The efficiency of outpatient care deeply affects patient services in all downstream departments within a hospital. West China Hospital (WCH) is the largest public hospital in Southwest China. Nevertheless, WCH still experienced relatively high patient no-shows. WCH offered patients the option to prepay appointment fees to motivate them to keep scheduled appointments. This study aims to investigate the impacts of optional application fees on the scheduling system and, specifically, to gain insights into the scheduling policy: Should WCH use different scheduling windows (SWs) for patients depending on whether they prepay or do not pay the appointment fee? We developed an$M/M /1/N$queueing model to determine the optimal SWs for two patient types - prepaid or unpaid. Our study shows that WCH should use two different SWs when adopting optional appointment fees. Furthermore, we derived theoretical findings and validated them using actual WCH data. Empirical results show that there could be an average of 20% cost savings if two optimal SWs are used for scheduling. Note to Practitioners—This paper was motivated by the problem of no-shows in the outpatient department at West China Hospital (WCH). The two most common approaches to mitigating patient no-shows are overbooking and scheduling window (SW). However, excessive overbooking may lead to physician overtime and long patient wait time. This paper examined if different SWs should be used to reduce patient no-shows. Due to the high patient demand, WCH provided multiple appointment channels, using one common SW, for outpatient scheduling. WCH yet still experienced relatively high patient no-shows. For the curiosity of outpatient management, WCH considered if an option for patients to prepay appointment fees could motivate them to attend appointments. This paper aims to answer WCH’s questions by examining the overall cost differences between a system with the prepaid option and a system without it. We developed an$M/M /1/N$queueing model to determine the optimal SWs for two patient types - prepaid or unpaid. Our study shows that WCH should consider using two different SWs when charging optional appointment fees. We derived theoretical findings and validated them using actual data from WCH. Moreover, the empirical analysis shows that the system could achieve an average of 20% cost savings if two optimal SWs are used for outpatient scheduling.

In the era of big data, both the size and the number of features, samples, and classes continue to increase, resulting in high-dimensional classification tasks. One characteristic, among others, of big data is there exist complex structures between different classes. Hierarchical structure may be treated as the most representative one, which is mathematically depicted as a tree-like structure or directed acyclic graph. In this article, considering data in the real world may arrive dynamically, we propose an incremental feature selection approach in hierarchical classification by employing fuzzy rough set technique. First, we use the sibling strategy to reduce the scope of negative samples. Second, we present a theoretical analysis of the incremental updating of the lower approximation, positive region and dependency degree at the arrival of new samples, respectively. Third, we perform the algorithmic design of the incremental approaches. To do that, we first present two improved versions (NIDC and NIFS for short) of the existing nonincremental methods, based on NIDC, NIFS, and the aforementioned theoretical analysis, two incremental algorithms (IDU and IFS for short) are then designed to perform incremental feature selection. Finally, a numerical experiment is conducted on some commonly used datasets for hierarchical classification tasks, whose true classes are distributed to both leaf nodes and internal nodes. A comparative study is further performed to show that our approach is effective and feasible.

Abstract In this paper, we further study the variety of monadic nilpotent minimum (NM)-algebras and their corresponding logic. In order to solve the drawback of monadic NM-algebras, we review some well-known classes of monadic t-norm-based fuzzy logical algebras and then revise the axiomatic system of monadic NM-algebras. Then we show that the variety of monadic NM-algebras is the equivalent algebraic semantics of monadic predicate fuzzy logic $\textbf {mNM}_{\forall }$, which is equivalent to the modal fuzzy logic $\textbf {S5(NM)}$. Moreover, we show that the propositional case of the modal fuzzy logic $\textbf {S5(NM)}$, which is $\textbf{S5}^{\prime}\textbf{(NM),}$ is also complete with respect to the variety of monadic NM-algebras in the sense of Blok and Pigozzi and obtain a necessary and sufficient condition for this logic to be semilinear. Finally, we give some representations of monadic NM-algebras. In particular, we give some characterizations of representable and directly indecomposable monadic NM-algebras.

Rough set theory, initiated by Pawlak, is a mathematical tool in dealing with inexact and incomplete information. Numerical characterizations of rough sets such as accuracy measure, roughness measure, etc, which aim to quantify the imprecision of a rough set caused by its boundary region, have been extensively studied in the existing literatures. However, very few of them are explored from the viewpoint of rough logic, which, however, helps to establish a kind of approximate reasoning mechanism. For this purpose, we introduce a kind of numerical approach to the study of rough logic in this paper. More precisely, we propose the notions of accuracy degree and roughness degree for each formula in rough logic with the intension of measuring the extent to which any formula is accurate and rough, respectively. Then, to measure the degree to which any two formulae are roughly included in each other and roughly similar, respectively, the concepts of rough inclusion degree and rough similarity degree are also proposed and their properties are investigated in detail. Lastly, by employing the proposed notions, we develop two types of approximate reasoning patterns in the framework of rough logic.

A propositional logic PRL for rough sets was proposed in [1]. In this paper, we initially introduce the concepts of rough (upper, lower) truth degrees on the set of formulas in PRL. Then, by grading the rough equality relations, we propose the concepts of rough (upper, lower) similarity degree. Finally, three different pseudo-metrics on the set of rough formulas are obtained, and thus an approximate reasoning mechanism is established.

A propositional logic PRL for rough sets was proposed in [1]. In this paper, we initially introduce the concepts of rough (upper, lower) truth degrees on the set of formulas in PRL. Then, by grading the rough equality relations, we propose the concepts of rough (upper, lower) similarity degree. Finally, three different pseudo-metrics on the set of rough formulas are obtained, and thus an approximate reasoning mechanism is established.

With technology migration into nano and molecular scales several hybrid CMOS/nano logic and memory architectures have been proposed thus far that aim to achieve high device density with low power consumption. The discovery of the memristor has further enabled the realization of denser nanoscale logic and memory systems. This work describes the design of such a multilevel memristor memory (MLMM) system, and the design constraints imposed in the realization of such a memory. In particular, the limitations on load, bank size, number of bits achievable per device, placed by the required noise margin (NM) for accurately reading the data stored in a device are analyzed.