On maxitive integration

Abstract A functional is said to be maxitive if it commutes with the (pointwise) supremum operation. Such functionals find application in particular in decision theory and related fields. In the present paper, maxitive functionals are characterized as integrals with respect to maxitive measures (also known as possibility measures or idempotent measures). These maxitive integrals are then compared with the usual additive and nonadditive integrals on the basis of some important properties, such as convexity, subadditivity, and the law of iterated expectations.

• Publication year

  2016

• Venue

  Fuzzy Sets Syst.

• Publication date

  2016-12-01

• Fields of study

  Mathematics, Computer Science

• Identifiers
  DOI 10.1016/j.fss.2016.02.008
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Theory of Probability: A Critical Introductory Treatment

  2017cited by this paper
• Non Additive Measure And Integral

  2016cited by this paper
• Foundations Of Statistics

  2016cited by this paper
• Superdecomposition integrals

  2015cited by this paper
• Maxitive Integral of Real-Valued Functions

  2014cited by this paper
• Iterated Choquet expectations: A possibility result

  2013cited by this paper
• Stochastic Finance

  2013influential reference
• Likelihood decision functions

  2013cited by this paper
• Theory of Charges: A Study of Finitely Additive Measures

  2012cited by this paper
• Bipolar fuzzy integrals

  2012cited by this paper
• Generalized Measure Theory

  2008cited by this paper
• Possibility theory

  2007cited by this paper
• Modeling decisions - information fusion and aggregation operators

  2007cited by this paper
• Statistical decisions based directly on the likelihood function

  2007cited by this paper
• A new characterization of distortion premiums via countable additivity for comonotonic risks

  2006cited by this paper
• Aggregation operators: new trends and applications

  2002cited by this paper
• Real Analysis and Probability: Measurability: Borel Isomorphism and Analytic Sets

  2002cited by this paper
• Stochastic Finance: An Introduction in Discrete Time

  2002cited by this paper
• CHAPTER 33 – Monotone Set Functions-Based Integrals

  2002cited by this paper
• Coherent Measures of Risk

  1999cited by this paper
• Fuzzy sets as a basis for a theory of possibility

  1999cited by this paper
• Supremum Preserving Upper Probabilities

  1999cited by this paper
• Idempotent Analysis and Its Applications

  1997influential reference
• The iterative law of expectation and non-additive probability measure

  1991cited by this paper
• Possibility Theory - An Approach to Computerized Processing of Uncertainty

  1988cited by this paper
• Integral representation without additivity

  1986cited by this paper
• The extent of non-conglomerability of finitely additive probabilities

  1984cited by this paper
• Maxitive measure and integration

  1971influential reference
• A LOGIC FOR EVIDENTIAL SUPPORT (II)*

  1966cited by this paper
• Foundations of the theory of probability

  1960cited by this paper
• The Foundations of Statistics

  1955cited by this paper
• Theory of capacities

  1954cited by this paper
• Expectation in Economics

  1951cited by this paper
• On the Theory of Scales of Measurement.

  1946cited by this paper
• ON THE USE AND INTERPRETATION OF CERTAIN TEST CRITERIA FOR PURPOSES OF STATISTICAL INFERENCE PART I

  1928cited by this paper

• Asymptotic Optimality in Data-Driven Decision Making

  2025cites this paper
• Maxitive functions with respect to general orders

  2024influential citation
• A subjective interpretation of Liu–Liu’s credibility measures and expectations

  2023cites this paper
• On the representation of weakly maxitive monetary risk measures and their rate functions

  2022influential citation
• Maxitive Monetary Risk Measures: Worst-Case Risk Assessment and Sharp Large Deviations

  2022cites this paper
• Weakly maxitive set functions and their possibility distributions

  2021influential citation
• Large deviations built on max-stability

  2019cites this paper
• The likelihood interpretation as the foundation of fuzzy set theory

  2017cites this paper
• On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

  2015cites this paper
• The Likelihood Approach to Statistical Decision Problems

  2014cites this paper
• Representation of maxitive measures: An overview

  2014cites this paper
• Maxitive Integral of Real-Valued Functions

  2014cites this paper