Abstract
Existing intuitionistic linguistic variables can describe the linguistic information of both the truth/membership and falsity/non-membership degrees, but it cannot represent the indeterminate and inconsistent linguistic information. To deal with the issue, this paper originally proposes the concept of a linguistic neutrosophic number (LNN), which is characterized independently by the truth, indeterminacy, and falsity linguistic variables. Then, we define the basic operational laws of LNNs and the score and accuracy functions of LNN for comparing LNNs. Next, we develop an LNN-weighted arithmetic averaging (LNNWAA) operator and an LNN-weighted geometric averaging (LNNWGA) operator to aggregate LNN information and investigate their properties. Further, a multiple attribute group decision-making method based on the proposed LNNWAA or LNNWGA operator is established under LNN environment. Finally, an illustrative example about selecting problems of investment alternatives is presented to demonstrate the application and effectiveness of the developed approach.
Highlights
In complex decision-making problems, human judgments, including preference information, may be difficultly stated in numerical values due to the ambiguity of human thinking about the complex objective things in the real world, and may be expressed in linguistic terms, especially for some qualitative attributes
A single-valued neutrosophic number (SVNN), which is a basic element in a single-valued neutrosophic set (SVNS) [12,13], can only express the truth, indeterminacy, and falsity degrees independently, and describe the incomplete, indeterminate, and inconsistent information in SVNN rather than linguistic information; it cannot express linguistic information in linguistic decision-making problems, while linguistic variables can represent the qualitative information for attributes in complex multiple attribute decision-making (MADM) problems
Ye [13] proposed the single-valued neutrosophic linguistic number (SVNLN), which is composed of a linguistic variable and an SVNN, where the linguistic variable is represented as the decision-maker’s judgment to an evaluated object and the SVNN is expressed as the reliability of the given linguistic variable, and developed an extended TOPSIS method for multiple attribute group decision-making (MAGDM) problems with SVNLNs
Summary
In complex decision-making problems, human judgments, including preference information, may be difficultly stated in numerical values due to the ambiguity of human thinking about the complex objective things in the real world, and may be expressed in linguistic terms, especially for some qualitative attributes. A single-valued neutrosophic number (SVNN), which is a basic element in a single-valued neutrosophic set (SVNS) [12,13], can only express the truth, indeterminacy, and falsity degrees independently, and describe the incomplete, indeterminate, and inconsistent information in SVNN rather than linguistic information; it cannot express linguistic information in linguistic decision-making problems, while linguistic variables can represent the qualitative information for attributes in complex MADM problems. Ye [13] proposed the single-valued neutrosophic linguistic number (SVNLN), which is composed of a linguistic variable and an SVNN, where the linguistic variable is represented as the decision-maker’s judgment to an evaluated object and the SVNN is expressed as the reliability of the given linguistic variable, and developed an extended TOPSIS method for MAGDM problems with SVNLNs. SVNLN cannot describe the truth, indeterminacy, and falsity linguistic information according to a linguistic term set.
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