Preideals in EQ-algebras

Autor: M. Aaly Kologani, N. Akhlaghinia, Rajab Ali Borzooei
Rok vydání: 2021
Předmět:
Zdroj: Soft Computing. 25:12703-12715
ISSN: 1433-7479
1432-7643
Popis: EQ-algebras were introduced by Nov´ak in [15] as an algebraic structure of truth values for fuzzy type theory (FFT). Nov´ak and De Baets in [17] introduced various kinds of EQ-algebras such as good, residuated, and IEQ-algebras. In this paper, we define the notion of (pre)ideal in bounded EQ-algebras (BEQ-algebras) and investigate some properties. Then we introduce a congruence relation on good BEQ-algebras by using ideals, and then we solve an open problem in [18]. Moreover, we show that in IEQ-algebras, there is an one-to-one corresponding between congruence relations and the set of ideals. In the follows, we characterize the generated preideal in BEQ-algebras and by using this, we prove that the family of all preideals of a BEQ-algebra, is a complete lattice. Then we show that the family of all preideals of a prelinear IEQ-algebras, is a distributive lattice and become a Heyting algebra. Finally, we show that we can construct an MV-algebra form the family of all preideals of a prelinear IEQ-algebra.
Databáze: OpenAIRE
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