On the expected values of fuzzy events

Erich Klement; Radko Mesiar

doi:10.1142/S021848851540005X

On the expected values of fuzzy events

Erich Klement, Radko Mesiar

Institute for Mathematical Methods in Medicine and Data Based Modeling

Research output: Contribution to journal › Article › peer-review

Abstract

Generalizing a first approach by L.A. Zadeh (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).

Original language	English
Pages (from-to)	57-74
Number of pages	18
Journal	International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Volume	23 Suppl. 1
DOIs	https://doi.org/10.1142/S021848851540005X
Publication status	Published - 2015

Fields of science

101 Mathematics
101013 Mathematical logic
101024 Probability theory
102001 Artificial intelligence
102003 Image processing
102019 Machine learning
603109 Logic
202027 Mechatronics

JKU Focus areas

Computation in Informatics and Mathematics
Mechatronics and Information Processing
Nano-, Bio- and Polymer-Systems: From Structure to Function

Access to Document

10.1142/S021848851540005X

Cite this

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title = "On the expected values of fuzzy events",

abstract = "Generalizing a first approach by L.A. Zadeh (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).",

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AB - Generalizing a first approach by L.A. Zadeh (J. Math. Anal. Appl. 23, 1968), expected values of fuzzy events are studied which are (up to standard boundary conditions) only required to be monotone. They can be seen as an extension of capacities, i.e., monotone set functions satisfying standard boundary conditions. Some of these expected values can be characterized axiomatically, others are based on some distinguished integrals (Choquet, Sugeno, Shilkret, universal, and decomposition integral).

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DO - 10.1142/S021848851540005X

M3 - Article

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VL - 23 Suppl. 1

SP - 57

EP - 74

JO - International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

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