JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (8): 14-19.doi: 10.6040/j.issn.1671-9352.0.2018.587

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Strong hyper deductive systems in hyper equality algebras

CHENG Xiao-yun1, XIN Xiao-long2   

  1. 1. School of Science, Xian Aeronautical University, Xian 710077, Shaanxi, China;
    2. School of Mathematics, Northwest University, Xian 710069, Shaanxi, China
  • Online:2019-08-20 Published:2019-07-03

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Abstract: Some types of strong hyper deductive systems in hyper equality algebras are introduced and investigated. Some representations of generated strong hyper deductive systems are given. Then, Two types of important strong hyper deductive systems, namely, implicative and positive implicative strong hyper deductive systems are studied. In particular, characterizations of them are given and the relations between them are discussed.

Key words: hyper equality algebra, strong hyper deductive system, generated strong hyper deductive system, (positive)implicative strong deductive system

CLC Number: 

  • O153
[1] NOVÁK V, BAETS B D. EQ-algebras[J]. Fuzzy Sets and Systems, 2009, 160(20):2956-2978.
[2] JENEI S. Equality algebras[J]. Studia Logica, 2012, 100(6):1201-1209.
[3] SAEID A B, REZAEI A, BORZOOEI R A. Some types of filters in BE-algebras[J]. Mathematics in Computer Science, 2013, 7(3):341-352.
[4] ZEBARDAST F, BORZOOEI R A, KOLOLOGANI M A. Results on equality algebras[J]. Information Sciences, 2017, 381:270-282.
[5] MARTY F. Surune generalization de la notion de group[C] // The 8th Congress Math, Sweden, Scandinaves[s.n.] , 1934.
[6] JUN Y B, ZAHEDI M M, XIN Xiaolong, et al. On hyper BCK-algebras[J]. Italian Journal of Pure and Applied Mathematics-N, 2000, 8:127-136.
[7] XIN Xiaolong. Hyper BCI-algebras[J]. Discussiones Mathematicae General Algebra and Applications, 2006, 26:5-19.
[8] GHORBANI S, HASANKHANI A, ESLAMI E. Hyper MV-algebras[J]. Set-Valued Mathematiics Applications, 2008, 1:205-222.
[9] BORZOOEI R A, BAKHSHI M, ZAHIRI O. Filter theory on hyper residuated lattice[J]. Quasigroups and Related Systems, 2014, 22:33-50.
[10] BORZOOEI R A, SAFFAR B G, AMERI R. On hyper EQ-algebras[J]. Italian Journal of Pure and Applied Mathematics-N, 2013, 31:77-96.
[11] CHENG Xiaoyun, XIN Xiaolong, JUN Y B. Hyper equality algebras[M] // Quantitative Logic and Soft Computing. Berlin: Springer, 2017: 415-428.
[12] CORSINI P, LEOREANU V. Applications of hyperstructure theory[M]. Dordrecht: Kluwer, 2003.
[13] DAVVAZ B, NEZHAD A D, HEIDARI M M. Inheritance examples of algebraic hyperstructures[J]. Information Sciences, 2013, 224:180-187.
[14] CHENG Xiaoyun, XIN Xiaolong. Filter theory on hyper BE-algebras[J]. Italian Journal of Pure and Applied Mathematics-N, 2015, 35:509-526.
[15] CHENG Xiaoyun, XIN Xiaolong, YANG Yongwei. Deductive systems in hyper EQ-algebras[J]. Journal of Mathematical Research with Applications, 2017, 37(2):183-193.
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