{"product_id":"choquet-capacities-and-fuzzy-integrals-gleb-beliakov-9783031970696","title":"Choquet Capacities and Fuzzy Integrals","description":"\u003cp\u003eChoquet 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. \u003c\/p\u003e \u003cp\u003eWhile 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.\u003c\/p\u003e \u003cp\u003e\u003cstrong\u003eTopics and features: \u003c\/strong\u003e\u003c\/p\u003e - 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 \u003cp\u003eThis 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. \u003c\/p\u003e \u003cp\u003eThe authors are all affiliated with the School of Information Technology at Deakin University, Australia. \u003cstrong\u003eGleb Beliakov\u003c\/strong\u003e is a professor, \u003cstrong\u003eSimon James\u003c\/strong\u003e is an Associate Professor, \u003cstrong\u003e \u003c\/strong\u003eand \u003cstrong\u003eJian-Zhang Wu\u003c\/strong\u003e is a Research Fellow.\u003c\/p\u003e \u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Gleb Beliakov,Simon James,Jian-Zhang Wu\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3031970691\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783031970696\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/18\/2025\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 373\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.59lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 0.88d","brand":"Gleb Beliakov","offers":[{"title":"Hardcover","offer_id":48446921965823,"sku":"9783031970696","price":89.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_e2be2f4e-c52e-4fb3-807d-cfafc5efee0c.jpg?v=1777227618","url":"https:\/\/www.whiterainbookhouse.com\/products\/choquet-capacities-and-fuzzy-integrals-gleb-beliakov-9783031970696","provider":"WR Book House","version":"1.0","type":"link"}