Abstract
Picture fuzzy nano topological spaces is an extension of intuitionistic fuzzy nano topological spaces. Every decision in life ends with an answer such as yes or no, or true or false, but we have an another component called abstain, which we have not yet considered. This work is a gateway to study such a problem. This paper motivates an enquiry of the third component—abstain—in practical problems. The aim of this paper is to investigate the contemporary notion of picture fuzzy nano topological spaces and explore some of its properties. The stated properties are quantified with numerical data. Furthermore, an algorithm for Multiple Attribute Decision-Making (MADM) with an application regarding the file selection of building material under uncertainty by using picture fuzzy nano topological spaces is developed. As a practical problem, a comparison table is presented to show the difference between the novel concept and the existing methods.
Highlights
Multiple Attribute Decision-Making (MADM) is a method that considers the best possible alternatives
The notion of picture fuzzy set (PFS) [12], nano topological spaces [6], and neutrosophic complex topological space [6] motivates us to propose this novel notion of picture fuzzy nano topological space and apply this notion in the MADM problem
We introduced boundary of a region on picture fuzzy set along with upper and lower approximation
Summary
Multiple Attribute Decision-Making (MADM) is a method that considers the best possible alternatives. There is a choice called abstinence, different from yes or no choices, in decision making Problems related to these cases are interesting and develop a theory for the same motived many researched to pay attention on it. Peng and Dai [21] proposed an algorithm for PFS and applied in decision making based on new distance measure. In this era, several mathematicians have been focusing on correlation coefficients, similarity measures, aggregation operators, topological spaces, and applications for decision-making. Several mathematicians have been focusing on correlation coefficients, similarity measures, aggregation operators, topological spaces, and applications for decision-making These structures provide different formula for different sets and have better solution to decision-making problems. It has various applications in different fields, such as medical diagnosis, pattern recognition, social sciences, artificial intelligence, business, and decision making problems with multi-attributes
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