Group decision-making based on bipolar neutrosophic fuzzy prioritized muirhead mean weighted averaging operator

Bipolar neutrosophic WINGS for green technology innovation

Green technology innovation is a crucial assurance of achieving sustainable economic and environmental development, so improving the capability of green technology innovation is an urgent problem. In order to provide a more objective and accurate tool for identifying the most important impact factor of green technology innovation, this study innovatively proposes a new method by combining the bipolar neutrosophic sets with Weighted Influence Nonlinear Gauge System (WINGS) method. Furthermore, this paper intends to provide recommendations in improving green technology innovation capability. We invite five experts to evaluate fifteen factors influencing green technology innovation using the bipolar neutrosophic linguistic variables. Then, the proposed bipolar neutrosophic set WINGS (Bipolar NS-WINGS) method is applied to measure the influence of each impact factor of green technology innovation. Finally, we divide all the factors into cause group and effect group. Moreover, the network relation map is constructed to visualize the interrelationships between all impact factors. The Bipolar NS-WINGS suggests that Science and Technology Innovation Environment (Ω7) is the most important factor of green technology innovation. The result also indicates that R&D Investment (Ω8) is the most influential factor in which it has impacted many other factors. It is obvious that the integrated method not only enriches the research in the field of decision theory, which has not combined the bipolar-NS and WINGS method for analyzing relationships of factors, but also contributes to the improvement of green technology innovation capabilities.

Improved CoCoSo Method Based on Frank Softmax Aggregation Operators for T-Spherical Fuzzy Multiple Attribute Group Decision-Making

In this article, a novel CoCoSo (Combined compromise solution) method based on Frank operational laws and softmax function is investigated to handle multiple attribute group decision-making problems for T-spherical fuzzy sets. We extend Frank operations in T-spherical fuzzy environment and develop a series of aggregation operators, including T-spherical fuzzy Frank softmax (T-SFFS) average and geometric operators, and their weighted forms, i.e., T-SFFS weighted averaging (T-SFFSWA) and T-SFFS weighted geometric (T-SFFSWG) operators. Some of their basic properties and particular cases are discussed. Meanwhile, the monotonicity of proposed operators is also analyzed, and it is discussed that how they indicate the decision-makers’ optimistic and pessimistic decision attitudes with risk preference. Furthermore, a novel CoCoSo method based on Hamming distance measure is proposed, which considers both decision-maker’s decision attitude and attribute priority, and a multiple attribute group decision-making framework with two independent and parallel T-spherical fuzzy information processing processes are designed. Lastly, a real case of spent power battery recycling technology (SPBRT) selection is presented to show the practicability of the proposed method. Also sensitivity and comparative analyses are carried out to prove the reliability, effectiveness, and superiority of our proposed method.

An Improved EDAS Method Based on Bipolar Neutrosophic Set and Its Application in Group Decision-Making

The bipolar neutrosophic set is a suitable instrument to tackle the information with vagueness, complexity, and uncertainty. In this study, we improved the original EDAS (the evaluation based on distance from average solution) with bipolar neutrosophic numbers (BNNs) for a multiple-criteria group decision-making (MCGDM) problem. We calculated the average solution under all the criteria by two existing aggregation operators of BNNs. Then, we computed the positive distance and the negative distance from each alternative to the average ideal solution and determined the appraisal score of alternatives. Based on these scores, we obtained the ranking result. Finally, we demonstrated the practicability, stability, and capability of the improved EDAS method by analyzing the influence parameters and comparing results with an extended VIKOR method.

Domination of Bipolar Fuzzy Graphs in Various Settings

Bipolar fuzzy sets are used to describe the positive and negative of the uncertainty of objects, and the bipolar fuzzy graphs are used to characterize the structural relationship between uncertain concepts in which the vertices and edges are assigned positive and negative membership function values to feature the opposite uncertainty elevation. The dominating set is the control set of vertices in the graph structure and it occupies a critical position in graph analysis. This paper mainly contributes to extending the concept of domination in the fuzzy graph to the bipolar frameworks and obtaining the related expanded concepts of a variety of bipolar fuzzy graphs. Meanwhile, the approaches to obtain the specific dominating sets are presented. Finally, a numeral example on city data in Yunnan Province is presented to explain the computing of domination in bipolar fuzzy graph in the specific application.