Abstract
Picture fuzzy set (PFS) is one the reliable tool to handle the uncertainties in the data as compared to the intuitionistic fuzzy set (IFS) or fuzzy set. PFS simultaneously handle the four degrees namely, membership, neutrality, non-membership, and refusal, and thus widely applicable to solve the real-life decision-making problems more accurately. Keeping their advantages, in this paper, we present some interactive operational laws for the picture fuzzy numbers (PFNs) to aggregate picture fuzzy information. Also, we state some new information measures namely picture fuzzy similarity measures (PFSimMs) based on fuzzy strict negations, which can overcome the various drawbacks of the existing PFSimMs. The various properties and their features are studied in detail to show their advantages. Finally, we develop a prospect theory-based multi-attributive border approximation area comparison (MABAC) method under picture fuzzy environment by using the proposed operational laws and PFSimMs to solve the decision-making problems. The applicability of the developed algorithm is explained through a numerical example and show its superiorities.
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