Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

doi:10.23919/JSEE.2024.000019

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (1): 178-185.doi: 10.23919/JSEE.2024.000019

• SYSTEMS ENGINEERING • Previous Articles

Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

Youliang LIN¹(), Wu LI²^,*(), Gang LIU³(), Dong HUANG³()

¹ School of Economics and Management, Hunan Institute of Science and Technology, Yueyang 414000, China
² Hunan Vocational College for Nationalities, Yueyang 414000, China
³ School of Information Science and Engineering, Hunan Institute of Science and Technology, Yueyang 414000, China

Received:2021-10-18 Online:2024-02-18 Published:2024-03-05
Contact: Wu LI E-mail:linyouliang_cn@163.com;liwu0817@163.con;liugang@hnist.edu.cn;huangdong2318@163.com
About author:
LIN Youliang was born in 1979. He received his Ph.D. degree from Center South University in 2018. He is an associate professor at Hunan Institute of Science and Technology. His main research interest is decision analysis and evaluation. E-mail: linyouliang_cn@163.com

LI Wu was born in 1977. He received his Ph.D. degree from Huazhong University of Science and Technology in 2009. He is a professor at Hunan Vocational College for Nationalities. His main research interests are decision analysis and system engineering. E-mail: liwu0817@163.con

LIU Gang was born in 1983. He received his B.S. and M.S. degrees from Naval Arms Command Institute, China in 2005 and 2008, respectively, and Ph.D. degree from National University of Defense Technology, China, 2013. Now he is the Deputy Dean of the School of Information Science and Engineering, Hunan Institute of Science and Technology. His research interests include intelligent information processing, optimization and path planning. E-mail: liugang@hnist.edu.cn

HUANG Dong was born in 1990. He received his B.S., M.S. and Ph.D. degrees from China University of Petroleum, Beijing, China, in 2013, 2015 and 2018 respectively. Now he works in the School of Information Science and Engineering, Hunan Institute of Science and Technology. His main research interests are modeling, control and optimization of complex systems. E-mail: huangdong2318@163.com
Supported by:
This work was supported by the Natural Science Foundation ofHunan Province(2023JJ50047;2023JJ40306), the Research Foundation of Education Bureau of Hunan Province(23A0494;20B260), and the Key R & D Projects of Hunan Province(2019SK2331).

Abstract

Abstract:

Aiming at the triangular fuzzy (TF) multi-attribute decision making (MADM) problem with a preference for the distribution density of attribute (DDA), a decision making method with TF number two-dimensional density (TFTD) operator is proposed based on the density operator theory for the decision maker (DM). Firstly, a simple TF vector clustering method is proposed, which considers the feature of TF number and the geometric distance of vectors. Secondly, the least deviation sum of squares method is used in the program model to obtain the density weight vector. Then, two TFTD operators are defined, and the MADM method based on the TFTD operator is proposed. Finally, a numerical example is given to illustrate the superiority of this method, which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

Key words: fuzzy decision making, clustering, density operator, multi-attribute decision making (MADM)

Youliang LIN, Wu LI, Gang LIU, Dong HUANG. Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method[J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 178-185.

Figures/Tables 8

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Table 1

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Table 7

References 33

1	YAGER R R On the fusion of multiple multi-criteria aggregation functions with focus on the fusion of OWA aggregations. Knowledge-Based Systems, 2020, 191, 105216.
2	LIU H, LIN C Y Optimization for multi-objective location-routing problem of cross-docking with fuzzy time windows. Journal of University of Electronic Science and Technology of China (Social Sciences Edition), 2019, 21 (5): 72- 78, 112.
3	XU X H, HOU Y Z Research status and development trend of large group risk decision making theory and method. Journal of University of Electronic Science and Technology of China (Social Sciences Edition), 2021, 23 (4): 1- 6.
4	WALLENIUS J, DYER J S, FISHBURN P C, et al Multiple criteria decision making, multi-attribute utility theory: recent accomplishments and what lies ahead. Management Science, 2008, 54 (7): 1336- 1349. doi: 10.1287/mnsc.1070.0838
5	MEDINA J, YAGER R R. OWA operators with functional weights. Fuzzy Sets and Systems, 2020, 414(1): 38−56.
6	MARTHA F S, EZEQUIEL A O, JOSE M M, et al. Volatility GARCH models with the ordered weighted average (OWA) operators. Information Sciences, 2021, 565(3): 46−61.
7	SEVASTIANOV P Numerical methods for interval and fuzzy number comparison based on the probabilistic approach and Dempster-Shafer theory. Information Sciences, 2007, 177 (21): 4645- 4661. doi: 10.1016/j.ins.2007.05.001
8	WANG Y J Combining grey relation analysis with FMCGDM to evaluate financial performance of Taiwan container lines. Expert Systems with Applications, 2009, 36 (2): 2424- 2432. doi: 10.1016/j.eswa.2007.12.027
9	ZHAO J, WANG Y J, ZHAO Q, et al Evaluation of distribution center location by FMCGDM based on extended fuzzy preference relation. Journal of Marine Science and Technology, 2020, 28 (1): 41- 50.
10	TIAN M, HE Y Y, LIU S F Extension of TOPSIS for fuzzy multi-attribute decision making problem based on experimental analysis. Journal of Systems Engineering and Electronics, 2010, 21 (3): 416- 422. doi: 10.3969/j.issn.1004-4132.2010.03.011
11	WANG Y J The evaluation of financial performance for Taiwan container shipping companies by fuzzy TOPSIS. Applied Soft Computing, 2014, 22, 28- 35. doi: 10.1016/j.asoc.2014.03.021
12	AFRANE S, AMPAH J D, JIN C, et al. Techno-economic feasibility of waste-to-energy technologies for investment in Ghana: a multicriteria assessment based on fuzzy TOPSIS approach. Journal of Cleaner Production, 2021, 318: 128515.
13	RUI Z F, LI D F Fuzzy distances based FMAGDM compromise ratio method and application. Journal of Systems Engineering and Electronics, 2010, 21 (3): 455- 460. doi: 10.3969/j.issn.1004-4132.2010.03.016
14	LIU J P, LINS, CHEN H Y Fuzzy Bonferroni mean operator and its application to multi-criteria group decision making. Systems Engineering and Electronics, 2012, 34 (1): 115- 119.
15	QIN Y C, QI Q F, SCOTT P J, et al An additive manufacturing process selection approach based on fuzzy Archimedean weighted power Bonferroni aggregation operators. Robotics and Computer-Integrated Manufacturing, 2020, 64, 101926.
16	LIU H C, FAN X J, LI P, el Evaluating the risk of failure modes with extended MULTIMOORA method under fuzzy environment. Engineering Applications of Artificial Intelligence, 2014, 34, 168- 177. doi: 10.1016/j.engappai.2014.04.011
17	CHEN Y, RAN Y, HUANG G, et al A new integrated MCDM approach for improving QFD based on DEMATEL and extended MULTIMOORA under uncertainty environment. Applied Soft Computing, 2021, 105, 107222.
18	WANG F, LI H Novel method for hybrid multiple attribute decision making based on TODIM method. Journal of Systems Engineering and Electronics, 2015, 26 (5): 1023- 1031. doi: 10.1109/JSEE.2015.00111
19	TIAN X L, LI W Q, LIU L, et al Development of TODIM with different types of fuzzy sets: a state-of-the-art survey. Applied Soft Computing, 2021, 111, 107661.
20	SAYADI M K, HEYDARI M, SHAHANAGHI K Extension of VIKOR method for decision making problem with interval numbers. Applied Mathematical Modelling, 2009, 33 (5): 2257- 2262. doi: 10.1016/j.apm.2008.06.002
21	JIANG W Q, SHANG J Multi-criteriagroup decision making with fuzzy data: an extension of the VIKOR method. Journal of Systems Engineering and Electronics, 2015, 26 (4): 764- 773.
22	AKRAM M, KAHRAMAN C, ZAHID K Group decision-making based on complex spherical fuzzy VIKOR approach. Knowledge-Based Systems, 2021, 216, 106793.
23	HUANG Z L, LUO J Similarity programming model for triangular fuzzy number-based uncertain multi-attribute decision making and its application. Systems Engineering and Electronics, 2016, 38 (5): 1100- 1106.
24	JIANG D Y, ZHANG X J Multi attribute group decision making of triangular fuzzy numbers based on TFNCD operator. Systems Engineering and Electronics, 2019, 41 (9): 2065- 2071.
25	DONG J Y, WAN S P, CHEN S M. Fuzzy best-worst method based on triangular fuzzy numbers for multi-criteria decision-making. Information Sciences, 2021, 547: 1080−1104.
26	XU X Q, YANG K W, DOU Y J, et al High-end equipment development task decomposition and scheme selection method. Journal of Systems Engineering and Electronics, 2021, 32 (1): 118- 135.
27	LI Z Q, DOU Y J, XIA B Y, et al System portfolio selection based on GRA method under hesitant fuzzy environment. Journal of Systems Engineering and Electronics, 2022, 33 (1): 120- 133.
28	YI P T, GUO Y J, ZHANG D N Density weighted averaging middle operator and application in multi-attribute decision making. Control and Decision, 2007, 22 (5): 515- 524.
29	LIU P D, YU X C Density aggregation operators based on the intuitionistic trapezoidal fuzzy numbers for multiple attribute decision making. Technological and Economic Development of Economy, 2013, 19, 454- 470.
30	LIN Y L, LI W, HAN Q L Intuitionistic fuzzy number density aggregation operator and its application. Control and Decision, 2017, 32 (6): 1026- 1032.
31	ZHANG F M, GUO Y J, YI P T A method of group evaluation information aggregation based on two-dimensional density operator. Journal of Systems & Management, 2009, 18 (4): 397- 401.
32	LI Y, CHEN Y Y, LI Q A clustering algorithm for triangular fuzzy normal random variables. International Journal of Fuzzy Systems, 2020, 22 (7): 2083- 2100. doi: 10.1007/s40815-020-00933-7
33	LIN Y L, HAN Q L, LI W Triangular fuzzy number density operator and its application. Statistics and Decision, 2017, 32 (6): 1026- 1032.

$ \lambda $	Feature of $ {\xi }_{i} $	Definition
0	$ \xi_m $=1	Complete preference for low information density attributes
(0, 0 .5)	$ \xi $₁$ \leqslant\xi $₂$ \leqslant \cdots \leqslant \xi $_m	Prefer attributes with low information density
0 .5	$ {\xi }_{1}={\xi }_{2}=\cdots ={\xi }_{m} $	Equal preference for each attribute
(0 .5, 1)	$ \xi_m $$ \leqslant\xi_{m-1} $$ \leqslant \cdots \leqslant \xi _1$	Prefer attributes with high information density
1	$ \xi $₁=1	Complete preference for high information density attributes

Attribute	E1					E2					E3
Attribute	1st	2nd	3rd	4th	5th	lst	2nd	3rd	4th	5th	lst	2nd	3rd	4th	5th
F1	27.84	26.69	25.47	23.67	19.13	41.86	39.68	34.22	47.79	40.91	60.05	57.10	56.87	54.36	55.33
F2	66.52	1.05	50.26	44.70	35.57	62.10	81.79	97.61	115.87	129.04	201.70	203.33	218.06	68.04	73.31
F3	19.63	18.57	16.90	15.47	12.44	25.01	26.72	25.34	33.84	31.06	46.27	44.58	45.11	30.22	31.53
F4	42.91	48.19	49.00	48.34	45.61	51.27	45.32	40.30	47.38	43.64	39.65	39.99	41.60	57.94	52.85
F5	133.05	107.51	104.07	106.87	119.25	95.04	120.64	148.15	111.06	129.14	152.20	150.05	140.38	72.60	89.21
F6	238.92	228.73	197.32	188.85	185.91	148.34	206.15	285.22	242.46	315.47	335.88	356.11	383.43	125.16	132.49
S1	104.02	94.65	118.86	128.23	196.13	336.43	333.38	342.18	221.46	213.69	130.00	125.48	124.23	172.43	194.11
S2	96.05	0.39	114.79	121.62	189.50	314.37	315.62	317.21	207.74	202.04	121.73	119.20	117.86	166.62	185.76
S3	9.54	14.58	44.92	42.85	6.70	21.05	22.12	17.79	14.22	19.55	15.89	20.57	23.69	16.61	33.85
S4	9.93	13.85	53.39	54.95	13.15	70.82	73.75	60.88	31.50	41.78	20.66	25.81	29.43	28.65	65.70
S5	3.86	-5.65	15.87	22.01	49.01	70.28	70.00	70.78	54.85	53.20	23.08	20.31	19.50	42.00	48.48
T1	1.83	0.89	0.95	0.79	0.98	3.10	2.68	2.63	1.54	1.66	1.84	1.55	1.43	1.22	1.96
T2	0.94	1.03	1.00	1.09	1.40	2.58	2.19	1.63	1.72	2.22	3.00	3.22	3.68	3.41	3.65
T3	88.96	87.26	86.84	98.08	121.47	147.68	128.87	125.12	11.81	132.78	76.96	78.98	71.82	97.71	96.57
T4	14.14	12.07	11.28	11.99	12.64	30.13	27.96	25.56	28.12	30.61	27.89	27.06	23.85	22.34	25.19
T5	24.77	23.29	22.12	23.21	23.24	61.82	51.13	42.82	53.43	54.31	46.21	45.10	40.85	53.12	53.43
P1	3.58	8.00	11.23	14.59	25.28	12.40	9.62	5.43	12.02	13.95	10.09	6.46	5.86	14.06	14.10
P2	-3.19	-0.90	3.92	8.13	19.28	9.80	6.06	2.92	9.59	10.89	6.36	0.83	1.36	10.47	11.14
P3	17.42	22.52	23.88	28.44	45.19	18.12	13.37	12.50	14.61	18.16	17.16	9.00	13.37	13.99	20.39
P4	17.05	18.67	21.42	26.43	38.21	13.92	10.80	9.73	12.77	13.69	14.81	8.61	12.13	11.73	17.28
P5	2.41	2.25	2.42	3.17	4.83	4.19	3.02	2.49	3.59	4.19	4.13	2.33	2.89	2.62	4.35

Attribute	E1	E2	E3
F1	(0.268,0.330,0.358)	(0.481,0.550,0.628)	(0.714,0.764,0.800)
F2	(0.206,0.265,0.316)	(0.281,0.541,0.846)	(0.480,0.732,0.912)
F3	(0.271,0.318,0.350)	(0.445,0.555,0.706)	(0.630,0.755,0.829)
F4	(0.509,0.565,0.604)	(0.494,0.582,0.620)	(0.504,0.578,0.639)
F5	(0.454,0.554,0.627)	(0.425,0.585,0.655)	(0.426,0.571,0.681)
F6	(0.382,0.492,0.569)	(0.339,0.574,0.810)	(0.340,0.596,0.767)
S1	(0.257,0.364,0.562)	(0.612,0.805,0.905)	(0.324,0.425,0.559)
S2	(0.259,0.368,0.568)	(0.606,0.801,0.904)	(0.330,0.429,0.569)
S3	(0.169,0.534,0.891)	(0.296,0.506,0.751)	(0.345,0.564,0.854)
S4	(0.133,0.377,0.790)	(0.453,0.714,0.951)	(0.278,0.438,0.832)
S5	(−0.077,0.211,0.563)	(0.611,0.843,0.958)	(0.260,0.397,0.579)
T1	(0.276,0.352,0.453)	(0.604,0.753,0.837)	(0.455,0.536,0.713)
T2	(0.231,0.263,0.311)	(0.393,0.500,0.634)	(0.738,0.819,0.887)
T3	(0.471,0.527,0.595)	(0.628,0.708,0.782)	(0.408,0.462,0.549)
T4	(0.296,0.310,0.326)	(0.686,0.711,0.743)	(0.590,0.630,0.664)
T5	(0.292,0.313,0.350)	(0.678,0.702,0.763)	(0.570,0.637,0.674)
P1	(0.219,0.602,0.815)	(0.394,0.556,0.757)	(0.425,0.507,0.616)
P2	(−0.263,0.328,0.778)	(0.439,0.678,0.980)	(0.134,0.403,0.640)
P3	(0.572,0.770,0.856)	(0.344,0.451,0.595)	(0.325,0.424,0.564)
P4	(0.643,0.792,0.866)	(0.310,0.414,0.525)	(0.371,0.430,0.558)
P5	(0.379,0.526,0.625)	(0.542,0.618,0.682)	(0.480,0.572,0.650)

Group	E1	E2	E3
$ {{\boldsymbol{A}}}_{1} $	(0.357,0.547,0.684)	(0.424,0.573,0.708)	(0.426,0.564,0.694)
$ {{\boldsymbol{A}}}_{2} $	(0.248,0.304,0.341)	(0.402,0.549,0.727)	(0.608,0.75,0.847)
$ {{\boldsymbol{A}}}_{3} $	(0.317,0.63,0.833)	(0. 364,0.514,0.7)	(0.277,0.419, 0.587)
$ {{\boldsymbol{A}}}_{4} $	(0.258,0.366,0.565)	(0.609,0.803,0.905)	(0.327,0.427,0.564)
$ {{\boldsymbol{A}}}_{5} $	(0.294,0.311,0.337)	(0.682,0.707,0.752)	(0.581,0.633,0.669)
$ {{\boldsymbol{A}}}_{6} $	(0.133,0.377,0.79)	(0.453,0.714,0.951)	(0.278,0.438,0.832)
$ {{\boldsymbol{A}}}_{7} $	(−0.077,0.211,0.563)	(0.611,0.843,0.958)	(0.26,0.397,0.579)
$ {{\boldsymbol{A}}}_{8} $	(0.276,0.352,0.453)	(0.604,0.753,0.837)	(0.455,0.536,0.713)
$ {{\boldsymbol{A}}}_{9} $	(0.231,0.263,0.311)	(0. 393,0.5,0.634)	(0.738,0.819,0.887)
$ {{\boldsymbol{A}}}_{10} $	(0.471,0.527,0.595)	(0.628,0.708,0.782)	(0.408,0.462,0.549)

Enterprise	Value
E1	(0.279,0.424,0.563)
E2	(0.49,0.633,0.767)
E3	(0.452,0.564,0.69)

Method for triangular fuzzy multiple attribute decision making based on two-dimensional density operator method

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λ	ξ_j
λ	$ {\xi }_{1} $	$ {\xi }_{2} $=$ {\xi }_{3} $	$ {\xi }_{4} $=$ {\xi }_{5} $	$ {\xi }_{6} $=$ {\xi }_{7} $=$ {\xi }_{8} $=$ {\xi }_{9} $=$ {\xi }_{10} $
0.9	0.43	0.2	0.035	0
0.7	0.1982	0.16545	0.1218	0.04546
0.5	0.1	0.1	0.1	0.1
0.3	0.02	0.03445	0.07815	0.15456
0.1	0	0	0	0.2

λ	E1	E2	E3
0.9	(0.286,0.446,0.561)	(0.381,0.512,0.648)	(0.442,0.549,0.642)
0.7	(0.279,0.424,0.563)	(0.49,0.633,0.767)	(0.452,0.564,0.69)
0.5	(0.251,0.389,0.547)	(0.517,0.666,0.795)	(0.436,0.545,0.692)
0.3	(0.23,0.363,0.544)	(0.551,0.71,0.836)	(0.427,0.535,0.706)
0.1	(0.207,0.346,0.542)	(0.538,0.704,0.832)	(0.428,0.53,0.712)

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