广义多值直觉模糊软集及其在多属性决策中的应用

doi:10.12005/orms.2018.0229

运筹与管理 ›› 2018, Vol. 27 ›› Issue (10): 49-55.DOI: 10.12005/orms.2018.0229

广义多值直觉模糊软集及其在多属性决策中的应用

江立辉^1,2, 陈华友², 黄艳¹

1.合肥学院数学与物理系,安徽合肥 230601;
2.安徽大学数学科学学院,安徽合肥 230039

收稿日期:2017-08-04 出版日期:2018-10-25
作者简介:江立辉(1980-),男,安徽屯溪人,硕士,副教授,研究方向为预测与决策分析;陈华友( 1969-),男,安徽和县人,博士生导师,教授,研究方向为预测和决策分析;黄艳(1996-),女,安徽六安人,本科生。
基金资助:
国家自然科学基金(71371011, 71301001);安徽高校优秀青年骨干人才国内外访学研修项目(gxfx2017094);安徽省高校人文社科重点项目(SK2018A0605);合肥学院自科基金(17ZR06ZDA);合肥学院硕士点培育项目(2018xs03)

Generalized Multi-intuitionistic Fuzzy Soft Setand Its Application in Multi-attribute Decision Making

JIANG Li-hui^1,2, CHEN Hua-you², HUANG Yan¹

1.Department of Mathematics and Physics, Hefei University, Hefei 230601, China;
2.School of Mathematical Science, Anhui University, Hefei 230039, China

Received:2017-08-04 Online:2018-10-25

摘要/Abstract

摘要： 软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。

关键词: 软集, 广义模糊软集, 多值直觉模糊软集, 广义多值直觉模糊软集, 多属性决策

Abstract: As a new mathematical tool to deal with uncertainty problems, soft set theory makes up for the inadequacy of the parametrization tools of traditional uncertainty theories. In this paper, generalized multi-intuitionistic fuzzy soft set is proposed by combining the generalized fuzzy soft set and multi-intuitionistic fuzzy set. The operations of complement, union, intersection, “and”, “or” are defined on the generalized multi-intuitionistic fuzzy soft sets. The basic properties of generalized multi-intuitionistic fuzzy soft sets are also investigated. In addition, the generalized multi-intuitionistic fuzzy soft set is applied to the multi-attribute decision problems, and the corresponding algorithm is given. The feasibility and validity of this method are illustrated.

Key words: soft sets, generalized fuzzy soft sets, multi-intuitionistic fuzzy soft sets, generalized multi-intuitionistic fuzzy soft sets, multi-attribute decision making

中图分类号:

C934

江立辉, 陈华友, 黄艳. 广义多值直觉模糊软集及其在多属性决策中的应用[J]. 运筹与管理, 2018, 27(10): 49-55.

JIANG Li-hui, CHEN Hua-you, HUANG Yan. Generalized Multi-intuitionistic Fuzzy Soft Setand Its Application in Multi-attribute Decision Making[J]. Operations Research and Management Science, 2018, 27(10): 49-55.

参考文献

[1]Molodtsov D. Soft set theory-first results[J].Computer and Mathematics with Applications, 1999, 37(4-5): 19-31.
[2]Zou Y, Xiao Z. Data analysis approaches of soft sets under incomplete information[J]. Knowledge-Based Systems, 2008, 21(8): 941-945.
[3]Xiao Z, Gong K, Zou Y. A combined forecasting approach based on fuzzy soft sets[J]. Journal of Computational and Applied Mathematics, 2009, 228(1): 326-333.
[4]Das P K, Borgohain R. An application of fuzzy soft set in multicriteria decision making problem[J]. International Journal of Computer Applications, 2012, 38(12): 0975-8887.
[5]Maji P K, Biswas R, Roy A R. Soft set theory[J]. Computers and Mathematics with Applications, 2003, 45(4-5): 555-562.
[6]Maji P K, Roy A R, Biswas R. An application of soft sets in a decision making problem[J]. Computers and Mathematics with Applications, 2002, 44(8-9): 1077-1083.
[7]Maji P K, Biswas R, Roy A R. Fuzzy soft sets[J]. Journal of Fuzzy Mathematics, 2001, 9(3): 589-602.
[8]Maji P K, Biswas R, Roy A R. Intutionistic fuzzy soft sets[J]. Journal of Fuzzy Mathematics, 2001, 9(3): 677-692.
[9]Yang X, Lin T Y, Yang J, et al. Combination of interval-valued fuzzy set and soft set[J]. Computers and Mathematics with Applications, 2009, 58(3): 521-527.
[10]Majumdar P, Samanta S K. Generalised fuzzy soft sets[J]. Computers and Mathematics with Applications, 2010, 59(4): 1425-1432.
[11]张善文,李晓曼,雷英杰.多值直觉模糊集定义[J].计算机科学,2008,35(1):176-177.
[12]Sebastian S, Ramakrishnan T V. Multi-fuzzy sets: an extension of fuzzy sets[J]. Fuzzy Information and Engineering, 2011, 3(1): 35-43.
[13]江立辉,陈华友,丁芳清等.多值直觉模糊软集[J].计算机工程与应用,2014, 50(23) : 114-117.
[14]段梦雅,吴涛,马闯.多值区间直觉模糊软集[J].合肥学院学报(自科版),2016.(26)1:10-12.
[15]Alkhazaleh S, Salleh A R. Generalised interval-valued fuzzy soft set[J]. Journal of Applied Mathematics, 2012, 2012(11): 2607-2645.
[16]袁芳,周小强,胡满佳.广义直觉模糊软集及其代数性质[J].郑州大学学报(理学版),2012,44(04):46-49.
[17]Mao J, Yao D, Wang C. Group decision making methods based on intuitionistic fuzzy soft matrices[J]. Applied Mathematical Modelling,2013, 37(9): 6425-6436.
[18]胡永瑞,毛军军,赵愿.基于时序广义双极值模糊软集的群决策方法[J].佳木斯大学学报(自然科学版),2014(5):774-778.
[19]黄鹤,王艳平.广义犹豫模糊软集[J].辽宁工业大学学报(自然科学版),2017,37(1):62-66.
[20]Deschrijver G, Cornelis C, Kerre E E. On the representation of intuitionistic fuzzy t-norms and t-conorms[J]. IEEE transactions on fuzzy systems, 2004, 12(1): 45-61.
[21]Liu H W, Wang G J. Multi-criteria decision-making methods based on intuitionistic fuzzy sets[J]. European Journal of Operational Research, 2007, 179(1): 220-233.

广义多值直觉模糊软集及其在多属性决策中的应用

Generalized Multi-intuitionistic Fuzzy Soft Setand Its Application in Multi-attribute Decision Making

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

[1]	胡文发, 何新华. 绿色建筑前期设计阶段的多目标优化及多属性决策模型[J]. 运筹与管理, 2021, 30(7): 44-49.
[2]	吴澎, 吴群, 周礼刚, 陈华友. 基于多目标属性权重优化的犹豫模糊语言TOPSIS决策方法[J]. 运筹与管理, 2021, 30(6): 42-47.
[3]	杨敏, 张仕斌, 张航. 基于新模糊熵和得分函数的区间直觉模糊多属性决策[J]. 运筹与管理, 2021, 30(6): 63-68.
[4]	于倩, 廖娅, 曹俊, 侯福均. 基于QUALIFLEX和LINMAP的简化中性犹豫模糊多属性决策方法[J]. 运筹与管理, 2021, 30(6): 77-82.
[5]	李清水, 李登峰, 李辉, 余高锋. 基于前景理论的区域绿色经济发展水平多指标评价[J]. 运筹与管理, 2021, 30(6): 118-123.
[6]	李茹霞, 扈文秀, 齐晓亮. 区间二型模糊集效用函数和熵在风险决策中的应用[J]. 运筹与管理, 2021, 30(5): 102-109.
[7]	李鹏宇, 吴冲. 基于改进得分函数的直觉梯形模糊数群体多属性决策方法[J]. 运筹与管理, 2021, 30(4): 76-80.
[8]	朱峰, 刘玉敏, 徐济超, 苏冰杰. 基于相似度和改进雷达图的概率犹豫模糊多属性决策方法[J]. 运筹与管理, 2021, 30(4): 109-114.
[9]	汪兰林, 李登峰. 基于在线评价信息的概率语言多属性变权决策方法[J]. 运筹与管理, 2021, 30(2): 39-44.
[10]	刘政敏, 徐洪雪, 刘培德, 梁霞. 考虑多元关联关系和语义变换的直觉不确定语言多属性决策方法[J]. 运筹与管理, 2021, 30(2): 45-52.
[11]	李娜, 高雷阜, 王磊. 基于Pythagorean模糊熵的风险型决策方法——考虑后悔与失望规避[J]. 运筹与管理, 2020, 29(6): 130-138.
[12]	曾守桢, 骆丹丹. 基于投影模型的区间直觉模糊多属性决策方法研究[J]. 运筹与管理, 2020, 29(3): 10-15.
[13]	李鹏, 沈志杰. 基于广义WOWA算子的Pythagorean模糊决策方法[J]. 运筹与管理, 2020, 29(2): 58-65.
[14]	王磊, 陶刘芹. Picture模糊幂几何Heronian平均算子及其在多属性决策中的应用[J]. 运筹与管理, 2020, 29(12): 59-66.
[15]	朱峰, 徐济超, 刘玉敏, 王宁. 广义概率对偶犹豫模糊语言幂集结算子在多属性决策中的应用[J]. 运筹与管理, 2020, 29(10): 59-67.