Some Types of Filters in Equality Algebras

Publish Year: 1396
نوع سند: مقاله ژورنالی
زبان: English
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JR_CGASAT-7-1_002

تاریخ نمایه سازی: 23 شهریور 1400

Abstract:

Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras.

Authors

Rajabali Borzooei

Department of Mathematics, Shahid Beheshti University, Tehran, Iran.

Fateme Zebardast

Department of Mathematics, Payam e Noor University, Tehran, Iran.

Mona Aaly Kologani

Payam e Noor University

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  • Cignoli, R., D'ottaviano, I., and Mundici, D., "Algebraic Foundations of ...
  • Ciungu, L.C., Internal states on equality algebras, Soft Computing ۱۹(۴) ...
  • Esteva, F. and Godo, L., Monoidal t-normbased logic: towards a ...
  • H'ajek, P., "Metamathematics of Fuzzy Logic", Springer, Trends in Logic ...
  • Haveshki, M., Borumand Saeid, A., and Eslami, E., Some types ...
  • Jenei, S., Equality algebras, Studia Logica ۱۰۰(۶) (۲۰۱۲), ۱۲۰۱-۱۲۰۹ ...
  • Jenei, S. and K'or'odi, L., On the variety of equality ...
  • Liu, L., On the existence of states on MTL-algebras, Inform. ...
  • Liu, L. and Zhang, X., Implicative and positive implicative prefilters ...
  • Nov'ak, V. and De Baets, B., EQ-algebras, Fuzzy Sets and ...
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