AI 中文总结
针对含随机性和模糊性的现实决策问题，本文基于模糊随机变量推导高斯模糊过程和模糊采集函数的理论背景，开发贝叶斯模糊优化技术，在相关数据分析中表现有效，有广泛应用前景。
AI 中文摘要
在许多现实问题中，由于随机性和模糊性这两种不确定性来源，决策变得复杂，传统优化方法面临挑战。现有多数模糊优化技术忽略模糊性，概率优化技术忽略随机性。Kwakernaak引入模糊随机变量概念。本文旨在为高斯模糊过程和模糊采集函数推导理论背景，以开发优化模糊值目标函数的贝叶斯模糊优化技术。基于模糊随机变量开发高斯模糊过程，定义模糊采集函数。该方法在模糊均值 - 方差投资组合分配和印度温度数据分析中表现有效，具有广泛应用前景。
英文摘要
In many real-life problems, decision-making gets complicated due to dual sources of uncertainty, known as randomness and fuzziness or imprecision, which can be challenging for traditional optimization methods. Most of the existing fuzzy optimization techniques that optimize fuzzy-valued objective functions ignore fuzziness, while the probabilistic optimization techniques ignore randomness. To handle this dual source of uncertainty, Kwakernaak introduced the concept of a fuzzy random variable as ``random variables whose values are not real, but fuzzy numbers". This work aims to derive a theoretical background for the Gaussian fuzzy process and fuzzy acquisition functions, which will be used to develop a novel \emph{Bayesian fuzzy optimization} (BFO) technique that optimizes a fuzzy-values objective function. Based on fuzzy random variables, the Gaussian fuzzy process is developed, which is used as a prior belief about the fuzzy-valued objective function in the BFO. Fuzzy acquisition functions are defined to act as a guide for the search process of BFO with the help of posterior fuzzy mean and fuzzy variance. The proposed method demonstrated effective performance in both fuzzy mean-variance portfolio allocation and Indian temperature data analysis, showing robust predictive accuracy and adaptability. The proposed method can have broader applications in various fields like healthcare, material science, agriculture, etc.
