Probability and Fuzzy Working in Concert—Honoring the Reliability Contributions of Nozer D. Singpurwalla

IF 1.3 4区数学 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Applied Stochastic Models in Business and Industry Pub Date : 2025-01-29 DOI:10.1002/asmb.2918

Kimberly F. Sellers, Jane M. Booker

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引用次数: 0

Abstract

Since Lotfi Zadeh introduced fuzzy logic and fuzzy sets, this theory characterizing the uncertainty of classification has a proven record in fields of computation and engineering. These successful applications, however, have been falsely interpreted as competition or replacement of probability theory by those in many statistical and mathematical communities. Such misconceptions are the result of a lack of understanding about types of uncertainties, and anchored attitudes clinging to the past. Nozer Singpurwalla, among other statisticians, came to the realization that probability and fuzzy set theory can and should work in concert (i.e., not in competition) to accommodate two different types of uncertainty present within a problem or system. The authors had the honor to collaborate with Nozer; those works are featured as successful applications of the probability measure of fuzzy sets in reliability where respective uncertainties of the outcome of events and of classification exist. This paper features those works which embody the use of Bayesian analysis and the subjective interpretation of probability.

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概率与模糊协同工作——尊重Nozer D. Singpurwalla的可靠性贡献

自从Lotfi Zadeh引入模糊逻辑和模糊集以来，这种描述分类不确定性的理论在计算和工程领域得到了证明。然而，这些成功的应用被许多统计和数学团体错误地解释为对概率论的竞争或替代。这种误解是由于缺乏对各种不确定性的理解，以及固守过去的态度。Nozer Singpurwalla和其他统计学家认识到，概率和模糊集理论可以而且应该协同工作（即，不是竞争），以适应一个问题或系统中存在的两种不同类型的不确定性。作者有幸与诺泽合作；这些工作的特点是模糊集的概率测度在可靠性中的成功应用，其中事件结果和分类存在各自的不确定性。本文重点介绍了运用贝叶斯分析和对概率进行主观解释的作品。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Applied Stochastic Models in Business and Industry 数学-数学跨学科应用

CiteScore

2.70

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： ASMBI - Applied Stochastic Models in Business and Industry (formerly Applied Stochastic Models and Data Analysis) was first published in 1985, publishing contributions in the interface between stochastic modelling, data analysis and their applications in business, finance, insurance, management and production. In 2007 ASMBI became the official journal of the International Society for Business and Industrial Statistics (www.isbis.org). The main objective is to publish papers, both technical and practical, presenting new results which solve real-life problems or have great potential in doing so. Mathematical rigour, innovative stochastic modelling and sound applications are the key ingredients of papers to be published, after a very selective review process. The journal is very open to new ideas, like Data Science and Big Data stemming from problems in business and industry or uncertainty quantification in engineering, as well as more traditional ones, like reliability, quality control, design of experiments, managerial processes, supply chains and inventories, insurance, econometrics, financial modelling (provided the papers are related to real problems). The journal is interested also in papers addressing the effects of business and industrial decisions on the environment, healthcare, social life. State-of-the art computational methods are very welcome as well, when combined with sound applications and innovative models.