Fuzzy interval linguistic sets with applications in multi-attribute group decision making

doi:10.21629/JSEE.2018.06.11

Journal of Systems Engineering and Electronics ›› 2018, Vol. 29 ›› Issue (6): 1237-1250.doi: 10.21629/JSEE.2018.06.11

• Systems Engineering • Previous Articles Next Articles

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

Xiao LUO^1,*(), Weimin LI¹(), Xuanzi WANG²(), Zhenchong ZHAO¹()

¹ Air and Missile Defense College, Air Force Engineering University, Xi'an 710051, China
² School of Management, Xi'an Jiaotong University, Xi'an 710049, China

Received:2017-09-05 Online:2018-12-25 Published:2018-12-26
Contact: Xiao LUO E-mail:hngz@163.com;weimin_sx@163.com;834628194@qq.com;wwjyzzc@163.com
About author:LUO Xiao was born in 1990. He received his M.S. degree in computer application technology from the Air Force Engineering University in 2015 and now he is studying for his Ph.D. degree in the same school. His research interests include fuzzy decision making and intelligent information processing. E-mail: xiao hngz@163.com|LI Weimin was born in 1964. He received his M.S. degree and Ph.D. degree from University of Electronic Science and Technology of China in 1989 and 1992, respectively. He currently works as a distinguished professor and vice president of Air Force Engineering University, Xi'an, China. His research interests include intelligent information processing and aerospace defense system construction. He is the cochairman of military operational research and executive committee member of National High Technology Research and Development Program (863 Program). E-mail: weimin_sx@163.com|WANG Xuanzi was born in 1990. She received her B.B.A. degree in Xiamen University in 2015 and now she is studying for hev Ph.D. degree in Xi'an Jiaotong University. His research interests include management accounting and corporate social responsibility. E-mail: 834628194@qq.com|ZHAO Zhenchong was born in 1990. He received his M.S. degree in computer software and theory from the Air Force Engineering University in 2015 and now he is studying for his Ph.D. degree in the same school. His research interests include pattern recognition and machine learning. E-mail: wwjyzzc@163.com
Supported by:
the National Natural Science Foundation of China(61273275);This work was supported by the National Natural Science Foundation of China (61273275)

Abstract

Abstract:

Uncertain and hesitant information, widely existing in the real-world qualitative decision making problems, brings great challenges to decision makers. Hesitant fuzzy linguistic term sets (HFLTSs), an effective linguistic computational tool in modeling and eliciting such information, have hence aroused many scholars' interests and some extensions have been introduced recently. However, these methods are based on the discrete linguistic term framework with the limited expression domain, which actually depict qualitative information using several single values. Therefore, it is hard to ensure the integrity of the semantics representation and the accuracy of the computation results. To deal with this problem, a semantics basis framework called complete linguistic term set (CLTS) is designed, which adopts a separation structure of linguistic scale and expression domain, enriching semantics representation of decision makers. On this basis the concept of fuzzy interval linguistic sets (FILSs) is put forward that employs the interval linguistic term with probability to increase the flexibility of eliciting and representing uncertain and hesitant qualitative information. For practical applications, a fuzzy interval linguistic technique for order preference by similarity to ideal solution (FILTOPSIS) method is developed to deal with multi-attribute group decision making (MAGDM) problems. Through the cases of movie and enterprise resource planning (ERP) system selection, the effectiveness and validity of the proposed method are illustrated.

Key words: hesitant fuzzy sets, multi-attribute group decision making (MAGDM), fuzzy interval linguistic set (FILS), hesitant fuzzy linguistic term set (HFLTS), fuzzy linguistic approach

Xiao LUO, Weimin LI, Xuanzi WANG, Zhenchong ZHAO. Fuzzy interval linguistic sets with applications in multi-attribute group decision making[J]. Journal of Systems Engineering and Electronics, 2018, 29(6): 1237-1250.

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References 38

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Movie	$C_1$	$C_2$	$C_3$	$C_4$
$A_1$	$\{s_1 , s_2 , s_3 \}$	$\{s_3 , s_4\}$	$\{s_3 , s_4 , s_5\}$	$\{s_4 , s_5 \}$
$A_2$	$\{s_3 , s_4 , s_5 \} $	$\{s_4 , s_5\}$	$\{s_3 , s_4\}$	$\{s_3 , s_4 , s_5 \}$
$A_3$	$\{s_5 , s_6 \}$	$\{s_4 , s_5 , s_6\}$	$\{s_4 , s_5 \}$	$\{s_5 \}$
$A_4$	$\{s_3 , s_4 , s_5 \}$	$\{s_2 , s_3 , s_4 \}$	$\{s_4 , s_5 , s_6 \}$	$\{s_4 , s_5 \}$
$A_5 $	$\{s_2 , s_3 \}$	$\{s_3 , s_4 , s_5 \}$	$\{s_3 , s_4 , s_5 \}$	$\{s_3 , s_4 \}$

Movie	$C_1$	$C_2$	$C_3$	$C_4$
$A_1$	Between$s_1 $ and $s_3 $	Between $s_3 $ and $s_4 $	Between $s_3 $ and $s_5 $	Between $s_4 $ and $s_5 $
$A_2$	Between $s_3 $ and $s_5$	Between $s_4 $ and $s_5 $	Between $s_3 $ and $s_4 $	Between $s_3 $ and $s_5 $
$A_3$	At least $s_5 $	At least $s_4 $	Between $s_4 $ and $s_5 $	$s_5 $
$A_4$	Between $s_3 $ $and $s_5 $	Between $s_2 $ $and $s_4 $	Between $s_4 $ $and $s_6 $	Between $s_4 $ $and $s_5 $
$A_5$	Between $s_2 $and $s_3 $	Between $s_3 $ and $s_5 $	Between $s_3 $ and $s_5 $	Between $s_3 $ and $s_4 $

Movie	$C_1 $	$C_2 $	$C_3 $	$C_4 $
$A_1$	$\langle [s_1 , s_3 ], 1.0\rangle$	$\langle [s_3 , s_4 ], 1.0\rangle$	$\langle [s_3 , s_5], 1.0\rangle$	$\langle [s_4 , s_5 ], 1.0\rangle$
$A_2$	$\langle [s_3 , s_5 ], 1.0\rangle$	$\langle [s_4 , s_5 ], 1.0\rangle$	$\langle [s_3 , s_4 ], 1.0\rangle$	$\langle [s_3 , s_5 ], 1.0\rangle$
$A_3$	$\langle [s_5 , s_6 ], 1.0\rangle$	$\langle [s_4 , s_6 ], 1.0\rangle$	$\langle [s_4 , s_5 ], 1.0\rangle$	$\langle s_5 , 1.0\rangle$
$A_4$	$\langle [s_3 , s_5 ], 1.0\rangle$	$\langle [s_2 , s_4 ], 1.0\rangle$	$\langle [s_4 , s_6 ], 1.0\rangle$	$\langle [s_4 , s_5 ], 1.0\rangle$
$A_5$	$\langle [s_2 , s_3 ], 1.0\rangle$	$\langle [s_3 , s_5 ], 1.0\rangle$	$\langle [s_3 , s_5 ], 1.0\rangle$	$\langle [s_3 , s_4 ], 1.0\rangle$

Movie	$C_1 $	$C_2 $	$C_3 $	$C_4 $
$A_1$	$\langle [0.167, 0.5], 1.0\rangle$	$\langle \left[ 0.5, 0.667 \right], 1\rangle$	$\langle [ 0.5, 0.833], 1\rangle$	$\langle [0.667, 0.833], 1\rangle$
$A_2$	$\langle [0.5, 0.833], 1\rangle$	$\langle [0.667, 0.833], 1\rangle$	$\langle [0.5, 0.667], 1\rangle$	$\langle [0.5, 0.833], 1\rangle$
$A_3$	$\langle [0.833, 1], 1\rangle$	$\langle [0.667, 1], 1\rangle$	$\langle [0.667, 0.833], 1\rangle$	$0.833$
$A_4$	$\langle [ 0.5, 0.833], 1\rangle$	$\langle [ 0.333, 0.667], 1\rangle$	$\langle [0.667, 1], 1\rangle$	$\langle [0.667, 0.833], 1\rangle$
$A_5$	$\langle [0.333, 0.5], 1\rangle$	$\langle [0.5, 0.833], 1\rangle$	$\langle [ 0.5, 0.833 ], 1\rangle$	$\langle [0.5, 0.667], 1\rangle$

Linguistic label	Semantics
$s_0 $	Useless
$s_{0.25} $	Between useless and bad, and close to useless
$s_{0.5} $	Between useless and bad, and non-biased
$s_{0.75} $	Between useless and bad, and close to bad
$s_1 $	Bad
$s_{1.25} $	Between bad and medium, and close to bad
$s_{1.5} $	Between bad and medium, and non-biased
$s_{1.75} $	Between bad and medium, and close to medium
$s_2 $	Medium
$s_{2.25} $	Between medium and well, and close to medium
$s_{2.5} $	Between medium and well, and non-biased
$s_{2.75} $	Between medium and well, and close to well
$_3 $	Well
$s_{3.25} $	Between well and perfect, and close to well
$s_{3.5} $	Between well and perfect, and non-biased
$s_{3.75} $	Between well and perfect, and close to perfec
$s_4 $	Perfect

Fuzzy interval linguistic sets with applications in multi-attribute group decision making

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ERP system	$C_1 $	$C_2 $	$C_3 $	$C_4 $
$A_1 $	$\langle [s_0 , s_2 ], 0.8\rangle$ $\langle s_{3.5} , 0.2\rangle$	$\langle s_2, 0.2\rangle$ $\langle s_2, 0.4\rangle$ $\langle [s_3 , s_4 ], 0.4\rangle$	$\langle s_1 , 0.4\rangle$ $\langle [s_4 , s_6 ], 0.6\rangle$	$\langle [s_1 , s_2 ], 1.0\rangle$
$A_2 $	$\langle s_2, 0.4\rangle$ $\langle [s_3 , s_4 ], 0.6\rangle$	$\langle s_2 , 0.4\rangle$ $\langle s_3 , 0.4\rangle$ $\langle s_4 , 0.2\rangle$	$\langle s_3 , 0.6\rangle$ $\langle [s_4 , s_5 ], 0.4\rangle$	$\langle [s_3 , s_4 ], 0.4\rangle$ $\langle s_5 , 0.6\rangle$
$A_3 $	$\langle s_1 , 0.2\rangle$ $\langle s_2 , 0.4\rangle$ $\langle s_3 , 0.4\rangle$	$\langle s_1 , 0.2\rangle$ $\langle s_{2.75} , 0.8\rangle$	$\langle [s_1 , s_2 ], 0.4\rangle$ $\langle s_3 , 0.2\rangle$ $\langle s_4 , 0.2\rangle$ $\langle s_5 , 0.2\rangle$	$\langle [s_4 , s_5 ], 0.8\rangle$ $\langle s_6 , 0.2\rangle$
$A_4$	$\langle [s_2 , s_4 ], 1.0\rangle$	$\langle [s_1 , s_2 ], 0.8\rangle$ $\langle s_3 , 0.2\rangle$	$\langle [s_0 , s_2 ], 1.0\rangle$	$\langle s_2 , 0.2\rangle$$\langle s_3 , 0.4\rangle$ $\langle s_4 , 0.4\rangle$