Geodesic
Constructing some logical algebras from EQ-algebras
Filomat, Tome 35 (2021) no. 8, p. 2747

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DOI

EQ-algebras were introduced by Novàk in [16] as an algebraic structure of truth values for fuzzy type theory (FTT). 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
DOI : 10.2298/FIL2108747B
Classification : 06E15, 06F99
Keywords: EQ-algebras, filter, fantastic (positive implicative, implicative) filter, prelinear EQ-algebra, prelinear filter 
Rajab Ali Borzooei; Narges Akhlaghinia; Xiao Long Xin; Mona Aaly Kologani. Constructing some logical algebras from EQ-algebras. Filomat, Tome 35 (2021) no. 8, p. 2747 . doi: 10.2298/FIL2108747B
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     author = {Rajab Ali Borzooei and Narges Akhlaghinia and Xiao Long Xin and Mona Aaly Kologani},
     title = {Constructing some logical algebras from {EQ-algebras}},
     journal = {Filomat},
     pages = {2747 },
     year = {2021},
     volume = {35},
     number = {8},
     doi = {10.2298/FIL2108747B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2108747B/}
}
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