您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

《山东大学学报(理学版)》 ›› 2020, Vol. 55 ›› Issue (5): 55-70.doi: 10.6040/j.issn.1671-9352.0.2019.460

• • 上一篇    

一类S-一致模与几种聚合算子间的模方程

赵卫利,周红军*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710119
  • 发布日期:2020-05-06
  • 作者简介:赵卫利(1994— ), 女, 硕士研究生, 研究方向为不确定性推理. E-mail:zhaoweili2013@snnu.edu.cn*通信作者简介:周红军(1980— ), 男, 教授, 博士生导师, 研究方向为序代数与逻辑、不确定性推理. E-mail:hjzhou@snnu.edu.cn
  • 基金资助:
    陕西省青年科技新星计划资助项目(2016KJXX-24)

Modularity equations between a class of S-uninorms and several commonly-used aggregation operators

ZHAO Wei-li, ZHOU Hong-jun*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China
  • Published:2020-05-06

PDF (PC)

404

摘要： 以模糊逻辑和模糊决策为理论基础, 研究一类S-一致模分别与一致模、t-算子、S-一致模、T-一致模间的模方程,给出这些聚合算子满足模方程的结构刻画。并且,T-一致模关于S-一致模满足模方程的结构刻画部分推广2-一致模模方程的结构刻画。

关键词: 模方程, S-一致模, T-一致模, t-算子, 一致模

Abstract: Based on the fuzzy logic theory and fuzzy decision, the present paper focuses on the modularity equations between one class of S-uninorms and several aggregation operators such as uninorms, t-operators, S-uninorms and T-uninorms, and gives structural characterizations of these aggregation operators satisfying modularity equations. Moreover, the structural characterizations between T-uninorms and S-uninorms satisfying the modularity equations partially generalize the structural characterizations of 2-uninorms.

Key words: modularity equation, S-uninorm, T-uninorm, t-operator, uninorm

中图分类号: 

  • O142
[1] BELIAKOV G, PRADERA A, CALVO T. Aggregation functions: a guide for practitioners[M]. Berlin: Springer, 2007.
[2] ZIMMERMANN H J, ZYSNO P. Decisions and evaluations by hierarchical aggregation of information[J]. Fuzzy Sets and Systems, 1983, 10:243-260.
[3] GRABISCH M, MARICHAL J L, MESIAR R, et al. Aggregations functions[M]. New York: Cambridge University Press, 2009.
[4] KLEMENT E P, MESIAR R, PAP E. Triangular norms[M]. Dordrecht: Kluwer, 2000.
[5] FODOR J C, YAGER R R, RYBALOV A. Structure of uninorms[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1997, 5(4):411-427.
[6] YAGER R R, RYBALOV A. Uninorm aggregation operators[J]. Fuzzy Sets and Systems, 1996, 80:111-120.
[7] MAS M, MAYOR G, TORRENS J. T-operators[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1999, 7(1):31-50.
[8] CALVO T, BAETS B D, FODOR J C. The functional equations of Frank and Alsina for uninorms and nullnorms[J]. Fuzzy Sets and Systems, 2001, 120(3):385-394.
[9] AKELLA P. Structure of n-uninorms[J]. Fuzzy Sets and Systems, 2007, 158(15):1631-1651.
[10] ZONG Wenwen, SU Yong, LIU Huawen, et al. On the structure of 2-uninorm[J]. Information Sciences, 2018, 467:506-527.
[11] BUSTINCE H, PAGOLA M, MESIAR R, et al. Grouping, overlap, and generalized bientropic functions for fuzzy modeling of pairwise comparisons[J]. IEEE Transactions on Fuzzy Systems, 2012, 20(3):405-415.
[12] 周红军, 兰淑敏. 闭区间上单调不减函数的右连续伪逆及其在三角余模构造中的应用[J]. 陕西师范大学学报(自然科学版), 2019, 47(5):71-80. ZHOU Hongjun, LAN Shumin. Right-continuous pseudo-inverse of monotone functions on closed intervals and its applications in the construction of triangular conorms[J]. Journal of Shaanxi Normal University(Natural Science Edition), 2019, 47(5):71-80.
[13] ACZÉL J. Lectures on functional equations and their applications[M]. New York: Academic Press, 1966.
[14] CARBONELL M, MAS M, SUNER J, et al. On distributivity and modularity in De Morgan triplets[J]. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 1996, 4(4):351-368.
[15] DAVEY B A, PRIESTLEY H A. Introduction to lattices and order[M]. New York: Cambridge University Press, 1990.
[16] MAS M, MAYOR G, TORRENS J. The modularity condition for uninorms and t-operators[J]. Fuzzy Sets and Systems, 2002, 126(2):207-218.
[17] QIN Feng. Uninorm solutions and(or)nullnorm solutions to the modularity condition equations[J]. Fuzzy Sets and Systems, 2004, 148(2):231-242.
[18] RAK E. The modularity equation in the class of 2-uninorms[C] // IEEE International Conference Intelligent Systems. Advances in Intelligent Systems and Computing. [S.l.] : Springer, 2015: 45-54.
[19] FECHNER W, RAK E, ZEDAM L. The modularity law in some classes of aggregation operators[J]. Fuzzy Sets and Systems, 2018, 332:56-73.
[20] WANG Yaming, CHEN Xiangjun, LIU Huawen. A note on the modularity law in some classes of aggregation operators[J]. Fuzzy Sets and Systems, 2019, 372:142-147.
[21] ZHAN Hang, WANG Yaming, LIU Huawen. The modularity condition for semi-t-operators and semi-uninorms[J]. Fuzzy Sets and Systems, 2018, 334:36-59.
[22] ZHAN Hang, WANG Yaming, LIU Huawen. The modularity condition for semi-t-operators[J]. Fuzzy Sets and Systems, 2018, 346:108-126.
[23] SU Yong, RIERA J V, RUIZ-AGUILERA D, et al. The modularity condition for uninorms revisited[J]. Fuzzy Sets and Systems, 2019, 357:27-46.
[24] WANG Yaming, LIU Huawen. The modularity condition for overlap and grouping functions[J]. Fuzzy Sets and Systems, 2019, 372:97-110.
[25] MAS M, MESIAR R, MONSERAT M, et al. Aggregation operations with annihilator[J]. International Journal of General Systems, 2005, 34(1):1-22.
[26] JOCIC D, ŠTAJNER-PAPUGA I. Distributivity and conditional distributivity for T-uninorms[J]. Information Sciences, 2018, 424:91-103.
[27] FANG Bowen, HU Baoqing. Distributivity and conditional distributivity for S-uninorms[J]. Fuzzy Sets and Systems, 2019, 372:1-33.
[1] 程亚菲,赵彬. 模糊蕴涵关于合取2-一致模满足输入律的刻画[J]. 《山东大学学报(理学版)》, 2019, 54(8): 20-32.
[2] 宋一凡,赵彬. 2-一致模基于重叠函数的(α,O)-迁移性[J]. 《山东大学学报(理学版)》, 2019, 54(11): 97-107.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发