TY  - JOUR
KW  - Fuzzy systems; Mathematical operators
KW  -  Aggregation operator; Bonferroni mean; Decisions makings; Fuzzy Decision making; Fuzzy measures; Interval-valued; Interval-valued neutrosophic set; Neutrosophic sets; Property; Shapley
KW  -  Decision making
EP  - 336
AV  - none
VL  - 22
JF  - International Journal of Fuzzy Systems
N2  - Previous theories have suggested that Bonferroni mean (BM) and its extensions can fulfil the desired properties to become a good aggregation operator in managing interrelationship between arguments under fuzzy decision-making environment. However, along with this growth, there are concerns regarding the limitation of the BM and its extensions where interrelationship between arguments is limited to a pair of input arguments. In contrast to previous works, a novel normalized weighted Bonferroni mean aggregation operator considering Shapley fuzzy measure has been introduced, where the overall interactions of input arguments are combined. Unlike other extensions of BM that are mostly considered under fuzzy environment, this aggregation operation introduces the Shapley fuzzy measure to deal with interactions of all arguments under the interval-valued neutrosophic environment. Specifically, the interval-valued neutrosophic Shapley normalized weighted Bonferroni mean (INSNWBM) is proposed in this paper. The properties of INSNWBM such as reducibility, idempotency, monotonicity, commutativity, and boundedness are also presented as to reflect the interrelationship among multiple input arguments. In addition, we have also proposed successive steps of a decision-making procedure in which the proposed INSNWBM is included. Together included is a numerical example as to illustrate the applicability of the INSNWBM in decision-making. The consistency of the ranking results is confirmed by variations of parameters of INSNWBM. It is shown that the ranking results are almost consistent despite the different usages of parameter values. Results obtained appear to support the idea that the proposed aggregation operator is able to address the interrelationship between arguments in decision-making. © 2019, Taiwan Fuzzy Systems Association.
SP  - 321
IS  - 1
N1  - cited By 12
A1  - Awang, A.
A1  - Aizam, N.A.H.
A1  - Ab Ghani, A.T.
A1  - Othman, M.
A1  - Abdullah, L.
Y1  - 2020///
SN  - 15622479
TI  - A Normalized Weighted Bonferroni Mean Aggregation Operator Considering Shapley Fuzzy Measure Under Interval-valued Neutrosophic Environment for Decision-Making
ID  - scholars13505
UR  - https://www.scopus.com/inward/record.uri?eid=2-s2.0-85076785027&doi=10.1007%2fs40815-019-00752-5&partnerID=40&md5=c00c6e2fa43aed0179eb4f062dae1919
PB  - Springer Science and Business Media Deutschland GmbH
ER  -