# Uncertain linguistic aggregation operators based approach to multiple attribute group decision making under uncertain linguistic environment

Inf. Sci., no. 1-4 (2004): 171-184

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摘要

In this paper, two uncertain linguistic aggregation operators called uncertain linguistic ordered weighted averaging (ULOWA) operator and uncertain linguistic hybrid aggregation (ULHA) operator are proposed. An approach to multiple attribute group decision making with uncertain linguistic information is developed based on the ULOWA and th...更多

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简介

- 3. Uncertain linguistic ordered weighted averaging (ULOWA) operator Definition 3.
- ; ~snÞ 1⁄4 w1~g1 È w2~g2 ÈÁÁÁÈ wn~gn where ~gj is the jth largest of the uncertain linguistic weighted argument
- From Theorems 1 and 2, the authors know that the ULHA operator generalizes both the ULWA and the ULOWA operators, and reflects the importance degrees of both the given arguments and their ordered positions.

重点内容

- The existing main aggregation operators can be briefly classified into the following four categories: (1) The operators, which can only be used in situations where the arguments are exact numeric variables, such as the ordered weighted averaging (OWA) operator [2,3], ordered weighted geometric averaging (OWGA) operator [4,5,6], weighted arithmetic averaging (WAA) operator [7,8], weighted geometric averaging (WGA) operator [9,10], generalized ordered weighted averaging (GOWA) operator [11], weighted ordered weighted averaging (WOWA) operator [12], and hybrid weighted averaging (HWA) operator [1]. (2) The operators, which can only be used in situations where the arguments are inexact numeric variables, such as the fuzzy weighted averaging (FWA) operator [13,14], uncertain ordered weighted averaging (UOWA) operator [15,16], uncertain ordered weighted geometric averaging [17], and fuzzy ordered weighted geometric averaging (FOWGA) operator [1,16,18]
- Based on the uncertain linguistic ordered weighted averaging (ULOWA) and the uncertain linguistic hybrid aggregation (ULHA) operators, we shall develop an approach to multiple attribute group decision making with uncertain linguistic information and give a practical application of the developed approach to the problem of evaluating university faculty for tenure and promotion, and some concluding remarks are included
- In the following we shall utilize the uncertain linguistic weighted averaging (ULWA) and the ULHA operators to propose an approach to multiple attribute group decision making with uncertain linguistic information
- We have developed the uncertain linguistic ordered weighted averaging (ULOWA) operator and the uncertain linguistic hybrid aggregation (ULHA) operator
- Based on the ULOWA and the ULHA operators, we have proposed an approach to multiple attribute group decision making with uncertain linguistic information

结果

- Consider a multiple attribute group decision making with uncertain linguistic information: let X 1⁄4 fx1; x2; .
- Decision ð~aðijkÞÞmÂn is the decision matrix, where ~aðijkÞ 2 eS is a preference value, which takes the form of uncertain linguistic variable, given by the decision maker dk 2 D, for alternative xj 2 X with respect to attribute ui 2 U .
- In the following the authors shall utilize the ULWA and the ULHA operators to propose an approach to multiple attribute group decision making with uncertain linguistic information.
- Step 1: Utilize the decision information given in matrix AeðkÞ, and the ULWA operator:
- ~a3ð4Þ 1⁄4 1⁄2s6:3; s7:7; Step 2: Utilize the weight vector of decision makers, v 1⁄4 ð0:24; 0:26; 0:23; 0:27ÞT, and the ULHA operator: ~aj 1⁄4 ULHAv;w0 ð~ajð1Þ; ~aðj2Þ; ~aðj3Þ; ~ajð4ÞÞ ðj 1⁄4 1; 2; 3; 4; 5Þ to aggregate the individual overall preference values ~aðjkÞðk 1⁄4 1; 2; 3; 4Þ and get the collective overall preference value ~aj of alternative xj:
- Step 3: To rank these collective overall preference values ~ajðj 1⁄4 1; 2; 3; 4; 5Þ, the authors first compare each ~aj with all ~ajðj 1⁄4 1; 2; 3; 4; 5Þ by using (1), and construct a complementary matrix p1 1⁄4 2:4703; p2 1⁄4 2:6546; p3 1⁄4 3:2160; p4 1⁄4 2:0801; p5 1⁄4 2:0790
- The authors have developed the uncertain linguistic ordered weighted averaging (ULOWA) operator and the uncertain linguistic hybrid aggregation (ULHA) operator.
- The ULOWA operator, which is an extension of Yager’s OWA operator, can be used in situations where the input arguments are uncertain linguistic variables.

结论

- The ULHA operator generalizes both the uncertain linguistic weighted averaging (ULWA) operator and the ULOWA operator, and reflects the importance degrees of both the given arguments and their ordered positions.
- Based on the ULOWA and the ULHA operators, the authors have proposed an approach to multiple attribute group decision making with uncertain linguistic information.
- The authors have applied the proposed approach to the problem of evaluating university faculty for tenure and promotion

总结

- 3. Uncertain linguistic ordered weighted averaging (ULOWA) operator Definition 3.
- ; ~snÞ 1⁄4 w1~g1 È w2~g2 ÈÁÁÁÈ wn~gn where ~gj is the jth largest of the uncertain linguistic weighted argument
- From Theorems 1 and 2, the authors know that the ULHA operator generalizes both the ULWA and the ULOWA operators, and reflects the importance degrees of both the given arguments and their ordered positions.
- Consider a multiple attribute group decision making with uncertain linguistic information: let X 1⁄4 fx1; x2; .
- Decision ð~aðijkÞÞmÂn is the decision matrix, where ~aðijkÞ 2 eS is a preference value, which takes the form of uncertain linguistic variable, given by the decision maker dk 2 D, for alternative xj 2 X with respect to attribute ui 2 U .
- In the following the authors shall utilize the ULWA and the ULHA operators to propose an approach to multiple attribute group decision making with uncertain linguistic information.
- Step 1: Utilize the decision information given in matrix AeðkÞ, and the ULWA operator:
- ~a3ð4Þ 1⁄4 1⁄2s6:3; s7:7; Step 2: Utilize the weight vector of decision makers, v 1⁄4 ð0:24; 0:26; 0:23; 0:27ÞT, and the ULHA operator: ~aj 1⁄4 ULHAv;w0 ð~ajð1Þ; ~aðj2Þ; ~aðj3Þ; ~ajð4ÞÞ ðj 1⁄4 1; 2; 3; 4; 5Þ to aggregate the individual overall preference values ~aðjkÞðk 1⁄4 1; 2; 3; 4Þ and get the collective overall preference value ~aj of alternative xj:
- Step 3: To rank these collective overall preference values ~ajðj 1⁄4 1; 2; 3; 4; 5Þ, the authors first compare each ~aj with all ~ajðj 1⁄4 1; 2; 3; 4; 5Þ by using (1), and construct a complementary matrix p1 1⁄4 2:4703; p2 1⁄4 2:6546; p3 1⁄4 3:2160; p4 1⁄4 2:0801; p5 1⁄4 2:0790
- The authors have developed the uncertain linguistic ordered weighted averaging (ULOWA) operator and the uncertain linguistic hybrid aggregation (ULHA) operator.
- The ULOWA operator, which is an extension of Yager’s OWA operator, can be used in situations where the input arguments are uncertain linguistic variables.
- The ULHA operator generalizes both the uncertain linguistic weighted averaging (ULWA) operator and the ULOWA operator, and reflects the importance degrees of both the given arguments and their ordered positions.
- Based on the ULOWA and the ULHA operators, the authors have proposed an approach to multiple attribute group decision making with uncertain linguistic information.
- The authors have applied the proposed approach to the problem of evaluating university faculty for tenure and promotion

- Table1: Decision matrix Aeð1Þ
- Table2: Decision matrix Aeð2Þ
- Table3: Decision matrix Aeð3Þ
- Table4: Decision matrix Aeð4Þ

基金

- Keywords: Aggregation; Multiple attribute group decision making; Uncertain linguistic ordered weighted averaging (ULOWA) operator; Uncertain linguistic hybrid aggregation (ULHA) operator q This project was supported by China Postdoctoral Science Foundation

引用论文

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