Abstract
This paper focuses on the multiattribute group decision making problems with linguistic intuitionistic fuzzy information. Firstly the concept of linguistic intuitionistic fuzzy numbers (LIFNs) is introduced, and then based on the LIFNs, some new aggregation operators based on Bonferroni mean and power operator are proposed, such as linguistic intuitionistic fuzzy power Bonferroni mean (LIFPBM) operator, linguistic intuitionistic fuzzy weighted power Bonferroni mean (LIFWPBM) operator, linguistic intuitionistic fuzzy geometric power Bonferroni mean (LIFGPBM) operator, and linguistic intuitionistic fuzzy weighted geometric power Bonferroni mean (LIFWGPBM) operator. Then, some properties are proved such as idempotency, permutation, and boundedness. Besides, some special situations of the operators are explored. After that, an approach based of the LIFWGPBM and LIFWGPBM operators is proposed. Finally an example is used to illustrate the validity of the developed method.
Highlights
Multiple attributes group decision making (MAGDM) plays an important role in the field of decision sciences
The linguistic intuitionistic fuzzy numbers (LIFNs), in which membership degree and the nonmembership degree were expressed by linguistic terms, can better express fuzzy evaluation information
We firstly introduce the concept of the LIFNs
Summary
Multiple attributes group decision making (MAGDM) plays an important role in the field of decision sciences. A possible solution is that membership degree and nonmembership degree are represented by linguistic variables, which is called the linguistic intuitionistic fuzzy numbers (LIFNs) firstly developed by Chen et al [13]. Xu and Yager [23] extended the BM operator to IFSs. Xu and Yager [23] extended the BM operator to IFSs Zhou and He [24] developed a normalized weighted Bonferroni mean (IFNWBM) operator for intuitionistic fuzzy numbers. Because of the complexity of the decision making problems and environment, the linguistic intuitionistic fuzzy numbers (LIFNs) can express the fuzzy information by combined intuitionistic fuzzy numbers (IFNs) with linguistic information, and PA can relieve the effect of too large or too small data by the inputting different weights and BM can catch the interrelationship of individual input arguments.
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