• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • On the closure of families of fuzzy measures under eventwise aggregations
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2028
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
September 15, 2026
Immunity to Chaos: How Personal Resources Help Us Cope with the Challenges of a Turbulent World
International conflicts, crises and digital overload—the modern world puts our minds to the test every day. Traditional psychology often focuses on the consequences: anxiety, depression, and psychosomatic disorders. But what if we looked at the problem differently—through the lens of the resources that prevent us from breaking down? Psychological immunity is precisely this set of resources. Alena Zolotareva and her group, Psychological Immunity as a Resource for Positive Functioning, are developing an integrative model of this phenomenon, adapting diagnostic tools and preparing for large-scale empirical research. Why do psychologists need to collaborate with medical professionals, and how could their research transform preventive care in clinics and corporations?
September 11, 2026
How to Assess Students Knowledge in the Age of AI
A researcher at HSE University has proposed a flowchart to help lecturers decide how to assess students who use artificial intelligence. It shows where the use of AI should be restricted and where it can be incorporated into the learning process. The article has been published in IT Professional.
September 9, 2026
‘Balkan Hospitality Opens Doors: Studying Dialects on the Verge of Extinction
You cannot study spoken dialects from books. Instead, you need to go to a village, seek out its elders, and earn the trust of local residents before you can record hours of spontaneous stories. This is how Natalia Muravleva, Associate Professor at the Faculty of Humanities, conducts her research. Her internship in Serbia continued her long-standing study of dialects spoken by Macedonian settlers. In this interview, she discusses how diaspora cultural centres help researchers reach informants, why native speakers need to be interviewed only in their own language (otherwise, as she puts it, they may 'break'), and how a single field season helped her finalise her monograph. She also shares warm memories of autumn in Belgrade and of colleagues with whom grammar can be discussed in three languages at once.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

On the closure of families of fuzzy measures under eventwise aggregations

Fuzzy Sets and Systems. 2005. Vol. 153. P. 45–70.
Bronevich A.

The paper contains some results on eventwise aggregation of fuzzy measures from the various families of lower probabilities. This investigation includes coherent lower probabilities, k-monotone measures, beliefmeasures, etc. We study sufficient and necessary conditions on aggregation operators satisfying the closure property: it is necessary to guarantee that the aggregation belongs to the same family, as generating measures. We also propose an efficient way for constructing aggregation operators, using the found unique properties of multilinear extension. This representation method for fuzzy measures generalizes to the n-dimensional case the well-known one giving distorted probabilities.

Language: English
Keywords: fuzzy measuresmultilinear extensioncoherent lower probabilitiesaggregation operatorsk-monotonicitydistortion functions
Similar publications
The fuzzy representation of prior information for separating outliers in statistical experiments.
Bronevich A., Мацыпаев Д. А., , in: Strengthening Links Between Data Analysis and Soft ComputingVol. 315.: Dordrecht, L., Heidelberg, NY: Springer, 2015. P. 167–174.
The paper presents a new fuzzy set based description which helps to distinguish the expected values of the statistical experiment from the outliers. Since the Neyman-Pearson criterion is not adequate in some real applications for such purpose, we propose to use triangular norms for conjuction of two propositions about typical and non-typical values and describe ...
Added: March 5, 2015
An investigation of ideals in the set of fuzzy measures
Bronevich A., Fuzzy Sets and Systems 2005 Vol. 152 P. 271–288
This work is devoted to the investigation of sets of fuzzy measures that are closed with respect to convex sum and product of fuzzy measures, which we call ideals. It is shown that the basic convex families of fuzzy measures, which are interpreted as lower probabilities, possess such properties. ...
Added: April 10, 2014
Necessary and sufficient consensus conditions for the eventwise aggregation of lower probabilities
Bronevich A., Fuzzy Sets and Systems 2007 Vol. 158 P. 881–894
The paper gives sufficient and necessary conditions of consensus requirement for eventwise aggregation of various families of lower probabilities, in particular, of coherent lower probabilities, and properties of the corresponding aggregation functions. ...
Added: April 10, 2014
The description of extreme 2-monotone measures.
Bronevich A., Розенберг И. Н., , in: Proceedings of the Eighth International Symposium on Imprecise Probability: Theories and Applications (ISIPTA;13).: Compiegne: Universite de Technologie de Compiegne, 2013. P. 23–32.
The paper is devoted to the description of extreme points in the set of 2-monotone measures. We describe them using lattices on which an extreme 2-monotone measure is additive. We also propose the way of generation extreme monotone measures based on the aggregation of extreme measures with the help of multilinear extension. We describe also ...
Added: September 25, 2013
Условные нечеткие меры, функциональные отображения и нечеткие величины в рамках вероятностного подхода
Bronevich A., Розенберг И. Н., Нечеткие системы и мягкие вычисления 2012 Т. 7 № 1 С. 5–22
В данной работе рассматриваются основные принципы теории нечетких мер в рамках вероятностного подхода, которые являются обобщением классических принципов традиционной теории вероятностей. В результате вводятся понятия условных нечетких мер, нечетких величин, а также их числовых характеристик. ...
Added: March 14, 2013
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit