) durations are consistent with a Gaussian basic interval generator and multiple interval SP durations occur more frequently in the presence of the DRT. Hence, OKN shows dual-task interference in a manner observed in voluntary movements, such as saccades.

Inflections of Periodicities of Background Photon Spectral Power Densities Are Predicted by the Lorentz Contraction for a Potential Indicator for the Intrinsic Structure of Space

         The value for the Lorentz contraction to produce a discrepancy for a hypothetical number that reflects a property (21.3π4) of sub-matter space was calculated. When applied to time the contraction would be ~35 min. The difference in mass-equivalent energy for an electron at c (the velocity of light in a vacuum) and the required v was ~2 ·10-20 J which has emerged as a significant quantity that may permeate from the force at Planck’s Length when applied across the wavelength of the neutral hydrogen line. Two separate types of photomultiplier instruments (digital and analogue) measuring with different sampling rates for background photon quantities over 50 randomly selected days demonstrated averaged conspicuous inflections of standardized spectral power densities around 35 min. This is the same basic interval where microvariations in the value of the gravitational constant (G) approached a limit at which white noise dominated. The possibility is considered that this value for temporal inflections in photon power spectral densities may reflect the intrinsic nature of space-time contractions that relate gravity and photons.

Efficient Queries of Stand-off Annotations for Natural Language Processing on Electronic Medical Records

In natural language processing, stand-off annotation uses the starting and ending positions of an annotation to anchor it to the text and stores the annotation content separately from the text. We address the fundamental problem of efficiently storing stand-off annotations when applying natural language processing on narrative clinical notes in electronic medical records (EMRs) and efficiently retrieving such annotations that satisfy position constraints. Efficient storage and retrieval of stand-off annotations can facilitate tasks such as mapping unstructured text to electronic medical record ontologies. We first formulate this problem into the interval query problem, for which optimal query/update time is in general logarithm. We next perform a tight time complexity analysis on the basic interval tree query algorithm and show its nonoptimality when being applied to a collection of 13 query types from Allen's interval algebra. We then study two closely related state-of-the-art interval query algorithms, proposed query reformulations, and augmentations to the second algorithm. Our proposed algorithm achieves logarithmic time stabbing-max query time complexity and solves the stabbing-interval query tasks on all of Allen's relations in logarithmic time, attaining the theoretic lower bound. Updating time is kept logarithmic and the space requirement is kept linear at the same time. We also discuss interval management in external memory models and higher dimensions.

A Non-Probabilistic Model for Structural Reliability Analysis

By representing uncertain parameters as interval variables, a novel structural non-probabilistic reliability model is proposed, which can deal with the case that the domain constructed by the basic interval variables locates in the safe domain. Two numerical examples are conducted to illustrate the validity and feasibility of the proposed non-probabilistic model.