International Journal of
Physical Sciences

  • Abbreviation: Int. J. Phys. Sci.
  • Language: English
  • ISSN: 1992-1950
  • DOI: 10.5897/IJPS
  • Start Year: 2006
  • Published Articles: 2570

Full Length Research Paper

Fuzzy ideals in partially ordered pseudoeffect algebras

Feng Feng and Xiaoyan Liu*      
School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China.  
Email: [email protected]

  •  Accepted: 15 September 2011
  •  Published: 16 October 2011

Abstract

Pseudoeffect algebras are non-commutative generalizations of effect algebras, which can serve as models of both quantum structures and non-commutative logics. The main contribution of this study is twofold. Firstly, we initiate an order-theoretic extension of pseudoeffect algebras, called partially ordered pseudoeffect algebras (abbreviated po-PEAs). Secondly, we investigate the fuzzy ideal theory of po-PEAs. In particular, we show that a fuzzy ideal in a po-PEA is finitely generated if and only if it is finitely valued, and every fuzzy ideal in a Noetherian po-PEA is finitely generated.

 

Key words: Pseudoeffect algebra, fuzzy set, fuzzy ideal, fuzzy logic.