### Theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras

LIU Chun-hui1,2

1. 1. Office of Teaching Affairs, Chifeng University, Chifeng 024001, Inner Mongolia, China;
2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
• Received:2013-12-30 Online:2014-10-20 Published:2014-11-10

Abstract: The theory of interval valued (∈,∈∨ q)-fuzzy filters in BL-algebras is studied systematically. Firstly, two notions of interval valued (∈,∈∨ q)-fuzzy involution filters and interval valued (∈,∈∨ q)-fuzzy associative filters are introduced and some characterizations of them are obtained. Secondly, the relations among all kinds of interval valued (∈,∈∨ q)-fuzzy filters are discussed. It is proved that an interval valued fuzzy set is an interval valued (∈,∈∨ q)-fuzzy Boolean (implicative) filter if and only if it is both an interval valued (∈,∈∨ q)-fuzzy positive implicative and an interval valued (∈,∈∨ q)-fuzzy involution filter.

CLC Number:

• O141.1
 [1] WANG Guojun, ZHOU Hongjun. Introduction to mathematical logic and resolution principle[M]. Beijing: Science in China Press, 2009. [2] HJEK P. Metamathematics of fuzzy logic[M]. Dordrecht: Kluwer Academic Publishers, 1998. [3] TURUNEN E. BL-algebras of basic fuzzy logic[J]. Mathware and Soft Computing, 1999, 6(1):49-61. [4] 周建仁, 吴洪博. WBR0-代数的正则性及与其它逻辑代数的关系[J]. 山东大学学报:理学版, 2012, 47(2):86-92. ZHOU Jianren, WU Hongbo. The regularness of WBR0-algebras and relationship with other logic algebras[J]. Journal of Shandong University:Natural Science, 2012, 47(2): 86-92. [5] XU Yang, RUAN Da, QIN Keyun, et al. Lattice-valued logic[M]. Berlin: Springer, 2004. [6] ZADEH L A. The concept of a linguistic variable and its application to approxinate reason[J]. Informtion and Control, 1975, 18:199-249. [7] 刘春辉. 布尔代数的区间值(∈,∈∨q)-模糊子代数[J]. 山东大学学报:理学版, 2013, 48(10):94-98. LIU Chunhui. Interval valued (∈,∈∨ q)-fuzzy subalgebras of Boolean algebras[J]. Journal of Shandong University:Natural Science, 2013, 48(10):94-98. [8] 刘春辉. 泛逻辑学中UB代数系统的广义模糊滤子[J]. 模糊系统与数学, 2011, 25(2):13-20. LIU Chunhui. Generalized fuzzy filters of UB algebras systems in universal logic[J]. Fuzzy Systerms and Mathematics, 2011, 25(2):13-20. [9] XUE Zhan-ao, XIAO Yun-hua, LIU Wei-hua, et al. Intuitionistic fuzzy filter theory of BL-algebras[J]. Int J Mach Learn ＆ Cyber, 2013, 4:659-669. [10] ZHAN Jianming, XU Yang. Some types of generalized fuzzy filters of BL-algebras[J]. Computers and Mathenatics with Applications, 2008, 56:1604-1616.
 [1] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110. [2] PENG Jia-yin. Disturbing fuzzy ideals of BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(10): 78-94. [3] YANG Yong-wei, HE Peng-fei, LI Yi-jun. Falling fuzzy ideals of BL-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(02): 83-89. [4] WEN Xian-hong, WU Hong-bo*. The prime reverse deductive system of locally finite #br# BL-algebras with properties [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(2): 36-41. [5] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br# [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63-67. [6] ZHOU Jian-ren, WU Hong-bo*. The regularness of WBR0-algebras and relationship with other logic algebras [J]. J4, 2012, 47(2): 86-92.
Viewed
Full text

Abstract

Cited

Shared
Discussed