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On effect algebras of fuzzy sets

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Abstract

We introduce the category IE of effect algebras of fuzzy sets and sequentially continuous effect homomorphisms and describe its fundamental properties. We show that IE and the category ID of D-posets of fuzzy sets are isomorphic, hence the constructions and properties of ID related to applications to probability theory are valid for the corresponding effect algebras. We describe basic properties of categorical coproducts in ID and dually of categorical products in the corresponding category MID of measurable spaces. We end with remarks on fuzzy probability notions.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 040 01, Košice, Slovak Republic

    Martin Papčo

  2. Department of Mathematics, Pedagogical Faculty, Catholic University in Ružomberok, Námestie A. Hlinku 56/1, 034 01, Ružomberok, Slovak Republic

    Martin Papčo

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  1. Martin Papčo
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Correspondence to Martin Papčo.

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Supported by VEGA Grant 1/2002/05.

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Papčo, M. On effect algebras of fuzzy sets. Soft Comput 12, 373–379 (2008). https://doi.org/10.1007/s00500-007-0171-1

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  • DOI: https://doi.org/10.1007/s00500-007-0171-1

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