A systematic review of uncertainty theory with the use of scientometrical method

Abstract

Uncertainty theory is an area in axiomatic mathematics recently proposed by Professor Baoding Liu and aiming to deal with belief degrees. Retrieving 1004 journal articles from the Web of Science database between 2008 and 2019, and utilizing CiteSpace and Pajek software, we analyze the publications per year and by geographical distribution, productive scholars and their cooperation, key journals, highly cited articles and main paths of the field. In this way, seven key sub-fields of uncertainty theory and their research potential are derived. The results show the following: (1) The literature on uncertainty theory follows a linear growth trend, involves an extensive network of 1000 scholars worldwide and is published in 300 journals, indicating thus that uncertainty theory has become increasingly attractive, and its academic influence is gradually expanding. (2) Seven key sub-fields of uncertainty theory have clearly been identified, including the axiomatic system, uncertain programming, uncertain sets, uncertain logic, uncertain differential equations, uncertain risk analysis, and uncertain processes. Among them, uncertain differential equations and programming are the two main sub-fields with the largest numbers of published papers. Furthermore, for evaluating the research potential of sub-fields, maturity and recent attention indicators are calculated using the citations, total number of publications, quantity of most cited literature and half-life. Based on these indicators, uncertain processes shows the greatest development potential, and has remained a hot topic in recent years, being mainly concentrated on the uncertain renewal reward process, optimal control of discrete-time uncertain systems, and uncertain linear quadratic optimal control. Additionally, uncertain risk analysis is ranked second, and focuses on the analysis of expected losses, investment risk, and structural reliability of uncertain systems.

Knowledge mapping of immunotherapy for thyroid cancer from 1980 to 2022: A review

“…[31,32] CiteSpace (6.1.R6), Pajek (64 5.16), VOSviewer (1.6.17), and Scimago Graphics (Beta 1.0.26) were used as the analyzing tools to perform the visual analysis. [33][34][35][36][37][38][39][40][41] These software programs are based on co-occurrence analysis and cluster analysis to analyze the cooperation relationship between items such as countries or regions, institutions, authors and the cluster of keywords. [34,42] In general, the size of items (nodes) in the map indicates the value of the item, such as the number of published papers or citation.…”

Uncertainty Analysis and Optimization Modeling with Application to Supply Chain Management: A Systematic Review

“…To better deal with this uncertainty, Liu [34] proposed uncertainty theory, which thus became a branch of mathematics to model uncertainty through trustworthiness. Zhou et al [35] analyzed a review of 1004 journal papers in the field of uncertainty from 2008 to 2019 to derive seven key sub-fields of uncertainty theory and their research potential. The study finds a linear growth trend in the literature of uncertainty theory, involving an extensive network of 1000 scholars published in 300 journals worldwide, indicating the growing attractiveness of uncertainty theory and its gradual expansion of academic influence.…”

A Bi-Objective Optimization Model for a Low-Carbon Supply Chain Network with Risk of Uncertain Disruptions

“…m wkh Z wkph is due to m wkh = 0 for k = 0; thus, for raw material h, the disruption belief degree of the supplier to which manufacturer w is assigned at level p can be expressed as ∑ |S| k=1 m wkh Z wkph . The uncertainty theory has been considerably developed in terms of its theory and application since it was proposed; specific applications of the uncertainty theory can be found in the literature [49]. According to the uncertainty theory [15], and the literature on the application of the uncertainty theory [14], constraint (1h) calculates, for raw material h, the belief degree that manufacturer w can be served normally when supplier s is assigned to it for l = 2, .…”