Uncertain Number Research Articles

Robust location-allocation decision considering casualty prioritization in multi-echelon humanitarian logistics network

Timeliness of medical service delivery has become an important purpose of post-disaster relief, while its realization highly depends on an effective design of multi-echelon humanitarian logistics network (HLN). What complicates the design of HLN are multiple uncertainties in the decision-making process, especially casualty number and transportation time. This paper proposes a novel robust optimization model for designing a four-echelon HLN including disaster sites, temporary medical centers (TPCs) in affected areas and two-tier hospitals, thereby optimizing medical facilities location, medical resources allocation and casualty evacuation. In this model, we consider casualty prioritization by incorporating deprivation cost and casualty triage. After conducting extensive computational experiments and sensitivity analysis by case studies based on the Luding Earthquake, the main results obtained are as follows: (i) the proposed model performs good effectiveness and robustness; (ii) considering deprivation cost in HLN can effectively reduce both the suffering of casualty and social cost; (iii) compared to the uncertainty of transportation time, more attention needs to be paid to the risks caused by uncertain casualty number, especially the mild injured with a large number.

Assessment of digital economy development with the new multicriteria sorting method: DCMSort

We present a novel multiple criteria sorting method based on the deck of cards method, named DCMSort, which assigns alternatives to pre-defined and ordered classes. In contrast to prior multiple criteria sorting methods, DCMSort produces criteria weights and utility functions based on personalized preferences using comparisons between two consecutive levels. Meanwhile, it needs fewer comparisons with the aid of the ordinal relation. To improve the flexibility of preference representation, we adopt reference levels and representative profiles as auxiliary profiles to characterize the utility function finely. Additionally, this method permits both definite and uncertain number of blank cards between consecutive positions. To verify the practicality of DCMSort, we provide an illustrative case study in the domain of digital economy development assessment in China. Sensitivity and comparative analyses are conducted to demonstrate the stability and superiority of our proposal.

Shadowed AHP for Multi-Criteria Supplier Selection

Numerous techniques of multi-criteria decision-making (MCDM) have been proposed in a variety of business domains. One of the well-known methods is the Analytical Hierarchical Process (AHP). Various uncertain numbers are commonly used to represent preference values in AHP problems. In the case of multi-granularity linguistic information, several methods have been proposed to address this type of AHP problem. This paper introduces a novel method to solve this problem using shadowed fuzzy numbers (SFNs). These numbers are characterized by approximating different types of fuzzy numbers and preserving their uncertainty properties. The new Shadowed AHP method is proposed to handle preference values which are represented by multi-types of uncertain numbers. The new approach converts multi-granular preference values into unified model of shadowed fuzzy numbers and utilizes their properties. A new ranking approach is introduced to order the results of aggregation preferences. The new approach is applied to solve a supplier selection problem in which multi-granular information are used. The features of the new approach are significant for decision-making applications.

Dynamical Behavior of a Juvenile Predator, Adult Predator and Prey Model Through Uncertain and Parametric Technique

In this study, an interaction model involving a juvenile predator, an adult predator, and the prey has been developed. It is considered that juvenile predators are unable to reproduce. The adult predator is considered to have an impact on the growth rate of the juvenile predators. It is also assumed that a portion of juvenile predators may become adults. Also, it is considered that adult predators consume prey for food. The logistic growth of prey has been taken into consideration in the absence of an adult predator. The intra-species competition among adult predators is discussed here. It is also assumed that adult predators could chase and eat juvenile predators. Then most of the parametric values are considered interval-valued uncertain numbers. Since it is very hard for us to solve the model when the parametric values are interval-valued. Thus, all of the interval-valued parameters have been simplified into linear parametric form. After that, the nonnegativity and boundedness of the model were discussed. Various possible equilibrium points in the model are analyzed. The model’s local stability and global stability are investigated near these points. It has been noted that the proposed model’s solution is significantly impacted by the uncertain values of the model parameters. Uncertain estimates of intra-species competition among adult predators have been found to have a considerable impact on the stability of the model. It is observed that the increased uncertainty of intra-species competition for prey may stabilize the system. It is reported that the increasing rate of conversion of prey into adult predators can destabilize the ecosystem. It is found that the increasing rate of predation on juvenile predators by adults reduces the number of juveniles that can mature into adults which may create instability in the system.

Using Fuzzy Tsukamoto Method In Forecasting The Amount Medication Requrementsat In The Hospital

The pharmaceutical installation as one of the hospital service locations is an inseparable part of the hospital health service system which is oriented towards patient service, including pharmaceutical services needed by patients such as consumable medical equipment that is affordable for all levels of society and the provision of quality medicines. The problem that arises is the uncertain number of patients and the medicines needed by each patient are different and often the supply of medicines that are currently needed by the community is empty, while medicines that are less needed are in abundant stock. Mistakes in ordering medicines can cause shortages or excesses of medicine stock. They tend to only use estimates of the amount of remaining stock without any special methods being used. Even hospital pharmacies tend to buy too many medicines because of uncertain demand and fear of shortages. A method that can help in predicting the amount needed for medicines is by applying the fuzzy Tsukamoto method. The prediction process begins with testing drug data in 2022 to predict the amount needed for medicines in 2023 before finally the drug data for 2023 is used to predict the amount needed in 2024.The prediction process will use drug sales data in the form of the amount of inventory, the amount needed and remaining stock to build a prediction model that projects the amount of drug need in the year 2023. This approach will involve analyzing historical data and applying the Tsukamoto method to produce predictions of the amount needed for all drugs in the following year.

The Possibilistic Mean-Variance Model with Uncertain Possibility Distributions

The possibilistic mean–variance (MV) model is the counterpart of Markowitz’s MV model in the possibility theory. This study aims to examine the possibilistic MV model when the possibility distributions of stock returns are uncertain triangular fuzzy numbers. We define an uncertainty vector and use its ellipsoidal uncertainty set in a minimax optimization problem to model this uncertainty. We also show that this minimax optimization problem reduces to a strictly convex minimization problem. Thus, unlike the possibilistic MV model, we get diversified optimal portfolios uniquely with our approach. After laying down the theoretical points of our approach, we illustrate it with a real-world example in the literature by using a software package for convex optimization. To the best of our knowledge, this is the first paper that considers uncertain possibility distributions in the possibilistic MV model.

Symmetric Kullback–Leibler distance based generalized grey target decision method for mixed attributes

PurposeThe reported Kullback–Leibler (K–L) distance-based generalized grey target decision method (GGTDM) for mixed attributes is an asymmetric decision-making basis (DMB) that does not have the symmetric characteristic of distance in common sense, which may affect the decision-making result. To overcome the deficiency of the asymmetric K–L distance, the symmetric K–L distance is investigated to act as the DMB of GGTDM for mixed attributes.Design/methodology/approachThe decision-making steps of the proposed approach are as follows: First, all mixed attribute values are transformed into binary connection numbers, and the target centre indices of all attributes are determined. Second, all the binary connection numbers (including the target centre indices) are divided into deterministic and uncertain terms and converted into two-tuple (determinacy and uncertainty) numbers. Third, the comprehensive weighted symmetric K–L distance can be computed, as can the alternative index of normalized two-tuple (deterministic degree and uncertainty degree) number and that of the target centre. Finally, the decision-making is made by the comprehensive weighted symmetric K–L distance according to the rule that the smaller the value, the better the alternative.FindingsThe case study verifies the proposed approach with its sufficient theoretical basis for decision-making and reflects the preferences of decision-makers to address the uncertainty of an uncertain number.Originality/valueThis work compares the single-direction-based K–L distance to the symmetric one and uses the symmetric K–L distance as the DMB of GGTDM. At the same time, different coefficients are assigned to an uncertain number’s deterministic term and uncertain term in the calculation process, as this reflects the preference of the decision-maker.

Dynamic Home Care Routing and Scheduling with Uncertain Number of Visits per Referral

Despite the rapid growth of the home care industry, research on the scheduling and routing of home care visits in the presence of uncertainty is still limited. This paper investigates a dynamic version of this problem in which the number of referrals and their required number of visits are uncertain. We develop a Markov decision process (MDP) model for the single-nurse problem to minimize the expected weighted sum of the rejection, diversion, overtime, and travel time costs. Because optimally solving the MDP is intractable, we employ an approximate linear program (ALP) to obtain a feasible policy. The typical ALP approach can only solve very small-scale instances of the problem. We derive an intuitively explainable closed-form solution for the optimal ALP parameters in a special case of the problem. Inspired by this form, we provide two heuristic reduction techniques for the ALP model in the general problem to solve large-scale instances in an acceptable time. Numerical results show that the ALP policy outperforms a myopic policy that reflects current practice, and is better than a scenario-based policy in most instances considered. Funding: This work was supported by the Natural Sciences and Engineering Research Council of Canada [Grants RGPIN-2018-05225 and RGPIN-2020-210524] and by the Telfer School of Management SMRG Postdoctoral Research Fellowship Support [Grant 2020]. Supplemental Material: The electronic companion is available at https://doi.org/10.1287/trsc.2023.0120 .

A VIKOR Method Based on the Relative Closeness on Interval Linguistic Neutrosophic Uncertain Linguistic Numbers

In actual multi-attribute group decision-making problems, due to the complexity and uncertainty of objective things and the ambiguity of human thinking, decision-makers find it hard to give accurate evaluation information by crisp numbers. Even the weights of attribute values and decision-makers are ambiguous. At this time, we are more inclined to adopt the intuitive form of linguistic variables such as "excellent", "good" or "bad" to describe attribute values and weights. So in this paper, based on a neutrosophic set (NS), we further propose interval linguistic neutrosophic uncertain linguistic number (ILNULN). ILNULN combines interval linguistic neutrosophic and uncertain linguistic numbers, and it has the advantages of both. At the same time, due to the weighted arithmetic Bonferroni mean operator considering the interrelationship between aggregation parameters, therefore we combine the ILNULN and weighted arithmetic Bonferroni mean operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNULWABM) operator. Finally, under the environment of interval linguistic neutrosophic and uncertain linguistic numbers, this article uses the linguistic weights and ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example.

Bonferroni Mean Operator of Interval Linguistic Neutrosophic Uncertain Linguistic Number and its Application in Multi-Attribute Group Decision-Making

This paper proposes the concept of interval linguistic neutrosophic uncertain linguistic number (IL-NULN). As a new and effective way of NS expression, ILNULN combines interval linguistic neutrosophic numbers and uncertain linguistic numbers, which can better handle uncertain and inconsistent information. In the ILNULN, the first part “uncertain linguistic number” reflects the attitude of the decision maker (DM) towards the evaluation object, and the second part “interval linguistic neutrosophic number” reflects the subjective linguistic judgment of the DM on the given uncertain linguistic number. In addition, considering the weighted arithmetic Bonferroni mean (WABM) operator integrates the correlation of aggregation parameters, this paper combines the ILNULN and WABM operator to propose the interval linguistic neutrosophic uncertain linguistic weighted arithmetic Bonferroni mean (ILNUL-WABM) operator. Finally, under the environment of interval linguistic neutrosophic uncertain linguistic number, this paper uses the ILNULWABM operator to make VIKOR decision based on the relative closeness, and gives a practical example to solve multi-attribute group decision making (MAGDM) problems.

A scenario-based robust approach for joint planning of multi-blood product logistics and multi-casualty type evacuation

This paper presents a two-stage hybrid robust programming model that integrates multiple blood products scheduling and multiple casualty types evacuation under facility disruptions risk and casualty number uncertainty. The model seeks to maximize the rescue efficiency and minimize the total operations cost. Under a set of disruption scenarios, we adopt a scenario-based robust method to address disruption risks at temporary medical centres and two robust uncertainty sets to deal with uncertain casualty numbers. We propose a proximal bundle algorithm to solve large-scale instances of the proposed hybrid robust model approximately. Extensive numerical experiments show that: (i) the trade-off between model robustness and solution robustness can help the decision-makers determine an appropriate risk-aversion weight; (ii) compared with the corresponding stochastic and scenario-based robust models, the hybrid robust model can obtain more robust solutions with a slight increase in cost; (iii) the proximal bundle algorithm can produce near-optimal solutions within reasonable computational times; (iv) some model parameters have significant impact on the total cost, which can help decision-makers set the appropriate parameters to achieve the desired outcome. Finally, we also use the real data of the 2008 Wenchuan County Earthquake in Sichuan Province, China, to illustrate the application of the model.

Optimization of Nursing Scheduling in Emergency by Using Genetic Algorithm

Scheduling nurse duty is one of the problems in health organizations that is quite complicated to solve. Starting from the uncertain number of patients, serious patient illnesses, characteristics of organizational groups, requests for nurses to take time off, and the qualifications and specialization of the nurses themselves are why scheduling in the ER is difficult to optimize. The same thing is being experienced by one of the health institutions, RSUD Dr. Pirngadi. Preparing schedules or determining the number of nurses on duty is still done manually, resulting in a lack of optimization in scheduling and the number of nurses who must be on duty, especially in the emergency department. In solving this problem, an appropriate method is needed so that the process of scheduling and optimizing the number of nurses can be formed properly. This research applies the Genetic Algorithm in optimal emergency department (IGD) nurse duty scheduling. Genetic algorithms, also called search algorithms, are based on the mechanisms of natural selection and genetics. Genetic algorithms are one of the appropriate methods for solving complex optimization problems. This method is good enough to optimize shift scheduling for the Emergency Room Nursing Service in a Hospital. This Genetic Algorithm can be a solution to multi-criteria and multi-objective problems modeled using biological and evolutionary processes. So, the concept of this method can be applied in optimizing the Nursing Service schedule. The results of calculations using the Genetic Algorithm show quite significant comparisons, including several nurses losing their positions and being eliminated by mutation because they could not compete with several other strong individuals.

Data Wormholes and Speculative Rice Fields: An Infrastructural Politics of Anticipating Greenhouse Gas Emissions

The 2015 Paris declaration obligated international development organizations to assess the climate compatibility of their projects. For irrigation projects, like those negotiated between the Agence Française de Développement, and the Cambodian government in the early 2020s, calculations of estimated greenhouse gas emissions have become important requirements. But how to estimate emissions from future rice fields and the effects of irrigation infrastructures that do not exist? To address this issue, emissions calculators have been developed as a means to bridge climate science and development knowledge infrastructures, so that data and forms of calculation from climate science can easily enter the world of development. However, by engaging in an infrastructural inversion, we argue that this understanding is flawed. Drawing on a case study of an irrigation project in Cambodia, we show that heterogeneous data concatenations are continuously transformed in the movement across infrastructures until referentiality breaks down. Emission calculators operate as a data wormhole, emitting extremely uncertain numbers that contribute to a problematic and speculative politics of anticipation. In contrast with the dominant politics of anticipation, which depends on futile efforts to neutralize uncertainty, infrastructural inversion makes it possible to envision a decentered politics attentive to distributed agency.

Screening through a broad pool: Towards better diversity for lexically constrained text generation

Lexically constrained text generation (CTG) is to generate text that contains given constrained keywords. However, the text diversity of existing models is still unsatisfactory. In this paper, we propose a lightweight dynamic refinement strategy that aims at increasing the randomness of inference to improve generation richness and diversity while maintaining a high level of fluidity and integrity. Our basic idea is to enlarge the number and length of candidate sentences in each iteration, and choose the best for subsequent refinement. On the one hand, different from previous works, which carefully insert one token between two words per action, we insert an uncertain number of tokens following a well-designed distribution. To ensure high-quality decoding, the insertion number increases as more words are generated. On the other hand, we randomly mask an increasing number of generated words to force Pre-trained Language Models (PLMs) to examine the whole sentence via reconstruction. We have conducted extensive experiments and designed four dimensions for human evaluation. Compared with important baseline (CBART (He, 2021)), our method improves the 1.3% (B-2), 0.1% (B-4), 0.016 (N-2), 0.016 (N-4), 5.7% (M), 1.9% (SB-4), 0.6% (D-2), 0.5% (D-4) on One-Billion-Word dataset (Chelba et al., 2014) and 1.6% (B-2), 0.1% (B-4), 0.121 (N-2), 0.120 (N-4), 0.0% (M), 6.7% (SB-4), 2.7% (D-2), 3.8% (D-4) on Yelp dataset (Cho et al., 2018). The results demonstrate that our method is more diverse and plausible.

Pathological study on uncertain numbers and proposed solutions for discrete fuzzy fractional order calculus

Abstract A pathological study in the definition of uncertain numbers is carried out, and some solutions are proposed. Fundamental theorems for uncertain discrete fractional and integer order calculus are established. The concept of maximal solution for obtaining a unique uncertain solution is introduced. The solutions of uncertain discrete relaxation equations for the integer and the fractional order are obtained. Various numerical examples are accompanied to clarify the theoretical results and study of uncertain system behavior.

Intuitionistic uncertain linguistic prioritized aggregation operators and their application to multi-criteria decision making

The intuitionistic uncertain linguistic information aggregation problems considering different priority levels of criteria are investigated. Firstly, we extended the prioritized averaging (PA) operator to intuitionistic uncertain linguistic environment, defined two new prioritized aggregation operators called the intuitionistic uncertain linguistic prioritized weighted average (IULPWA) operator and the intuitionistic uncertain linguistic prioritized weighted geometric (IULPWG) operator, and established various desirable properties of the proposed operators. Secondly, we developed a multi-criteria decision making (MCDM) approach based on the IULPWA operator (or the IULPWG operator) to deal with the MCDM problems in which the criterion values take the form of intuitionistic uncertain linguistic numbers (IULNs) and the criteria are in different priority levels. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method, and a comparison analysis is conducted to make clear the differences among the IULPWA operator, the IULPWG operator, the intuitionistic uncertain linguistic number weighted averaging (IULNWA) operator and the intuitionistic uncertain linguistic weighted geometric average (IULWGA) operator.

Reorganization of a medical service network to manage pandemic waves: A real case study

During Covid-19, medical service networks (MSNs) faced new challenges, such as an impressive increase in hospital visits, a shortage of hospital beds and staff, and insufficient information to estimate the number of mild and critical cases. In addition, governments were encountered to implement appropriate quarantine policies. Dealing with these problems became more complex and challenging when a new wave of disease occurred. This study develops a mixed-integer linear programming model for reorganizing an MSN to manage future pandemic waves. The model aims at reallocation medical staff to prevent a shortage of hospital beds. A fuzzy approach is employed to estimate the uncertain number of patients in each period. As a result, direct hospital visits are decreased by 60% on average, and shortages of beds are avoided by adding the fewest beds possible in each period. The model can also optimize several performance ratios, e.g., the ratio of hospitalized patients to the specialized personnel assigned to each hospital, which is decreased by approximately 40% in our case.

Hesitant triangular fuzzy FlowSort method: the multi-criteria decision-making problems

Multi-criteria sorting problems have gained significant importance across various fields. However, when experts express their opinions using linguistic terms and quantitative evaluation criteria are not feasible, the fuzzy set theory proves to be a suitable framework. Moreover, in such scenarios, the use of hesitant fuzzy sets becomes necessary because each criterion might have multiple values compared with other alternatives. This paper introduces a novel method called Hesitant Triangular Fuzzy Sorting (HTFFS), which is a variation of the fuzzy FlowSort method based on the preference ranking organisation method for enrichment evaluation (PROMETHEE). The HTFFS method incorporates the theory of fuzzy sets and establishes theoretical foundations for calculating the degree of superiority of each alternative over others. This calculation uses mathematical operators specifically designed for uncertain fuzzy sets and uncertain triangular fuzzy numbers. To demonstrate the effectiveness and practicality of the proposed HTFFS method, two numerical examples are presented. The results obtained from these examples showcase the applicability and validity of the HTFFS method in handling multi-criteria sorting problems.

Ca2+ spark latency and control of intrinsic Ca2+ release dyssynchrony in rat cardiac ventricular muscle cells

Cardiac excitation-contraction coupling (ECC) depends on Ca2+ release from intracellular stores via ryanodine receptors (RyRs) triggered by L-type Ca2+ channels (LCCs). Uncertain numbers of RyRs and LCCs form ‘couplons’ whose activation produces Ca2+ sparks, which summate to form a cell-wide Ca2+ transient that switches on contraction. Voltage (Vm) changes during the action potential (AP) and stochasticity in channel gating should create variability in Ca2+ spark timing, but Ca2+ transient wavefronts have remarkable uniformity. To examine how this is achieved, we measured the Vm-dependence of evoked Ca2+ spark probability (Pspark) and latency over a wide voltage range in rat ventricular cells. With depolarising steps, Ca2+ spark latency showed a U-shaped Vm-dependence, while repolarising steps from 50 mV produced Ca2+ spark latencies that increased monotonically with Vm. A computer model based on reported channel gating and geometry reproduced our experimental data and revealed a likely RyR:LCC stoichiometry of ∼ 5:1 for the Ca2+ spark initiating complex (IC). Using the experimental AP waveform, the model revealed a high coupling fidelity (Pcpl ∼ 0.5) between each LCC opening and IC activation. The presence of ∼ 4 ICs per couplon reduced Ca2+ spark latency and increased Pspark to match experimental data. Variability in AP release timing is less than that seen with voltage steps because the AP overshoot and later repolarization decrease Pspark due to effects on LCC flux and LCC deactivation respectively. This work provides a framework for explaining the Vm- and time-dependence of Pspark, and indicates how ion channel dispersion in disease can contribute to dyssynchrony in Ca2+ release.

Improving relief operations via optimizing shelter location with uncertain covariates

Designing an efficient shelter location planning is crucial to the rapid implementation of relief operations under the uncertain number of casualties. In practice, the uncertain number of casualties is closely related to disaster severity, whereas previous studies ignore such correlations when modeling uncertainties. In this paper, the scenario-wise ambiguity set is adopted to capture the correlation between the uncertain number of casualties and uncertain covariates, i.e., disaster severity. We develop a two-stage scenario-wise distributionally robust (SDR) model, where the shelter location and capacity allocation decisions are made here-and-now, and recourse decisions to transport casualties are made after the uncertainties on the number of casualties and covariate information have been realized. We approximate the non-convex model into a tractable form, i.e., second-order cone programming (SOCP), which can be solved efficiently by an outer approximation (OA) algorithm for a large-scale computation case. The numerical results with real-world data show that covariate integration (CVI) can contribute to saving costs and improving relief efficiency, and illustrate the computational superiority of the proposed OA algorithm. The results further demonstrate that establishing shelters with large capacities and near the affected areas has indeed had a positive impact on improving relief efficiency.