Intervals In Order Research Articles

Design of stochastic model for the distribution interval between fetal development stage and post-partum amenorrhoea

Abstract In human reproduction process, analysing the birth interval is a crucial and important aspect. Normally, the distribution of fetal development stage interval of any exact order may be the same as the distribution of Post-partum Amenorrhoea interval of the same order but it cannot be same. Here the interval between the distribution of a specific order of fetal development stage interval and Post-partum Amenorrhoea interval of the same order is analysed. In this context, it is demonstrated the distinction between the Post-partum Amenorrhoea interval and fetal development stage interval empirically by allowing for a actual data set. Further, the distinction between these distributions is demonstrated theoretically, by taking certain proposed values of fertility factors involved in the stochastic model proposed for the purpose.

Interval Subsethood Measures with Respect to Uncertainty for the Interval-Valued Fuzzy Setting

In this paper, the problem of measuring the degree of subsethood in the interval-valued fuzzy setting is addressed. Taking into account the widths of the intervals, two types of interval subsethood measures are proposed. Additionally, their relation and main properties are studied. These developments are made both with respect to the regular partial order of intervals and with respect to admissible orders. Finally, some construction methods of the introduced interval subsethood measures with the use interval-valued aggregation functions are examined.

An interval optimization strategy of household multi-energy system considering tolerance degree and integrated demand response

Under the background of the popularity of household gas-electric equipment, an interval optimization method considering the Integrated Demand Response (IDR) and tolerance degree is proposed to deal with the household load scheduling. The proposed method mainly tackles the dynamic switching of energy forms (natural gas and electricity) and uncertain variables in the system caused by household load and photovoltaic (PV). The thermostatically controllable loads contain gas-electric heater and air conditioning, and the interruptible loads contain gas-electric kitchen stove and clothes washer. An interval optimization model is formulated to optimize the operation cost and emissions of a household multi-energy system. The uncertain parameters are modeled as interval numbers, and the constraints are relaxed by tolerance degree. To solve the equation, the interval optimization model is transformed into a deterministic optimization model based on the interval order relation and interval possibility degree. Then, Genetic Algorithm is applied to solve the deterministic optimization model. Simulation results indicate that interval optimization is robust to the uncertainties and flexible to meet users’ demands. Both IDR and tolerance degree are able to optimize users’ energy cost, and the optimization results are accumulative. For a gas-electric equipment installed home, the proposed method can reduce expenditures by up to 23.4% compared with traditional method that do not consider IDR, tolerance degree and interval optimization.

Uncertain optimization of in-bore launching performance of artillery based on interval method

In order to study the uncertainty optimization of the in-bore launching performance of larger-caliber artillery, the interior ballistic program was compiled and embedded in ABAQUS finite element software for secondary development, and the dynamic model of in-bore launching was built. The structural parameters of bore, the structural parameters of projectile and parameters of launching propellant were considered, and the uncertainty was described by interval number. BP neural network was used to construct a surrogate model for the dynamic model of in-bore launching. The deterministic transformation of uncertain objective function and uncertain constraints was carried out by using interval order model and interval probability model respectively. The interval uncertainty optimization model of the in-bore launching performance artillery was established by taking the interval radius and midpoint of the projectile muzzle velocity as objective functions and the maximum chamber pressure as constraint. Multi-objective genetic algorithm was used to solve the problem, and the optimal solution and reasonable interval of uncertain parameters were obtained.

Operational Semantics, Interval Orders and Sequences of Antichains

Operational Semantics, Interval Orders and Sequences of Antichains

Reliability reallocation for cost uncertainty of fuel cell vehicles via improved differential evolution algorithm

AbstractA fuel cell vehicle (FCV) is composed of many subsystems; it is necessary to reallocate subsystem reliability to improve FCV system reliability. A comprehensive evaluation method considering uncertainty is proposed to obtain the interval value of feasibility factor. The FCV cost uncertainty model is established on the basic of parameters such as feasibility factor, initial reliability, limit reliability, and subsystem cost. To solve the optimization problem for cost uncertainty, the cost interval model is transformed into a deterministic model by interval order relation. An improved differential evolution (DE) algorithm is proposed to reallocate subsystem reliability for minimum cost.

Translating Data From an Electronic Prescribing and Medicines Administration System Into Knowledge: Application to Doctor-Nurse Time Discrepancy in Antibiotic Ordering and Administration.

Electronic Prescribing and Medicines Administration (EPMA) systems are being widely implemented to facilitate medication safety improvement. However, translating the resulting big data into actionable knowledge has received relatively little attention. The objective of this study was to use routinely collected EPMA data in the study of exact time discrepancy between physicians' order and nurses' administration of systemic antibiotics. We evaluated first and follow-up dose administration and dose intervals and examined multifactorial determinants in ordering and administration explaining potential discrepancy. We conducted an observational study of electronic health records for all medical patient stays with antibiotic treatment from January to June 2018 (n=4392) in a large Belgian tertiary care hospital. Using an EPMA system with Barcode Medication Administration, we calculated time discrepancy between order and administration of first doses (n=6233), follow-up doses (n=87 960), and dose intervals. Multiple logistic regression analysis estimated the association between time discrepancy and various determinants in ordering and administration. Time discrepancy between physician order and nurse administration was <30 minutes for 48.7% of first doses and 61.7% of follow-up doses, with large variation across primary diagnoses. Greater dose intervals, oral versus intravenous administration, and order diversion from regular nurse administration rounds showed strongest association with less timely administration. EPMA systems show huge potential to generate actionable knowledge. Concerning antibiotic treatment, having physicians' orders coincide with regular nurse administration rounds whenever clinically appropriate, further taking contextual factors into account, could potentially improve antibiotic administration timeliness.

Provider-directed education to reduce unnecessary neuroimaging in uncomplicated headache disorders.

More than 1.9 million annual outpatient visits to neurologists in the United States are associated with headache diagnoses. For uncomplicated headache disorders, the evidence-based practice (EBP) guidelines recommend against neuroimaging unless specific neurological signs and symptoms are present; however, neuroimaging rates have only modestly decreased since the guidelines were developed. We evaluated unnecessary neuroimaging rates in patients with uncomplicated headache at the Emory Department of General Neurology. The rate of unnecessary neuroimaging suggested a provider knowledge gap in the use of neuroimaging in patients with uncomplicated headaches. A provider-directed educational session was delivered, and outcomes were evaluated 8 weeks after implementation. The postintervention rates of unnecessary neuroimaging were compared with preintervention rates. A 15-minute educational session on the EBP guidelines for neuroimaging use in uncomplicated headache was presented to all general neurology providers (n = 9). The providers were given an electronic version of the presentation and a pocket-sized EBP algorithm for neuroimaging in this population. Data collected from the project site's neuroimaging dashboard showed a significantly lower proportion of unnecessary neuroimaging orders in the 8-week posteducational interval (4.2%) compared with the 8-week preeducation interval (7.2%) (t = 2.78, p = .014), a 41.6% reduction. We found that a provider-directed educational session reviewing the EBP guidelines for neuroimaging in patients with uncomplicated headache disorders was successful in lowering rates of neuroimaging. Implementing similar projects in other departments could further reduce unnecessary neuroimaging use across the organization.

Two Problems on Interval Counting

Let F be a family of intervals on the real line. An interval graph is the intersection graph of F. An interval order is a partial order (F,≺) such that for all I1,I2∈F, I1 ≺ I2 if and only if I1 lies entirely at the left of I2. Such a family F is called a model of the graph (order). The interval count of a given graph (resp. order) is the smallest number of interval lengths needed in any model of this graph (resp. order). The first problem we consider is related to the classes of graphs and orders which can be represented with two interval lengths, regarding to the inclusion hierarchy among such classes. The second problem is an extremal problem which consists of determining the smallest graph or order which has interval count at least k. In particular, we study a conjecture by Fishburn on this extremal problem, verifying its validity when such a conjecture is constrained to the classes of trivially perfect orders and split orders.

Interval orders with two interval lengths

A poset P=(X,≺) has an interval representation if each x∈X can be assigned a real interval Ix so that x≺y in P if and only if Ix lies completely to the left of Iy. Such orders are called interval orders. In this paper we give a surprisingly simple forbidden poset characterization of those posets that have an interval representation in which each interval length is either 0 or 1. In addition, for posets (X,≺) with a weight of 1 or 2 assigned to each point, we characterize those that have an interval representation in which for each x∈X the length of the interval assigned to x equals the weight assigned to x. For both problems we can determine in polynomial time whether the desired interval representation is possible and in the affirmative case, produce such a representation.

A two-warehouse EOQ model with interval-valued inventory cost and advance payment for deteriorating item under particle swarm optimization

Generally, most of the inventory costs are not always fixed due to uncertainty of competitive market. In the existing literature, it is found that several researchers have worked on uncertainty considering inventory parameters as fuzzy valued. In this work, we have represented the inventory parameters as interval. Using this concept, we have developed a two-warehouse inventory model with advanced payment, partial backlogged shortages. Due to uncertainty, this problem cannot be solved by existing direct/indirect optimization technique. For this purpose, different variants of particle swarm optimization techniques (viz. PSO-CO, WQPSO and GQPSO) have been developed to solve the problem of the proposed inventory model by using interval arithmetic and interval order relations. Finally, to illustrate and also to validate the proposed model, a numerical example has been solved and the best found solutions (which is either optimal solution or near optimal solution) obtained from different variants of PSO have been compared. Then, a sensitivity analysis has been performed to study the effect of changes of different parameters of the model on the optimal policy.

The uncertain optimization algorithm to suppress vibration of the crankshaft system with random-interval hybrid variables

This study proposes a new uncertain optimization algorithm to suppress vibration of the crankshaft system. In this new algorithm, the interval expression with random-interval hybrid variables is obtained by the confidence level. In addition, the interval order relation, interval probability, radial basis function neural network technology, and multi-objective genetic algorithm are applied to construct uncertain optimization algorithm with random-interval hybrid variables. Moreover, typical examples are used to demonstrate the effectiveness of the proposed algorithm. To suppress vibration of the crankshaft system, the optimization–Latin hypercube sampling design is used to obtain the experimental scheme and the data sampling is performed by multi-body system simulation of the vibration performance. Then, the radial basis function neural network is built considering the torsional displacement and transient stress of the crankshaft. Finally, the uncertain optimization algorithm is operated on the crankshaft structure design of the high-power reciprocating compressor. The results demonstrate that the robustness of the vibration performance and strength property is improved through the uncertain optimization algorithm, compared with that through deterministic optimization. The uncertain optimization algorithm to suppress vibration of the crankshaft system with random-interval hybrid variables is an efficient and effective approach, which is finally proved by the prototype test.

Optimal allocation of test times for reliability growth testing with interval-valued model parameters

Reliability growth testing is widely used to identify and remove failure modes in the development of complex systems. Different models have been proposed to track the progress of reliability growth during test, and previous research has addressed the improvement of after-testing system reliability by allocating limited testing resources. The majority of reliability growth testing models are based on the AMSAA/Crow model with known parameters, but there is a lack of work focusing on the situation when the AMSAA/Crow parameters are subject to uncertainty. In this article, we investigate a reliability growth testing allocation problem to series–parallel systems that considers parameter uncertainty in the AMSAA/Crow models. The model parameters are assumed to be known as uncertain-but-bounded values. Interval arithmetic and an interval order relation reflecting decision maker’s preference are used to analyze the uncertain parameters. In order to determine the optimal allocation of testing time for each component or subsystem aiming to maximize the after-testing system reliability, a modified genetic algorithm is developed. A penalty function is used to handle the testing resource limitations, and the techniques of dual mutation and random keys are used in the algorithm to improve searching efficiency. Computational results indicate that the interval analysis is a useful tool to deal with parameter uncertainty of reliability growth testing allocation problems.

Interval orders, semiorders and ordered groups

We prove that the order of an ordered group is an interval order if and only if it is a semiorder. Next, we prove that every semiorder is isomorphic to a collection J of intervals of some totally ordered abelian group, these intervals being of the form [x,x+α[ for some positive α. We describe ordered groups such that the ordering is a semiorder and we introduce threshold groups generalizing totally ordered groups. We show that the free group on finitely many generators and the Thompson group F can be equipped with a compatible semiorder which is not a weak order. On another hand, a group introduced by Clifford cannot.

Extended formulations for order polytopes through network flows

Mathematical psychology has a long tradition of modeling probabilistic choice via distribution-free random utility models and associated random preference models. For such models, the predicted choice probabilities often form a bounded and convex polyhedral set, or polytope. Polyhedral combinatorics have thus played a key role in studying the mathematical structure of these models. However, standard methods for characterizing the polytopes of such models are subject to a combinatorial explosion in complexity as the number of choice alternatives increases. Specifically, this is the case for random preference models based on linear, weak, semi- and interval orders. For these, a complete, linear description of the polytope is currently known only for, at most, 5–8 choice alternatives. We leverage the method of extended formulations to break through those boundaries. For each of the four types of preferences, we build an appropriate network, and show that the associated network flow polytope provides an extended formulation of the polytope of the choice model. This extended formulation has a simple linear description that is more parsimonious than descriptions obtained by standard methods for large numbers of choice alternatives. The result is a computationally less demanding way of testing the probabilistic choice model on data. We sketch how the latter interfaces with recent developments in contemporary statistics.

Comparing the magnitude of fuzzy intervals and fuzzy random variables from the standpoint of gradual numbers

Gradual numbers have been introduced to separate fuzziness (understood as gradation) from uncertainty in so-called fuzzy numbers. Then a fuzzy number can be viewed as a standard interval of functions, each interpreted as a gradual number. Gradual numbers are naturally met when representing probabilities of fuzzy events, midpoints of fuzzy intervals, etc. They can be viewed as a non-monotonic generalization of cumulative probability distributions. This paper presents three methods for comparing gradual numbers that generalize stochastic orderings to such non-monotonic functions. Then it proposes joint extensions of stochastic dominance and statistical preference to random fuzzy intervals when the fuzzy intervals are understood as intervals of gradual numbers. This approach, which combines known probabilistic orderings with known forms of interval orderings, can be viewed as a systematic way of constructing methods for ranking fuzzy random variables.

Tolerance Orders of Open and Closed Unit Intervals

In this paper we combine ideas from tolerance orders with recent work on OC interval orders. We consider representations of posets by unit intervals Iv in which the interval endpoints (L(v) and R(v)) may be open or closed as well as the center point (c(v)). This yields four types of intervals: A (endpoints and center points closed), B (endpoints and center points open), C (endpoints closed, center points open), and D (endpoints open, center points closed). For any non-empty subset S of {A, B, C, D}, we define an S-order as a poset P that has a representation as follows: each element v of P is assigned a unit interval Iv of type belonging to S, and x ≺ y if and only if either (i) R(x) < c(y) or (ii) R(x) = c(y) and at least one of R(x), c(y) is open and at least one of L(y), c(x) is open. We characterize several of the classes of S-orders and provide separating examples between unequal classes. In addition, for each S ⊆{A, B, C, D} we present a polynomial-time algorithm that recognizes S-orders, providing a representation when one exists and otherwise providing a certificate showing it is not an S-order.

Preorder-based triangle: a modified version of bilattice-based triangle for belief revision in nonmonotonic reasoning

Bilattice-based triangle provides an elegant algebraic structure for reasoning with vague and uncertain information. But the truth and knowledge ordering of intervals in bilattice-based triangle cannot handle repetitive belief revisions which is an essential characteristic of nonmonotonic reasoning. Moreover, the ordering induced over the intervals by the bilattice-based triangle is not sometimes intuitive. In this work, we construct an alternative algebraic structure, namely preorder-based triangle and we formulate proper logical connectives for this. It is also demonstrated that Preorder-based triangle serves to be a better alternative to the bilattice-based triangle for reasoning in application areas, that involve nonmonotonic fuzzy reasoning with uncertain information.

A simple proof characterizing interval orders with interval lengths between 1 and k

A poset $P= (X, \prec)$ has an interval representation if each $x \in X$ can be assigned a real interval $I_x$ so that $x \prec y$ in $P$ if and only if $I_x$ lies completely to the left of $I_y$. Such orders are called \emph{interval orders}. Fishburn proved that for any positive integer $k$, an interval order has a representation in which all interval lengths are between $1$ and $k$ if and only if the order does not contain $\mathbf{(k+2)+1}$ as an induced poset. In this paper, we give a simple proof of this result using a digraph model.

Interval semantics for Petri nets with inhibitor arcs

Interval semantics of elementary Petri nets with inhibitor arcs is discussed. First an operational semantics in terms of interval orders is provided, and next the concept of interval process is introduced, discussed, and used to describe concurrent histories of such nets. It is shown that the interval process semantics is equivalent to recently proposed interval traces semantics. It is also proven that if operational semantics is restricted to stratified orders (i.e. step sequences) the proposed model is equivalent to models based on step processes and comtraces.