将贝叶斯定理扩展为区间型2型模糊版本，更真实地处理专家提供的概率范围。
An Interval Type-2 Version of Bayes Theorem Derived from Interval Probability Range Estimates Provided by Subject Matter Experts
- 提出保守算法避免输入模糊函数不一致导致的无效输出。
- 设计新方法将专家给出的概率区间转化为区间型2型模糊隶属函数。
- 适合需要处理不确定专家意见的决策与风险评估场景。
贝叶斯推断广泛应用于各领域以检验假设与观测数据的匹配性。多数应用假定输入值精确，从而得到精确输出，但这在真实世界中不切实际。通常，领域专家（SME）所能提供的最佳信息是贝叶斯定理中涉及输入概率的区间估计。本文提出两个关键贡献：首先，开发了一种新的区间型2型（IT2）贝叶斯定理版本，采用新颖且保守的方法，避免因输入IT2隶属函数（MFs）不一致而引发的潜在无效输出；其次，提出一种新颖且灵活的算法，将专家提供的区间转换为IT2模糊隶属函数，用于指定贝叶斯定理中的输入概率。该算法推广并扩展了以往主要针对“计算于文字”（Computing with Words）应用中将区间编码为词语隶属函数的研究。
原文摘要 · Abstract (English)
Bayesian inference is widely used in many different fields to test hypotheses against observations. In most such applications, an assumption is made of precise input values to produce a precise output value. However, this is unrealistic for real-world applications. Often the best available information from subject matter experts (SMEs) in a given field is interval range estimates of the input probabilities involved in Bayes Theorem. This paper provides two key contributions to extend Bayes Theorem to an interval type-2 (IT2) version. First, we develop an IT2 version of Bayes Theorem that uses a novel and conservative method to avoid potential inconsistencies in the input IT2 MFs that otherwise might produce invalid output results. We then describe a novel and flexible algorithm for encoding SME-provided intervals into IT2 fuzzy membership functions (MFs), which we can use to specify the input probabilities in Bayes Theorem. Our algorithm generalizes and extends previous work on this problem that primarily addressed the encoding of intervals into word MFs for Computing with Words applications.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。