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2 Discussiones Mathematicae - General Algebra and Applications

2 2013

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Fuzzy n-fold integral filters in BL-algebras

100%

Borzooei R. , Paad A.

Discussiones Mathematicae - General Algebra and Applications

2013

tom 33

nr 1

57-71

In this paper, we introduce the notion of fuzzy n-fold integral filter in BL-algebras and we state and prove several properties of fuzzy n-fold integral filters. Using a level subset of a fuzzy set in a BL-algebra, we give a characterization of fuzzy n-fold integral filters. Also, we prove that the homomorphic image and preimage of fuzzy n-fold integral filters are also fuzzy n-fold integral filters. Finally, we study the relationship among fuzzy n-fold obstinate filters, fuzzy n-fold integral filters and fuzzy n-fold fantastic filters

On pseudo BE-algebras

70%

Borzooei R. , Saeid A. , Rezaei A. , Radfar A. , Ameri R.

Discussiones Mathematicae - General Algebra and Applications

2013

tom 33

nr 1

95-108

In this paper, we introduce the notion of pseudo BE-algebra which is a generalization of BE-algebra. We define the concepts of pseudo subalgebras and pseudo filters and prove that, under some conditions, pseudo subalgebra can be a pseudo filter. We prove that every homomorphic image and pre-image of a pseudo filter is also a pseudo filter. Furthermore, the notion of pseudo upper sets in pseudo BE-algebras introduced and is proved that every pseudo filter is an union of pseudo upper sets.