2型犹豫q阶三角不确定语言Schweizer-Sklar-Muirhead算子

doi:10.6040/j.issn.1671-9352.0.2024.108

摘要/Abstract

摘要： 为了描述多属性决策问题中决策者们多层的犹豫性,本文结合犹豫模糊集、q阶三角犹豫模糊集和q阶犹豫模糊不确定语言集,提出2型犹豫q阶三角不确定语言集,定义了基于Schweizer-Sklar范数的模糊元的运算,证明运算的性质。为了有效处理评估属性之间相互关联的现实决策问题,将Muirhead平均算子推广至2型犹豫q阶三角不确定语言集,提出2型犹豫q阶三角不确定语言Schweizer-Sklar-Muirhead平均算子和加权Muirhead平均算子,并给出这些算子的计算公式和性质。最后,给出基于2型犹豫q阶三角不确定语言Muirhead平均算子的多属性决策方法,并进行算例分析。

关键词: 犹豫模糊集, 2型犹豫q阶三角不确定语言集, Muirhead平均算子, 多属性决策

Abstract: In order to describe the multi-layer hesitation of decision-makers in multi-attribute decision-making problems, the type-2 hesitant q-rung triangular uncertain linguistic set is defined by combining hesitant fuzzy set, q-rung triangular hesitant fuzzy set and q-rung hesitant fuzzy uncertain linguistic set. Based on the Schweizer-Sklar norm, the operation laws and properties of the type-2 hesitant q-rung triangular uncertain linguistic fuzzy elements are discussed. In addition, in order to better handle the practical problem with interrelated evaluation attributes, the Muirhead mean operator is extended to the type-2 hesitant q-rung triangular uncertain linguistic set, and the type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead mean operator and its weighted form are proposed. Moreover, the calculation formulae of the operators are given and their properties are discussed. Finally, a multi-attribute decision-making problem model based on the type-2 q-rung hesitant triangular fuzzy uncertain linguistic weighted Muirhead mean operator is established and further analyzed by a numerical example.

Key words: hesitant fuzzy set, type-2 hesitant q-rung triangular uncertain linguistic set, Muirhead mean operator, multi-attribute decision making

中图分类号:

O159

吕笑凡,袁修久,李京泰,赵学军. 2型犹豫q阶三角不确定语言Schweizer-Sklar-Muirhead算子[J]. 《山东大学学报(理学版)》, 2026, 61(1): 116-126.

LÜ Xiaofan, YUAN Xiujiu, LI Jingtai, ZHAO Xuejun. Type-2 hesitant q-rung triangular uncertain linguistic Schweizer-Sklar-Muirhead operators[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(1): 116-126.

参考文献

[1] 徐泽水,赵华. 犹豫模糊集理论及应用[M]. 北京:科学出版社,2018. XU Zeshui, ZHAO Hua. Hesitant fuzzy sets theory and applications[M]. Beijing: Science Press, 2018.
[2] WEI Guiwu. Hesitant fuzzy prioritized operators and their application to multiple attribute decision making[J]. Knowledge-Based Systems, 2012, 31:176-182.
[3] LIU Peide, WANG Peng. Some q-rung orthopair fuzzy aggregation operators and their applications to multiple-attribute decision making[J]. International Journal of Intelligent Systems, 2018, 33(2):259-280.
[4] ALWAER H, CLEMENTS-CROOME D J. Key performance indicators(KPIs)and priority setting in using the multi-attribute approach for assessing sustainable intelligent buildings[J]. Building and Environment, 2010, 45(4):799-807.
[5] ZADEH L A. Fuzzy sets[J]. Information and Control, 1965, 8(3):338-353.
[6] BELLMAN R E, ZADEH L A. Decision-making in a fuzzy environment[J]. Management Science, 1970, 17(4):141-164.
[7] TRIANTAPHYLLOU E, LIN C T. Development and evaluation of five fuzzy multiattribute decision-making methods[J]. International Journal of Approximate Reasoning, 1996, 14(4):281-310.
[8] LIU Weishu, LIAO Huchang. A bibliometric analysis of fuzzy decision research during 1970—2015[J]. International Journal of Fuzzy Systems, 2017, 19:1-14.
[9] TORRA V. Hesitant fuzzy sets[J]. International Journal of Intelligent Systems, 2010, 25(6):529-539.
[10] ZHU Bin, XU Zeshui, XIA Meimei. Dual hesitant fuzzy sets[J]. Journal of Applied Mathematics, 2012, 5:1-13.
[11] 徐玥,刘练珍. q阶犹豫模糊集及其在决策中的应用[J]. 模式识别与人工智能,2018,31(9):816-836. XU Yue, LIU Lianzhen. q-rung hesitant fuzzy fets and its application to multi-criteria decision-making[J]. Pattern Recognition and Artificial Intelligence, 2018, 31(9):816-836.
[12] 任耀军,袁修久,黄林. q阶三角犹豫模糊BM算子及其多属性决策应用[J]. 系统工程与电子技术,2022,44(1):181-191. REN Yaojun, YUAN Xiujiu, HUANG Lin. q-rung hesitant triangular fuzzy BM operator and its application in multipe criteria decision making[J]. Systems Engineering and Electronics, 2022, 44(1):181-191.
[13] WANG Jianqiang, WANG Dandan, ZHANG Hongyu, et al. Multi-criteria group decision making method based on interval 2-tuple linguistic information and Choquet integral aggregation operators[J]. Soft Computing, 2015, 19:389-405.
[14] LIU Peide, JIN Fang. Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision making[J]. Information Sciences, 2012, 205:58-71.
[15] CHIAO Kuoping. Multi-criteria decision making with interval type 2 fuzzy Bonferroni mean[J]. Expert Systems with Applications, 2021, 176:114789.
[16] GARG H, NAZ S, ZIAA F, et al. A ranking method based on Muirhead mean operator for group decision making with complex interval-valued q-rung orthopair fuzzy numbers[J]. Soft Computing, 2021, 25(22):14001-14027.
[17] RANI P, MISHRA A R. Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection[J]. Expert Systems with Applications, 2021, 182:115267.
[18] HUANG Lin, YUAN Xiujiu, REN Yaojun. The q-rung orthopair hesitant fuzzy uncertain linguistic aggregation operators and their application in multi-attribute decision making[J]. IEEE Access, 2020, 8:187084-187113.
[19] MUIRHEAD R F. Some methods applicable to identities and inequalities of symmetric algebraic functions of n letters[J]. Proceedings of the Edinburgh Mathematical Society, 1902, 21:144-162.
[20] VAN LAARHOVEN P J M, PEDRYCZ W. A fuzzy extension of Saatys priority theory[J]. Fuzzy Sets and Systems, 1983, 11(1/3):229-241.
[21] XU Zeishui. Fuzzy harmonic mean operators[J]. International Journal of Intelligent Systems, 2009, 24(2):152-172.
[22] SCHWEIZER B. Associative functions and abstract semigroups[J]. Publicationes Mathematicae(Debrecen), 1963, 10:69-81.
[23] XIA Meimei, XU Zeishui. Hesitant fuzzy information aggregation in decision making[J]. International Journal of Approximate Reasoning, 2011, 52(3):395-407.

相关文章 13

[1]	江立辉,徐金辉,陈华友. 区间犹豫梯形模糊Choquet Muirhead平均算子及其在多属性决策中的应用[J]. 《山东大学学报(理学版)》, 2025, 60(8): 34-51.
[2]	郑颖春,周婉婷. 直觉犹豫模糊软专家集及其在决策中的应用[J]. 《山东大学学报(理学版)》, 2025, 60(1): 111-119.
[3]	杜文胜. q-阶正交模糊自对偶聚合算子及其应用[J]. 《山东大学学报(理学版)》, 2025, 60(1): 120-126.
[4]	吴维,张贤勇,杨霁琳. 广义区间值q阶orthopair犹豫模糊软集及其多属性决策[J]. 《山东大学学报(理学版)》, 2025, 60(1): 101-110.
[5]	刘梦迪,张贤勇,莫智文. 基于改进距离测度的概率犹豫模糊多属性群决策新方法[J]. 《山东大学学报(理学版)》, 2024, 59(3): 118-126.
[6]	周宇,周礼刚,林志超,徐鑫. 概率q阶犹豫模糊TODIM方法及其应用[J]. 《山东大学学报(理学版)》, 2023, 58(6): 9-17.
[7]	苏晓艳,陈京荣,尹会玲. 广义区间值Pythagorean三角模糊集成算子及其决策应用[J]. 《山东大学学报(理学版)》, 2022, 57(8): 77-87.
[8]	黄林,袁修久,索中英,庞梦洋,包壮壮,李智伟. 区间值q阶犹豫模糊Frank集成算子及其决策应用[J]. 《山东大学学报(理学版)》, 2021, 56(3): 54-66.
[9]	杜文胜,徐涛. 广义正交模糊混合平均算子及其在多属性决策中的应用[J]. 《山东大学学报(理学版)》, 2021, 56(1): 35-42.
[10]	王中兴,唐芝兰,牛利利. 基于相对优势度的区间直觉模糊多属性决策方法[J]. J4, 2012, 47(9): 92-97.
[11]	章玲,周德群 . λ模糊测度及其Mbius变换和关联系数间关系的推导[J]. J4, 2007, 42(7): 33-37 .
[12]	张方伟,曲淑英,王志强,姚炳学,曾现洋 . 偏差最小化方法及其在多属性决策中的应用[J]. J4, 2007, 42(3): 32-35 .
[13]	胡明礼,刘思峰 . 不完全信息下概率决策的扩展粗糙集方法[J]. J4, 2006, 41(6): 93-98 .

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed