Abstract
Problems in real life usually involve uncertain, inconsistent and incomplete information. An example of such problems is strategic decision making with respect to remediation planning of historic pedestrian bridges. The multiple decision makers and experts, as well as the various mutually conflicting criteria, unknown criteria weights, and vagueness and duality in final decisions, provide motivation to develop a methodology that is able to resist the challenges implicit in this problem. Therefore, the aim of this research was to propose an algorithm based on the theory of rough neutrosophic sets in order to solve the problem of strategic planning with respect to the remediation of historic pedestrian bridges. A new multicriteria decision-making model is developed that is a fusion of rough set and neutrosophic set theory. A new cross entropy is proposed under a rough neutrosophic environment that does not possess the shortcomings of asymmetrical character and unknown occurrences. Additionally, a weighted rough neutrosophic symmetric cross entropy is proposed. Furthermore, a rough neutrosophic VIKOR method is introduced, with which the values of the utility measure, regret measure and VIKOR index are obtained. These values, as well as the weighted rough neutrosophic symmetric cross entropy measure, are used to provide a ranking of historic pedestrian bridges favorable to remediation. Finally, an illustrative example of the strategic planning of remediation for historic pedestrian bridges is solved and compared to other research, demonstrating the robustness, feasibility and efficacy of the model when dealing with complex multicriteria decision-making processes.
Highlights
Complex real-life problems are difficult to solve for a single expert, and the application of simple methods and tools in decision-making processes is insufficient when dealing with such problems
The model is defined by newly developed cross entropy combined with the VIKOR method under the rough neutrosophic set environment
The newly developed cross entropy under rough neutrosophic set theory does not contain the shortcomings of asymmetrical character and unknown occurrences
Summary
Complex real-life problems are difficult to solve for a single expert, and the application of simple methods and tools in decision-making processes is insufficient when dealing with such problems. The theory of rough sets was first proposed by Pawlak [1], and has been used as a tool to process incomplete and indistinct information. The main advantage of rough set theory, when it comes to data analysis, is that there is no need for past or supplementary information regarding the data, such as probability distribution or membership grades [2,3,4]. Different models have been proposed for various aspects of rough set theory, amalgamating it with fuzzy sets, vague sets, intuitionistic fuzzy sets, grey sets and neutrosophic sets [5]
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