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Logics for belief functions on MV-algebras

Logics for belief functions on MV-algebras
Logics for belief functions on MV-algebras
In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.
Belief functions, Fuzzy events, Modal logics, Łukasiewicz logic
0888-613X
491-512
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96
Flaminio, Tommaso
10824669-cfbb-4724-aa74-e1b31574dae8
Godo, Lluís
0518f088-84ec-4816-ad43-4e240ae66dc1
Marchioni, Enrico
729c9984-5949-438e-8de7-0e079bdb9f96

Flaminio, Tommaso, Godo, Lluís and Marchioni, Enrico (2013) Logics for belief functions on MV-algebras. International Journal of Approximate Reasoning, 54 (4), 491-512. (doi:10.1016/j.ijar.2012.08.006).

Record type: Article

Abstract

In this paper we present a generalization of belief functions over fuzzy events. In particular we focus on belief functions defined in the algebraic framework of finite MV-algebras of fuzzy sets. We introduce a fuzzy modal logic to formalize reasoning with belief functions on many-valued events. We prove, among other results, that several different notions of belief functions can be characterized in a quite uniform way, just by slightly modifying the complete axiomatization of one of the modal logics involved in the definition of our formalism.

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More information

e-pub ahead of print date: 4 September 2012
Published date: June 2013
Keywords: Belief functions, Fuzzy events, Modal logics, Łukasiewicz logic

Identifiers

Local EPrints ID: 416588
URI: http://eprints.soton.ac.uk/id/eprint/416588
ISSN: 0888-613X
PURE UUID: 228dc942-2fb5-4bb9-b26c-7cd1672ffdd5

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Date deposited: 03 Jan 2018 17:30
Last modified: 15 Mar 2024 17:37

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Contributors

Author: Tommaso Flaminio
Author: Lluís Godo
Author: Enrico Marchioni

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