软关联环

doi:10.6040/j.issn.1671-9352.0.2017.283

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 31-35.doi: 10.6040/j.issn.1671-9352.0.2017.283

软关联环

于晓丹,董丽,吴聪,孔祥智^*

江南大学理学院, 江苏无锡 214122

收稿日期:2017-06-07 出版日期:2018-04-20 发布日期:2018-04-13
通讯作者: 孔祥智(1971— ),男,博士,教授,研究方向为模糊代数. E-mail:xiangzhikong@jiangnan.edu.cn E-mail:1031799851@qq.com
作者简介:于晓丹(1994— ),女,硕士研究生,研究方向为模糊代数. E-mail:1031799851@qq.com
基金资助:
国家自然科学基金资助项目(11371174,11301227);江苏省自然科学基金资助项目(BK20130119)

Soft incidence ring

YU Xiao-dan, DONG Li, WU Cong, KONG Xiang-zhi^*

School of Science, Jiangnan University, Wuxi 214122, Jiangsu, China

Received:2017-06-07 Online:2018-04-20 Published:2018-04-13

摘要/Abstract

摘要： 将关联代数与软集相结合,提出新概念软关联环并研究它的基本代数性质;证明了两个软关联环同构当且仅当它们的基础软集同构,以及软关联环反同构等相关定理。

关键词: 软集, 关联代数, 软关联环

Abstract: The incidence ring will be associated to soft set to form a new concept, that is a soft incidence ring, whose basic algebraic properties are studied. Its shown that two soft incidence rings are isomorphic if and only if their basis of soft sets are isomorphic, soft incidence rings’ anti-isomorphism theorem and other related results are proved.

Key words: soft set, incidence algebra, soft incidence ring

中图分类号:

O159

于晓丹,董丽,吴聪,孔祥智. 软关联环[J]. 山东大学学报（理学版）, 2018, 53(4): 31-35.

YU Xiao-dan, DONG Li, WU Cong, KONG Xiang-zhi. Soft incidence ring[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 31-35.

参考文献

[1] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[2] MOLODTSOV D A. Soft set theory-first results[J]. Computers and Mathematics with Applications, 1999, 37(4-5):19-31.
[3] MAJI P K, BISWAS R, ROY A R. Soft set theory[J]. Computers and Mathematics with Applications, 2003, 45(4):555-562.
[4] MAJI P K, BISWAS R, ROY A R. An application of soft sets in a decision making problem[J]. Computers and Mathematics with Applications, 2002, 44(8):1077-1083.
[5] IRFAN ALI M, FENG Feng, LIU Xiaoyan, et al. On some new operations in soft set theory[J]. Computers and Mathematics with Applications, 2009, 57(9):1547-1553.
[6] MAJI P K, BISWAS R, ROY A R. Fuzzy soft sets[J]. Journal of Fuzzy Mathematics, 2001, 9(3):589-602.
[7] MAJI P K, ROY A R. A fuzzy soft set theoretic approach to decision making problems[J]. Journal of Computational and Applied Mathematics, 2007, 203(2):412-418.
[8] KONG Z, GAO L Q, WANG L F. Comment on a fuzzy soft set theoretic approach to decision making problems[J]. Journal of Computational and Applied Mathematics, 2009, 223(2):540-542.
[9] FENG F, JUN Y B, LIU X. An adjustable approach to fuzzy soft set based decision making[J]. Journal of Computational and Applied Mathematics, 2010, 234(1):10-20.
[10] JUN Y B. Soft BCK/BCI-algebras[J]. Computers and Mathematics with Applications, 2008, 56(5):1408-1413.
[11] Hacı Akta, Naim Çagman. Soft sets and soft groups[J]. Information Sciences, 2007, 177(13):2726-2735.
[12] 宋焕新, 袁志玲, 孔祥智. 软交Clifford半群[J]. 模糊系统与数学, 2016, 30(1):28-32. SONG Huanxin, YUAN Zhiling, KONG Xiangzhi. Soft intersection Clifford semigroup[J]. Fuzzy systems and Mathematics, 2016, 30(1):28-32.
[13] ROTA G C. On the foundations of combinatorial theory I. theory of Möbius functions[J]. Probability Theory and Related Fields, 1964, 2(4):340-368.
[14] SPIEGEL E. Involutions in incidence algebras[J]. Linear Algebra and its Applications, 2005, 405(1):155-162.
[15] STANLEY R P. Structure of incidence algebras and their automorphism groups[J]. Bull Amer Math Soc, 1970, 76(6):1236-1239.
[16] REINER VICTO, STAMATE DI. Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals[J]. Advances in Mathematics, 2010, 224(6):2312-2345.
[17] MAGNIFO F, ROSENBERG I G. Generalization of convolution and incidence algebras[J]. European Journal of Combinatorics, 2014, 37(3):100-114.
[18] FENG F, LI Y, LEOREANU-FOTEA V. Application of level soft sets in decision making based on interval-valued fuzzy soft sets[J]. Computers and Mathematics with Applications, 2010, 60(6):1756-1767.
[19] JOSE CARLOS R Alcantud. A novel algorithm for fuzzy soft set based decision making from multiobserver input-parameter data set[J]. Information Fusion, 2016, 29(C):142-148.
[20] GONG K, WANG P, PENG Y. Fault-tolerant enhanced bijective soft set with applications[J]. Applied Soft Computing, 2016, 54:431-439.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

软关联环

Soft incidence ring

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 2

多维度评价

本文评价

推荐阅读 0

[1]	彭家寅. 关联模糊集理论的伪BL-代数的软滤子[J]. 山东大学学报（理学版）, 2015, 50(08): 40-45.
[2]	刘春辉1,2. 滤子化软FI代数[J]. J4, 2012, 47(11): 94-98.