q阶三角犹豫模糊BM算子及其多属性决策应用

doi:10.12305/j.issn.1001-506X.2022.01.23

摘要/Abstract

摘要：

为解决更为广泛的模糊决策问题, 同时使决策信息与人的认知思维更为贴近, 结合q阶犹豫模糊集和三角模糊数, 提出了q阶三角犹豫模糊集的概念并定义了q阶三角犹豫模糊集运算。为了刻画信息集成过程中评价信息之间存在的关联关系, 将Bonferroni平均算子推广至q阶三角犹豫模糊集, 提出了q阶三角犹豫模糊Bonferroni平均算子。为了刻画更多的关联关系, 将广义Bonferroni平均算子推广至q阶三角犹豫模糊集, 提出了q阶三角犹豫模糊广义Bonferroni平均算子。考虑不同属性的评价信息的重要程度不同, 提出了其加权形式。最后, 提出了q阶三角犹豫模糊环境下的多属性决策方法, 并以算例验证了实验结果。

关键词: q阶三角犹豫模糊集, Bonferroni平均算子, 广义Bonferroni平均算子, 多属性决策

Abstract:

In order to solve a wider range of fuzzy decision-making problems, and at the same time make decision information closer to human cognitive thinking, combining q-rung hesitant fuzzy sets and triangular fuzzy numbers, the concept of q-rung hesitant triangular fuzzy sets is proposed and the operation of q-rung hesitant triangular fuzzy sets is defined. In order to describe the relationship between evaluation information in the process of information integration, the Bonferroni mean operator is extend to the q-rung hesitant triangular fuzzy set, and the q-rung hesitant triangular fuzzy Bonferroni mean operator is proposed. In order to describe more correlations, the generalized Bonferroni mean operator is extend to the q-rung hesitant triangular fuzzy set, and the q-rung hesitant triangular fuzzy generalized Bonferroni mean operator is proposed. Considering that the importance of different attributes of evaluation information is different, their weighted form is proposed. In the end, a multi-attribute decision-making method under q-rung hesitant triangular fuzzy environment is proposed and verified the experimental results by an example.

Key words: q-rung hesitant triangular fuzzy set, Bonferroni mean operator, generalized Bonferroni mean operator, multiple criteria decision-making

中图分类号:

TP311

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.

Yaojun REN, Xiujiu YUAN, Lin HUANG. q-rung hesitant triangular fuzzy BM operator and its application in multiple criteria decision making[J]. Systems Engineering and Electronics, 2022, 44(1): 181-191.

图/表 5

图1

表1

表2

表3

表4

排序结果"

算子	参数选择	得分函数	排序结果
q-HTFWBM	s=1, t=1	S(h₁)=(0.171 1, 0.220 7, 0.274 2), S(h₂)=(0.193 6, 0.250 9, 0.310 0), S(h₃)=(0.160 9, 0.207 8, 0.261 4), S(h₄)=(0.180 1, 0.229 5, 0.286 0), S(h₅)=(0.166 2, 0.215 4, 0.275 4)	(2, 4, 1, 5, 3)
q-HTFWBM	s=1, t=2	S(h₁)=(0.192 6, 0.243 4, 0.298 9), S(h₂)=(0.201 8, 0.258 5, 0.318 2), S(h₃)=(0.176 3, 0.224 4, 0.279 5), S(h₄)=(0.200 4, 0.251 2, 0.308 9), S(h₅)=(0.187 4, 0.237 8, 0.302 4)	(2, 4, 1, 5, 3)
q-HTFWBM	s=2, t=2	S(h₁)=(0.184 3, 0.235 8, 0.291 4), S(h₂)=(0.203 3, 0.258 8, 0.318 4), S(h₃)=(0.174 8, 0.223 0, 0.278 7), S(h₄)=(0.196 1, 0.247 7, 0.304 6), S(h₅)=(0.183 0, 0.233 9, 0.297 0)	(2, 4, 5, 1, 3)
q-HTFGWBM	s=1, t=1, r=1	S(h₁)=(0.374 2, 0.470 8, 0.569 0), S(h₂)=(0.389 3, 0.499 2, 0.596 7), S(h₃)=(0.338 6, 0.434 9, 0.539 9), S(h₄)=(0.389 5, 0.486 4, 0.586 8), S(h₅)=(0.370 8, 0.466 9, 0.578 9)	(2, 4, 5, 1, 3)
q-HTFGWBM	s=1, t=1, r=2	S(h₁)=(0.391 4, 0.484 9, 0.581 0), S(h₂)=(0.404 8, 0.511 6, 0.607 5), S(h₃)=(0.351 6, 0.445 8, 0.549 5), S(h₄)=(0.403 8, 0.498 5, 0.596 5), S(h₅)=(0.387 6, 0.480 9, 0.592 6)	(2, 4, 5, 1, 3)
q-HTFGWBM	s=1, t=2, r=2	S(h₁)=(0.402 0, 0.493 3, 0.587 7), S(h₂)=(0.414 2, 0.518 7, 0.613 4), S(h₃)=(0.359 5, 0.452 2, 0.554 9), S(h₄)=(0.412 5, 0.505 6, 0.601 8), S(h₅)=(0.397 9, 0.489 1, 0.600 3)	(2, 4, 5, 1, 3)
q-HTFGWBM	s=2, t=2, r=2	S(h₁)=(0.409 3, 0.498 9, 0.592 0), S(h₂)=(0.420 4, 0.523 4, 0.617 1), S(h₃)=(0.364 9, 0.456 4, 0.558 3), S(h₄)=(0.418 4, 0.510 2, 0.605 2), S(h₅)=(0.404 9, 0.494 3, 0.605 1)	(2, 4, 5, 1, 3)
q-HTFWA	—	S(h₁)=(0.393 0, 0.493 8, 0.599 2), S(h₂)=(0.407 8, 0.519 9, 0.624 7), S(h₃)=(0.407 2, 0.510 1, 0.616 1), S(h₄)=(0.425 5, 0.526 5, 0.632 3), S(h₅)=(0.393 8, 0.494 5, 0.616 7)	(4, 2, 3, 5, 1)
q-HTFWG	—	S(h₁)=(0.320 3, 0.426 9, 0.529 4), S(h₂)=(0.350 8, 0.467 0, 0.567 3), S(h₃)=(0.278 6, 0.388 6, 0.499 9), S(h₄)=(0.341 2, 0.446 6, 0.556 0), S(h₅)=(0.308 5, 0.416 4, 0.527 0)	(2, 4, 1, 5, 3)
DHq-ROFWMM^[29]	P=(1, 1, 0, 0)	S(h₁^L)=0.203 1, S(h₂^L)=0.235 8, S(h₃^L)=0.195 6, S(h₄^L)=0.212 6, S(h₅^L)=0.199 1 S(h₁^M)=0.220 7, S(h₂^M)=0.250 9, S(h₃^M)=0.207 8, S(h₄^M)=0.229 5, S(h₅^M)=0.215 4 S(h₁^R)=0.242 2, S(h₂^R)=0.267 8, S(h₃^R)=0.226 7, S(h₄^R)=0.253 5, S(h₅^R)=0.242 5	(2, 4, 1, 5, 3) (2, 4, 1, 5, 3) (2, 4, 5, 1, 3)

表4

参考文献 29

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网络系统	评估因素
网络系统	M₁	M₂	M₃	M₄
A₁	〈{(0.6, 0.7, 0.8), (0.7, 0.8, 0.9)}, {(0.4, 0.5, 0.6)}〉	〈{(0.3, 0.4, 0.5)}, {(0.7, 0.8, 0.9)}〉	〈{(0.4, 0.5, 0.6)}, {(0.5, 0.6, 0.7), (0.6, 0.7, 0.8)}〉	〈{(0.3, 0.4, 0.5), (0.4, 0.5, 0.6)}, {(0.6, 0.7, 0.8), (0.7, 0.8, 0.9)}〉
A₂	〈{(0.4, 0.5, 0.6)}, {(0.4, 0.5, 0.6), (0.5, 0.6, 0.8)}〉	〈{(0.6, 0.7, 0.8), (0.7, 0.8, 0.9)}, {(0.3, 0.4, 0.5), (0.4, 0.5, 0.6)}〉	〈{(0.4, 0.6, 0.7), (0.6, 0.7, 0.8)}{(0.2, 0.3, 0.4), (0.3, 0.4, 0.5)}〉	〈{(0.3, 0.4, 0.5)}, {(0.6, 0.7, 0.8)}〉
A₃	〈{(0.5, 0.6, 0.7), (0.6.0.7.0.8)}, {(0.4, 0.5, 0.6), (0.5, 0.6, 0.7)}〉	〈{(0.1, 0.2, 0.3), (0.2, 0.3, 0.4)}, {(07, 0.8, 0.9)}〉	〈{(0.5, 0.6, 0.7)}, {(0.4, 0.5, 0, 6), (0.6, 0.7, 0.8)}〉	〈{(0.3, 0.4, 0.5), (0.4, 0.5, 0.6)}, {(0.5, 0.7, 0.8), (0.7, 0.8, 0.9)}〉
A₄	〈{(0.6, 0.7, 0.8), (0.7, 0.8, 0.9)}, {(0.4, 0.5, 0.6)}〉	〈{(0.2, 0.3, 0.5), (0.4, 0.5, 0.6)}, {(0.6, 0.7, 0.8)}〉	〈{(0.3, 0.4, 0.5), (0.4, 0.5, 0.6)}, {(0.5, 0.6, 0.7), (0.6, 0.7, 0.8)}〉	〈{(0.4, 0.5, 0.6)}, {(0.6, 0.7, 0.8), (0.7, 0.8, 0.9)}〉
A₅	〈{(0.5, 0.6, 0.8), (0.7, 0.8, 0.9)}, {(0.3, 0.4, 0.5), (0.4, 0.5, 0.6)}〉	〈{(0.3, 0.4, 0.5), (0.5, 0.6, 0.7)}, {(0.5, 0.6, 0.7), (0.6, 0.7, 0.8)}〉	〈{(0.2, 0.3, 0.4)}, {(0.6, 0.7, 0.8)}〉	〈{(0.3, 0.4, 0.5)}, {(0.7, 0.8, 0.9)}〉

综合评估	取值
h₁	〈{(0.263 6, 0.330 5, 0.401 2), (0.285 0, 0.351 8, 0.423 1), (0.285 7, 0.355 9, 0.432 4), (0.308 6, 0.378 5, 0.455 5)}, {(0.870 8, 0.904 7, 0.935 7), (0.882 5, 0.915 7, 0.946 7), (0.876 7, 0.909 9, 0.940 4), (0.888 4, 0.920 8, 0.951 5)}〉
h₂	〈{(0.271 1, 0.346 9, 0.418 5), (0.293 2, 0.360 0, 0.433 3), (0.292 2, 0.370 6, 0.448 7), (0.313 9, 0.383 4, 0.463 1)}, {(0.803 6, 0.849 2, 0.887 8), (0.814 3, 0.857 0, 0.893 9), (0.815 7, 0.859 0, 0.896 0), (0.826 3, 0.866 7, 0.902 0), (0.816 1, 0.860 5, 0.909 6), (0.826 4, 0.868 0, 0.915 1), (0.827 5, 0.869 7, 0.916 7), (0.837 5, 0.876 9, 0.922 0)}〉
h₃	〈{(0.243 1, 0.304 1, 0.369 8), (0.263 1, 0.325 0, 0.391 6), (0.246 4, 0.309 5, 0.376 8), (0.265 7, 0.329 5, 0.397 5), (0.265 9, 0.328 6, 0.397 1), (0.286 8, 0.350 4, 0.419 8), (0.269 2, 0.333 9, 0.403 9), (0.289 3, 0.354 7, 0.425 4)}, {(0.852 2, 0.899 1, 0.930 8), (0.875 7, 0.910 0, 0.941 7), (0.865 0, 0.909 9, 0.940 4), (0.888 4, 0.920 8, 0.951 5), (0.862 5, 0.907 5, 0.938 4), (0.884 3, 0.917 7, 0.948 3), (0.875 0, 0.917 8, 0.947 2), (0.896 4, 0.927 8, 0.957 1)}〉
h₄	〈{(0.269 8, 0.334 9, 0.415 1), (0.277 8, 0.343 1, 0.423 1), (0.291 0, 0.358 1, 0.429 7), (0.297 1, 0.364 7, 0.436 8), (0.293 1, 0.361 3, 0.447 5), (0.301 2, 0.369 7, 0.455 5), (0.314 9, 0.384 9, 0.462 4), (0.321 0, 0.391 6, 0.469 5)}, {(0.861 6, 0.896 4, 0.927 8), (0.873 4, 0.907 4, 0.938 6), (0.867 6, 0.901 5, 0.932 4), (0.879 3, 0.912 5, 0.943 3)}〉
h₅	〈{(0.226 3, 0.291 0, 0.384 9), (0.265 1, 0.329 0, 0.425 6), (0.269 3, 0.339 7, 0.415 7), (0.313 7, 0.381 9, 0.458 6)}, {(0.861 2, 0.896 5, 0.928 9), (0.871 4, 0.905 6, 0.937 6), (0.869 7, 0.904 0, 0.935 4), (0.879 3, 0.912 5, 0.943 3)}〉

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