Abstract
In this paper, we investigate the multiple attribute decision making problems with fuzzy number intuitionistic fuzzy information. Firstly, some operational laws of fuzzy number intuitionistic fuzzy values, score function and accuracy function of fuzzy number intuitionistic fuzzy values are introduced. Then, we have developed two fuzzy number intuitionistic fuzzy Choquet integral aggregation operators: induced fuzzy number intuitionistic fuzzy choquet ordered averaging (IFNIFCOA) operator and induced fuzzy number intuitionistic fuzzy choquet ordered geometric (IFNIFCOG) operator. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. We have studied some desirable properties of the IFNIFCOA and IFNIFCOG operators, such as commutativity, idempotency and monotonicity, and applied the IFNIFCOA and IFNIFCOGM operators to multiple attribute decision making with fuzzy number intuitionistic fuzzy information. Finally an illustrative example has been given to show the developed method.
Highlights
Multiple attribute decision making (MADM) problems are wide spread in real life decision situations
Xu and Chen (2007) developed some arithmetic aggregation operators, such as the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator, and the interval-valued intuitionistic fuzzy hybrid aggregation (IIFHA) operator and gave an application of the IIFHA operator to multiple attribute group decision making with interval-valued intuitionistic fuzzy information
Wei (2010a) investigated the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionisticfuzzy numbers or interval-valued intuitionisticfuzzy numbers and proposed two new aggregation perators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator, and studied some desirable properties of the I-IFOWG and I-IIFOWG operators, such as commutativity, idempotency and monotonicity
Summary
Multiple attribute decision making (MADM) problems are wide spread in real life decision situations. Wei (2010a) investigated the multiple attribute group decision making (MAGDM) problems in which both the attribute weights and the expert weights take the form of real numbers, attribute values take the form of intuitionisticfuzzy numbers or interval-valued intuitionisticfuzzy numbers and proposed two new aggregation perators: induced intuitionistic fuzzy ordered weighted geometric (I-IFOWG) operator and induced interval-valued intuitionistic fuzzy ordered weighted geometric (I-IIFOWG) operator, and studied some desirable properties of the I-IFOWG and I-IIFOWG operators, such as commutativity, idempotency and monotonicity. Wang (2008b) propose some aggregation operators, including fuzzy number intuitionistic fuzzy weighted geometric (FNIFWG) operator, fuzzy number intuitionistic fuzzy ordered weighted geometric (FNIFOWG) operator and fuzzy number intuitionistic fuzzy hybrid geometric (FNIFHG) operator and develop an approach to multiple attribute group decision making (MAGDM) based on the FNIFWG and the FNIFHG operators with fuzzy number intuitionistic fuzzy information. In the last Section, we conclude the paper and give some remarks
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