Constructing some logical algebras from EQ-algebras

Abstract

EQ-algebras were introduced by Nova ́k in [16] as an algebraic structure of truth values for fuzzy type theory (FFT). Nova ́k and De Baets in [18] introduced various kinds of EQ-algebras such as good, residuated, and lattice ordered EQ-algebras. In any logical algebraic structures, by using various kinds of filters, one can construct various kinds of other logical algebraic structures. With this inspirations, by means of fantastic filters of EQ-algebras we construct MV -algebras. Also, we study prelinear EQ-algebras and introduce a new kind of filter and named it prelinear filter. Then, we show that the quotient structure which is introduced by a prelinear filter is a distributive lattice- ordered EQ-algebras and under suitable conditions, is a De Morgan algebra, Stone algebra and Boolean algebra.