Integral prefilters and integral Eq-algebras
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Akbar Paad
Abstract
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.
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Communicated by Anatolij Dvurečenskij
References
[1] Andrews, P.: An Introduction to Mathematical Logic and Type Theory: to Truth through Proof, Kluwer, Dordrecht, 2002.10.1007/978-94-015-9934-4Suche in Google Scholar
[2] Behzadi, M.—Torkzadeh, L.: Obstinate and maximal prefilters in EQ-algebras, An. Univ. Craiova Ser. Mat. Inform. 44(2) (2017), 228–237.Suche in Google Scholar
[3] Borzooei, R. A.—Paad, A.: Integral filters and integral BL-algebras, Ital. J. Pure Appl. Math. 30 (2013), 303–316.10.7151/dmgaa.1192Suche in Google Scholar
[4] c-Zekey, M.: Representable good EQ-algebras, Soft. Comput. 14(9) (2010), 1011–1023.10.1007/s00500-009-0491-4Suche in Google Scholar
[5] c-c, M.—NováK, V.—Mesiar, R.: On good EQ-algebras, Fuzzy Sets and Systems 178 (2011), 1–23.10.1016/j.fss.2011.05.011Suche in Google Scholar
[6] Liu, L.—Zhang, X.: Implicative and positive implicative prefilters of EQ-algebras, J. Intell. Fuzzy Syst. 26 (2014), 2087–2097.10.3233/IFS-130884Suche in Google Scholar
[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.Suche in Google Scholar
[8] Novák, V.: On fuzzy type theory, Fuzzy Sets and Systems 149 (2005), 235–273.10.1016/j.fss.2004.03.027Suche in Google Scholar
[9] Novák, V.—De Baets, B.: EQ-algebras, Fuzzy Sets and Systems 160 (2009), 2956–2978.10.1016/j.fss.2009.04.010Suche in Google Scholar
[10] Novák, V.—Dyba, M.: Non-commutative EQ-logics and their extensions. In: Proc. World Congress IFSA-EUSFLAT, University of Lisbon, Portugal, 2009.Suche in Google Scholar
[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 829527.10.1155/2014/829527Suche in Google Scholar PubMed PubMed Central
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Artikel in diesem Heft
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
Artikel in diesem Heft
- Regular Papers
- Logical and algebraic properties of generalized orthomodular posets
- Integral prefilters and integral Eq-algebras
- Modules with fusion and implication based over distributive lattices: Representation and duality
- Localization of k × j-rough Heyting algebras
- Meet infinite distributivity for congruence lattices of direct sums of algebras
- Some exponential diophantine equations II: The equation x2 – Dy2 = kz for even k
- On extensions of the Open Door Lemma
- Nevanlinna theory for holomophic curves from annuli into semi-Abelian varieties
- Stability and feedback stabilizability of delay periodic differential equations with pairwise permutable matrix functions
- On the behaviour solutions of fractional and partial integro differential heat equations and its numerical solutions
- Oscillatory and asymptotic behavior of solutions of third-order quasi-linear neutral difference equations
- Some properties of Kantorovich variant of Chlodowsky-Szász operators induced by Boas-Buck type polynomials
- A Study on statistical versions of convergence of sequences of functions
- Fuzzy fixed point theorems and Ulam-Hyers stability of fuzzy set-valued maps
- Notes on affine Killing and two-Killing vector fields
- Prediction of the exponential fractional upper record-values
- On concomitants of generalized order statistics from generalized FGM family under a general setting
- One-parameter generalization of dual-hyperbolic Pell numbers
