×

Integral prefilters and integral EQ-algebras. (English) Zbl 07504082

Summary: In this paper, the notion of some new classes of EQ-algebras which are called integral, O-local, and locally finite EQ-algebras are introduced, and relationships between locally finite EQ-algebras and maximal prefilters are described. Also, the notion of integral prefilters are introduced and several characteristics of them are presented. Moreover, relation among integral prefilters and some type of other prefilter such as positive implicative, maximal, prime, and fantastic prefilters in EQ-algebras are studied. Finally, Boolean prefilters in bounded lattice EQ-algebras are introduced, and it is proved that a filter of a prelinear involutive EQ-algebra \(L\) is a Boolean filter if and only if \(L/F\) is a Boolean algebra.

MSC:

03G25 Other algebras related to logic
03G05 Logical aspects of Boolean algebras
06D35 MV-algebras
06E99 Boolean algebras (Boolean rings)

Software:

ETPS
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Andrews, P.: An Introduction to Mathematical Logic and Type Theory: to Truth through Proof, Kluwer, Dordrecht, 2002. · Zbl 1002.03002
[2] Behzadi, M.—Torkzadeh, L.: Obstinate and maximal prefilters in EQ-algebras, An. Univ. Craiova Ser. Mat. Inform. 44(2) (2017), 228-237. · Zbl 1424.03072
[3] Borzooei, R. A.—Paad, A.: Integral filters and integral BL-algebras, Ital. J. Pure Appl. Math. 30 (2013), 303-316. · Zbl 1329.06004
[4] c-Zekey, M.: Representable good EQ-algebras, Soft. Comput. 14(9) (2010), 1011-1023. · Zbl 1201.03061
[5] c-c, M.—NováK, V.—Mesiar, R.: On good EQ-algebras, Fuzzy Sets and Systems 178 (2011), 1-23. · Zbl 1242.03089
[6] Liu, L.—Zhang, X.: Implicative and positive implicative prefilters of EQ-algebras, J. Intell. Fuzzy Syst. 26 (2014), 2087-2097. · Zbl 1305.03061
[7] Novák, V.: EQ-algebras: primary concepts and properties. In: Int. Joint, Czech Republic-Japan and Taiwan-Japan Symposium, Kitakyushu, Japan, 2006, pp. 219-223.
[8] Novák, V.: On fuzzy type theory, Fuzzy Sets and Systems 149 (2005), 235-273. · Zbl 1068.03019
[9] Novák, V.—De Baets, B.: EQ-algebras, Fuzzy Sets and Systems 160 (2009), 2956-2978. · Zbl 1184.03067
[10] Novák, V.—Dyba, M.: Non-commutative EQ-logics and their extensions. In: Proc. World Congress IFSA-EUSFLAT, University of Lisbon, Portugal, 2009.
[11] Xin, X. L.— He, P. F.—Yang, Y. W.: Characterizations of some fuzzy prefilters (filters) in EQ-algebras, Sci. World J. (2014), Art. ID 829527.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.