On the basis of Frank operators, the operational rules of intuitionistic fuzzy numbers are redefined, then the intuitionistic fuzzy Frank power average operator (IFFPA), intuitionistic fuzzy Frank power weighted average operator (IFFPWA) and intuitionistic fuzzy Frank power ordered weighted average operator (IFFPOWA) are proposed by combining Frank operations and power aggregation operators. At the same time, some desirable properties of these operators, such as idempotency, commutativity and boundedness, are studied, and some special cases are analyzed. Furthermore, with respect to multiple attribute group decision making (MAGDM) problems in which attribute values take the form of the intuitionistic fuzzy numbers, two group decision making methods based on IFFPWA and IFFPOWA operators are developed. Finally, an illustrative example is given to verify the proposed methods and to demonstrate their practicality and effectiveness.
AtanassovKTGargovG1989Interval-valued intuitionistic fuzzy setsFuzzy Sets and Systems33343349
6.
BeliakovGPraderaACalvoT2007Aggregation Functions: A Guide for PractitionersSpringerHeidelberg, Berlin, New York
7.
ChuTC2002A fuzzy number interval arithmetic based fuzzy MCDM algorithmInternational Journal of Fuzzy Systems4867872
8.
DeschrijverGKerreEE2002A generalization of operators on intuitionistic fuzzy sets using triangular norms and conformsNotes on Intuition Fuzzy Sets81927
9.
DelgadoMVerdegayJLVilaMA1993On aggregation operations of linguistic labelsInternational Journal of Intelligent Systems8351370
10.
FrankMJ1979On the simultaneous associativity of F (x, y) and x + y - F (x, y)Aequationes Mathematicae191194226
11.
LiDF2011The GOWA operator based approach to multi-attribute decision making using intuitionistic fuzzy setsMathematical and Computer Modelling5311821196
12.
LiuPD2014Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to Group Decision MakingIEEE Transactions on Fuzzy Systems2218397
13.
LiuPDJinF2012Methods for aggregating intuitionistic uncertain linguistic variables and their application to group decision makingInformation Sciences2055871
14.
LiuPDLiuY2014An approach to multiple attribute group decision making based on intuitionistic trapezoidal fuzzy power generalized aggregation operatorInternational Journal of Computational Intelligence Systems72291304
15.
LiuPDLiuZMZhangX2014Some intuitionistic uncertain linguistic heronian mean operators and their application to group decision makingApplied Mathematics and Computation230570586
16.
LiuPDQiXF2014Some generalized dependent aggregation operators with 2-dimension linguistic information and their application to group decision makingJournal of Intelligent & Fuzzy Systems2717611773
17.
LiuPDWangYM2014Multiple attribute group decision making methods based on intuitionistic linguistic power generalized aggregation operatorsApplied Soft Computing1790104
18.
LiuPDYuXC20142-dimension uncertain linguistic power generalized weighted aggregation operator and its application for multiple attribute group decision makingKnowledge-Based Systems5716980
19.
QinJDLiuXW2014Frank aggregation operators for triangular interval type-2 fuzzy set and its application to multiple attribute group decision makingJournal of Applied Mathematics2014124
20.
ShuMHChengCHChangJR2006Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assemblyMicroelectronics Reliability4621392148
21.
WanSPDongJY2010Method of intuitionistic trapezoidal fuzzy number for multi-attribute group decisionControl and Decision25773776
22.
WangJQ2006Multi-criteria interval intuitionistic fuzzy decision-making approach with incomplete certain informationControl and Decision21125312561263
23.
WangJQ2008Overview on fuzzy multi-criteria decision-making approachControl and Decision23601606
24.
WangJQLiJJ2009The multi-criteria group decision making method based on multi-granularity intuitionistic two semanticsScience & Technology Information389
25.
WangJQLuPZhangHYChenXH2014Method of multi-criteria group decision-making based on cloud aggregation operators with linguistic informationInformation Sciences274177191
26.
WangWSHeHC2009Research on flexible probability logic operator based on frank T/S normsChinese Journal of Electronics37511411145
27.
WeiGW2010Some induced geometric aggregation operators with intuitionistic fuzzy information and their application to group decision makingApplied Soft Computing10423431
28.
XiaMMXuZSZhuB2012Some issues on intuitionistic fuzzy aggregation operators based on Archimedean t-conorm and t-normKnowledge-Based Systems3117888
29.
XuYJMerigóJMWangHM2012Linguistic power aggregation operators and their application to multiple attribute group decision makingApplied Mathematical Modelling361154275444
30.
XuZS2007Models for multiple attribute decision-making with intuitionistic fuzzy informationInternational Journal of Uncertainty, Fuzziness and Knowledge-Based Systems15285297
31.
XuZS2007Intuitionistic fuzzy aggregation operatorsIEEE Transactions on Fuzzy Systems15611791187
XuZSYagerRR2006Some geometric aggregation operators based on intuitionistic fuzzy setsInternational Journal of General Systems35417433
34.
XuZSYagerRR2010Power-geometric operators and their use in group decision makingIEEE Transactions on Fuzzy Systems18194105
35.
YagerRR1988On ordered weighted averaging aggregation operators in multicriteria decision makingIEEE Transactions on Systems, Man and Cybernetics181183190
36.
YagerRR2001The power average operatorIEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans31724731
37.
YuDJ2012Group decision making based on generalized intuitionistic fuzzy prioritized geometric operatorInternational Journal of Intelligent Systems277635661
38.
ZadehLA1975The concept of a linguistic variable and its applications to approximate reasoning,199–249, 301-357Information Sciences9199249301-357, 9 (1975), 43–80
39.
ZadehLA1965Fuzzy setsInformation and Control8338356
40.
ZhangXLiuPD2010Method for aggregating triangular intuitionistic fuzzy information and its application to decision makingTechnological and Economic Development of Economy16280290
41.
ZhaoHXuZSNiMFLiuSS2010Generalized aggregation operators for intuitionistic fuzzy setsInternational Journal of Intelligent Systems251130
42.
ZengSZWangQFMerigóJMPanTJ2014Induced intuitionistic fuzzy ordered weighted averaging weighted average operator and its application to business decision-makingComputer Science and Information Systems112839857
