A Bonferroni mean considering Shapley fuzzy measure under hesitant bipolar-valued neutrosophic set environment for an investment decision

Abstract

Bonferroni mean (BM) operators have been established as a powerful tool for handling the interrelationship between the input arguments under various decision-making information. However, the existing BM operators do not take into account the overall interaction among decision makers or criteria. To overcome this limitation, this study considers the Shapley fuzzy measure (SFM) with the normalized weighted BM (NWBM) operator under a neutrosophic environment. In addition, the current research ignores the bipolarity and hesitancy during decision elicitations, resulting in the imprecise decision results. In this paper, the hesitant bipolar-valued neutrosophic set (HBNS) which is the extension of hesitant fuzzy set and bipolar neutrosophic set is employed. The main focus of this paper is in the development of an aggregation operator for HBNS. Based on the literature review, we would like to fill in the gaps by developing a hesitant bipolar-valued neutrosophic Shapley NWBM (HBN-SNWBM) operator where the overall interaction among decision makers can be considered. Besides that, a three-phase decision making framework is also proposed to show the applicability of the proposed aggregation operator to the real-world decision problems. The HBN-SNWBM operator and the decision making framework are applied to two examples of investment selection where evaluations are implemented using the proposed aggregations that based upon hesitant bipolar-valued neutrosophic sets. In the first example, it is found that a weapon company is the best alternative for investment followed by a food company. Sensitivity of parameters of the aggregation operator is also analysed and it is found that the ranking results are consistent despite of different parameter values used. This verifies the insensitivity of p,q parameters in the developed aggregation operator. The proposed decision making framework and hesitant bipolar-valued neutrosophic sets would be a great significance for the practical implementation of the aggregation operators.

Rough Neutrosophic Shapley Weighted Einstein Averaging Aggregation Operator and its Application in Multi-Criteria Decision-Making Problem

“…Insufficient weight information and distinct input arguments, which are frequently missing in aggregation operators, can be handled by SFM. Awang et al, [14] proposed SFM under a hesitant bipolar-valued neutrosophic set environment for an investment decision whereas Heronian mean operators were developed by Hashim et al, [15] while taking into account Shapley fuzzy measure in an interval neutrosophic vague environment. Hua and Jing [16] developed two interval-valued Pythagorean fuzzy aggregation operators based on Choquet integral operator and Shapley fuzzy measure, respectively.…”

Q-rung orthopair normal fuzzy Maclaurin symmetric mean aggregation operators based on Schweizer-Skla operations

“…6 Due to the complexity of practical problems, many scholars have paid attention to considering the interrelationships between input variables. Heronian mean 23 and Bonferroni mean 24 operators reflect this situation and have been expanded in other fuzzy setting, such as Ali et al 25 proposed complex linear diophantine uncertain linguistic variables, Awang et al 26 considered hesitant bipolar-valued neutrosophic set environment, Hu et al 27 proposed a new three-parameter linguistic generalized weighted Heronian mean. But Hronian mean 23 and Bonferroni mean 24 operators only focus on the correlation between two decision attributes.…”