Aggregation operators of neutrosophic linguistic numbers for multiple attribute group decision making.

Jun Ye

doi:10.1186/s40064-016-3247-5

Abstract

Based on the concept of neutrosophic linguistic numbers (NLNs) in symbolic neutrosophic theory presented by Smarandache in 2015, the paper firstly proposes basic operational laws of NLNs and the expected value of a NLN to rank NLNs. Then, we propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and discuss their properties. Further, we establish a multiple attribute group decision-making (MAGDM) method by using the NLNWAA and NLNWGA operators under NLN environment. Finally, an illustrative example on a decision-making problem of manufacturing alternatives in the flexible manufacturing system is given to show the application of the proposed MAGDM method.

Highlights

In decision theory, decision-making method is one of important research topics
The objects of this paper are: (1) to define basic operational laws of neutrosophic linguistic numbers (NLNs) and the expected value of a NLN for ranking NLNs, (2) to propose the NLN weighted arithmetic average (NLNWAA) and NLN weighted geometric average (NLNWGA) operators and to discuss their properties, and (3) to establish a multiple attribute group decision-making (MAGDM) method based on the NLNWAA and NLNWGA operators under NLN environment
In “MAGDM method using the NLNWAA and NLNWGA operators” section, a MAGDM method based on the NLNWAA and NLNWGA operators is developed under NLN environment

Summary

Background

Decision-making method is one of important research topics. various decision-making methods has been proposed and applied widely to engineering, economics, and management fields. The above operational results are still NLNs. we define an expected value of a NLN, which is an important index to rank NLNs in the following decision-making problems. Example 1 Letl1 = l3+2I andl2 = l2+3I be two NLNs for I ∈ [0.1, 0.3] and the cardinality of linguistic term sets L be s = 7 In this case the ranking order betweenl andl is given as follows: According to Eq (1) we have E( ̄l1) = 0.5667 > E( ̄l2) = 0.4333, ̄l1 ≻ ̄l2. Based on the operational laws in Definition 1, this section proposes the NLNWAA and NLNWGA operators to aggregate NLNs, which are usually utilized in decision-making problems.

Boundedness

Conclusion