JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 9-16.doi: 10.6040/j.issn.1671-9352.0.2017.645

Previous Articles     Next Articles

Topological properties analysis of logical metric spaces on the residuated lattice

DUAN Jing-yao   

  1. Department of Mathematics and Information Sciences, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Online:2018-12-20 Published:2018-12-18

Abstract: Firstly, the relation between logical metric space([0,1], ρR)and metric space (F(X),HR) is analysized. Secondly, convergence of the Cauchy-sequences are investigate. Finally, the uniform topology is constructed on the general residuated lattice. The work provides a new way to study the structure of residuated lattice, and lay a solid theoretical foundation for the robustness analysis of logical inference systems.

Key words: residuated lattice, Cauchy-sequence, complete, uniform topology

CLC Number: 

  • O153.1
[1] CAI Kaiyuan. Robustness of fuzzy reasoning and δ-equalities of fuzzy sets[J]. IEEE Transactions on Fuzzy Systems, 2001, 9(5):783-750.
[2] YING Mingsheng. Perturbation of fuzzy reasoning[J]. IEEE Transactions on Fuzzy Systems, 1999, 7(5):625-629.
[3] LI Yongming, LI Dechao. An approach of measure the robustness of fuzzy reasoning[J]. International Journal of Intelligent Systems, 2005, 20(2005):393-413.
[4] DAI Songsong, PEI Daowu. Robustness analysis of full implication inference method[J]. International Journal of Approximate Reasoning, 2013, 54(2013):653-666.
[5] JIN Jianhua,LI Yongming, LI Chunquan. Robustness of fuzzy reasoniog via logically equivalence measure[J]. Information Sciences, 2007, 177(2007):5103-5117.
[6] WANG Guojun, DUAN Jingyao. On robustness of the full implication triple I inference method with respect to finer measurements[J]. International Journal of Approximate Reasoning, 2014, 55(2014):787-796.
[7] LIU Huawen, WANG Guojun. Continuity of triple I methods based on several implications[J]. Computer and Mathematics with Applications, 2008, 56(8):2079-2087.
[8] DUAN Jingyao, LI Yongming. Robustness analysis of logic metrics on F(X)[J]. International Journal of Approximate Reasoning, 2015, 61(2015):33-42.
[9] PAN Haiyu, LI Yongming, CAO Yongzhi. Lattice-valued simulations for quantitative transition systems[J]. International Journal of Approximate Reasoning, 2015, 56(2015):28-42.
[10] PAN Haiyu, CAO Yongzhi, ZHANG Min, et al. Simulation for lattice-valued doubly labeled transition systems[J]. International Journal of Approximate Reasoning, 2014, 55(2014):797-811.
[11] 王国俊. 数理逻辑引论与归结原理[M].2版. 北京: 科学出版社, 2006. WANG Guojun. Introduction to mathematical logic and resolution principle[M]. 2nd. Beijing: Science Press, 2006.
[12] KLEMENT E P, MESIAR R, PAP E. Triangular norms[M]. Dordrecht: Kluwer Academic Publishers, 2000.
[13] LI Yingfang, QIN Keyun, HE Xingxing. Robustness of fuzzy connectives and fuzzy reasoning[J]. Fuzzy Sets and Systems, 2013, 225(2013):93-105.
[14] KELLEY J L. General topology[M]. New York: Springer-Verlag, 1975.
[15] 周建仁,谢晶晶,吴洪博. 基于剩余格的一类度量空间及性质[J]. 吉林大学学报(理学版),2012,50(5):897-901. ZHOU Jianren, XIE Jingjing, WU Hongbo. A metric structure and its properties based on metric residual lattece[J]. Journal of Jilin Univerdity(Science Edition), 2012, 50(5):897-901.
[16] 段景瑶,李永明. 模糊集的逻辑等价相似度[J]. 陕西师范大学学报(自然科学版), 2016,44(1):7-13. DUAN Jingyao, LI Yongming. Similarity degree via logic equivalence of fuzzy sets[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2016, 44(1):7-13.
[1] LI Tong-jun, HUANG Jia-wen, WU Wei-zhi. Attribute reduction of incomplete contexts based on similarity relations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 9-16.
[2] . Vertex-distinguishing IE-total coloring and general-total coloring of K1,3,p and K1,4,p [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(8): 53-60.
[3] GONG Chun-mei, FENG Li-xia, REN Xue-ming. (*,~)-good congruences on completely J *,~-simple semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 11-16.
[4] XU Wei-cheng, LI Xin-peng. Generalized Cav(u)theorem for repeated games with incomplete information on one side [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 42-45.
[5] LI Xiao-juan, GAO Qiang. Regularity for product space under sublinear expectation framework [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 66-75.
[6] LIU Chun-hui. On(∈,∈∨q(λ, μ))-fuzzy LI-ideals in lattice implication algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(2): 65-72.
[7] . Vertex-distinguishing E-total coloring of complete bipartite graph K10,n with 10≤n≤90 [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 23-30.
[8] SHAO Yong. Semilattice-ordered completely regular periodic semigroups [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 1-5.
[9] LIU Li-jun. Characterizations of n-fold positive implicative filter in residuated lattice [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 48-52.
[10] CHANG Xiao-xuan, JI Pei-sheng. Class of fuzzy bounded operators in Felbins type fuzzy normed linear spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(2): 49-54.
[11] LIANG Ying, CUI Yan-li, WU Hong-bo. Properties of residuated lattice of deduction systems set algebra in BL system [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 65-70.
[12] LUO Yong-gui. Maximal(regular)subsemigroups of the semigroup W(n,r) [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 7-11.
[13] LIU Chun-hui. Lattice of(,∨(-overq))-fuzzy filters in a BL-algebra [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 104-110.
[14] DENG Xiao-qin, WU Qun-ying. Precise asymptotics in the complete moment convergence for NA random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 102-110.
[15] ZHANG Yu, XIAO Ben-qiong, XU Ke, SHEN Ai-ting. Complete moment convergence for arrays of rowwise NSD random variables [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(6): 30-36.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[3] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[4] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[5] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[6] 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 .
[7] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
[8] TANG Xiao-hong1, HU Wen-xiao2*, WEI Yan-feng2, JIANG Xi-long2, ZHANG Jing-ying2, SHAO Xue-dong3. Screening and biological characteristics studies of wide wine-making yeasts[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 12 -17 .
[9] WANG Bi-yu, CAO Xiao-hong*. The perturbation for the Browder’s theorem of operator matrix#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 90 -95 .
[10] YU Xiu-qing. (σ,τ)-expansion model of P-sets and its properties#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(04): 90 -94 .