The Signed Distance Measure in Fuzzy Statistical Analysis: Theoretical, Empirical and Programming Advances

The main focus of this book is on presenting advances in fuzzy statistics, and on proposing a methodology for testing hypotheses in the fuzzy environment based on the estimation of fuzzy confidence intervals, a context in which not only the data but also the hypotheses are considered to be fuzzy. The proposed method for estimating these intervals is based on the likelihood method and employs the bootstrap technique. A new metric generalizing the signed distance measure is also developed. In turn, the book presents two conceptually diverse applications in which defended intervals play a role: one is a novel methodology for evaluating linguistic questionnaires developed at the global and individual levels; the other is an extension of the multi-ways analysis of variance to the space of fuzzy sets. To illustrate these approaches, the book presents several empirical and simulation-based studies with synthetic and real data sets. In closing, it presents a coherent R package called "FuzzySTs" which covers all the previously mentioned concepts with full documentation and selected use cases. Given its scope, the book will be of interest to all researchers whose work involves advanced fuzzy statistical methods.

本書的主要焦點是介紹模糊統計學的進展，並提出一種基於模糊置信區間估計的模糊環境下假設檢定方法。在這種情況下，不僅考慮數據，還考慮假設是模糊的。估計這些區間的提出方法基於最大概似法，並採用自助法技術。同時，還開發了一種推廣有符號距離度量的新度量方法。此外，本書還介紹了兩個概念上不同的應用，其中防禦區間起到了作用：一個是在全球和個體層面上開發的評估語言問卷的新方法；另一個是將多元變異數分析擴展到模糊集合空間。為了說明這些方法，本書提供了幾個基於合成和真實數據集的實證和模擬研究。最後，本書還提供了一個一致的 R 套件，名為 'FuzzySTs'，該套件涵蓋了所有前述概念，並提供完整的文檔和選定的使用案例。鑑於其範圍，本書將對所有涉及先進模糊統計方法的研究人員感興趣。