Choquet Capacities and Fuzzy Integrals
暫譯: Choquet 能力與模糊積分

Beliakov, Gleb, James, Simon, Wu, Jian-Zhang

Choquet Capacities and Fuzzy Integrals
  • 出版商: Springer
  • 出版日期: 2025-11-18
  • 售價: $3,720
  • 貴賓價: 9.5 折 $3,534
  • 語言: 英文
  • 頁數: 373
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 3031970691
  • ISBN-13: 9783031970696
  • 相關分類: Data-mining

    • 海外代購書籍(需單獨結帳)

相關主題

商品描述

Choquet capacities, which provide the weighting mechanism for the Choquet and other fuzzy integrals, model synergistic and antagonistic interactions between variables by assigning value to all subsets rather than individual inputs.

While the flexibility of capacities (also referred to as fuzzy measures and cooperative games) comes at the expense of an exponentially increasing number of parameters, the ability to explain their behavior using various value and interaction indices makes them appealing for applications requiring transparency and interpretability. As well as a number of useful indices that in some way capture the extent to which positive and negative interactions occur, significant progress has been made in addressing the scalability issues that arise in applications. This book provides a detailed overview of the background concepts relating to capacities and their role in fuzzy integration and aggregation, then presents specialised chapters on most recent results in learning, random sampling and optimization that involve Choquet capacities.

Topics and features:

- Fundamentals of Choquet capacities (fuzzy measures) and their use in modeling importance and interaction between variables

- Definitions, properties and mappings between alternative representations that allow capacities and fuzzy integrals to be interpreted and applied in different settings

- Various simplification assumptions, from k-additive, p-symmetric and l-measures to more recent concepts such as k-interactive and hierarchical frameworks

- Capacity learning formulations that allow the diverse types to be elicited from datasets or according to user-specified requirements

- Recent findings related to random sampling and optimisation with Choquet integral objectives

This book includes illustrative examples and guidance for implementation, including an appendix detailing functions found in the pyfmtools software library. It aims to be useful for practitioners and researchers in decision and data-driven fields, or those who wish to apply these emerging tools to new problems.

The authors are all affiliated with the School of Information Technology at Deakin University, Australia. Gleb Beliakov is a professor, Simon James is an Associate Professor, and Jian-Zhang Wu is a Research Fellow.

商品描述(中文翻譯)

Choquet 容量（Choquet capacities）提供了 Choquet 及其他模糊積分的加權機制，通過為所有子集而非單個輸入分配值來建模變數之間的協同和對抗互動。

雖然容量的靈活性（也稱為模糊測度和合作遊戲）以指標數量指數增長為代價，但使用各種值和互動指標解釋其行為的能力使其在需要透明度和可解釋性的應用中變得吸引人。除了捕捉正負互動發生程度的多個有用指標外，還在解決應用中出現的可擴展性問題方面取得了顯著進展。本書詳細概述了與容量及其在模糊整合和聚合中的角色相關的背景概念，然後介紹了涉及 Choquet 容量的學習、隨機抽樣和優化的最新結果的專門章節。

主題和特點：
- Choquet 容量（模糊測度）的基本原理及其在建模變數之間的重要性和互動中的應用
- 定義、性質及不同表示之間的映射，允許在不同環境中解釋和應用容量和模糊積分
- 各種簡化假設，從 k-additive、p-symmetric 和 l-measures 到更近期的概念，如 k-interactive 和層次框架
- 容量學習公式，允許從數據集或根據用戶指定的要求引出不同類型
- 與 Choquet 積分目標相關的隨機抽樣和優化的最新發現

本書包括插圖示例和實施指導，附錄詳細說明了在 pyfmtools 軟體庫中找到的函數。它旨在對決策和數據驅動領域的從業者和研究人員有用，或對希望將這些新興工具應用於新問題的人士有幫助。

作者均隸屬於澳大利亞迪肯大學（Deakin University）信息技術學院。**Gleb Beliakov** 是教授，**Simon James** 是副教授，**Jian-Zhang Wu** 是研究員。

作者簡介

Gleb Beliakov is a Professor in Mathematics at Deakin University, Australia. He completed his PhD in 1992 in Moscow and since then worked at various universities, for the last 25 years at Deakin University. His research is focused on computational mathematics, numerical optimisation and aggregation functions. He co-authored three monographs and numerous research papers in this area.

Simon James is an Associate Professor in Mathematics at Deakin University. He completed his Ph.D. there on the topic of aggregation functions in 2010 under the supervision of Gleb Beliakov and held an academic position there since 2011. His main research areas of aggregation and capacities (or fuzzy measures) are most commonly applied in computational intelligence and machine learning as prediction and analysis tools.

Jian-Zhang Wu was a Research Fellow at Deakin University. He received his PhD in Management Science and Engineering in 2011 from Beijing Institute of Technology and was previously a professor at Ningbo University. He has also worked as a chief data scientist in the finance industry. His research focuses on machine learning, decision-making, and explainable AI, especially using Choquet capacities and fuzzy integrals. He has led several national and provincial research projects in China.

作者簡介(中文翻譯)

格列布·貝利亞科夫是澳洲迪肯大學的數學教授。他於1992年在莫斯科完成博士學位，之後在多所大學任教，過去25年在迪肯大學工作。他的研究專注於計算數學、數值優化和聚合函數。他共同撰寫了三本專著和多篇相關研究論文。 西蒙·詹姆斯是迪肯大學的數學副教授。他於2010年在該校完成了聚合函數主題的博士學位，指導教授為格列布·貝利亞科夫，自2011年以來一直擔任學術職位。他的主要研究領域是聚合和能力（或模糊測度），這些領域通常應用於計算智能和機器學習，作為預測和分析工具。 吳建章曾是迪肯大學的研究員。他於2011年在北京理工大學獲得管理科學與工程博士學位，並曾擔任寧波大學的教授。他還曾在金融行業擔任首席數據科學家。他的研究專注於機器學習、決策制定和可解釋的人工智慧，特別是使用Choquet能力和模糊積分。他在中國主導了多個國家和省級研究項目。

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