Bidirectional projection measure of linguistic neutrosophic numbers and their application to multi-criteria group decision making

Abstract

A B S T R A C TLinguistic neutrosophic numbers (LNNs) are an effective tool in describing the incomplete and indeterminate evaluation information by using three linguistic variables (LVs) to denote the truth-degree (TD), indeterminacydegree (ID), and falsity-degree (FD), and the bidirectional projection measure has some advantages in dealing with multi-criteria group decision making (MCGDM) problems because it can consider both the distance and the included angle, but more importantly, it considers the bidirectional projection between each alternative and the ideal solution. In this paper, we define a new distance measure between two linguistic neutrosophic sets (LNSs), and build a model based on the maximum deviation to obtain fuzzy measure, further, we develop the bidirectional projection-based MCGDM method with LNNs in which a weight model based on fuzzy measure is proposed where the weights of evaluation criteria is partial unknown and the interactions among criteria are considered. Finally, we use some examples to verify the effectiveness of the proposed approach and demonstrate its advantages by comparing with some existing methods.

A Multi-Attribute Pearson’s Picture Fuzzy Correlation-Based Decision-Making Method

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Emergency decision making with extended axiomatic design approach under picture fuzzy environment

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Decision-Making Method Based on Grey Relation Analysis and Trapezoidal Fuzzy Neutrosophic Numbers Under Double Incomplete Information and its Application in Typhoon Disaster Assessment

“…Broumi et al and Tan et al [30] combined the neutrosophic sets and graph theory to propose neutrosophic graphs (NGs), including single-valued neutrosophic graphs [39], bipolar single neutrosophic graphs [40], interval-valued neutrosophic graphs, trapezoidal fuzzy neutrosophic graphs [30], and used them for the shortest path solving problem. Liu et al [41] studied linguistic neutrosophic sets (LNSs) and their application to MAGDM. Chen et al [42] redefined linguistic neutrosophic number (LNN) operations based on Archimedean copulas and co-copulas to prevent information loss, and then developed a generalized weighted Choquet Heronian mean operator based on new operations.…”