Operations and Aggregation Methods of Single-Valued Linguistic Neutrosophic Interval Linguistic Numbers and Their Decision Making Method

Jun Ye,Wenhua Cui

doi:10.3390/info9080196

Abstract

To comprehensively describe uncertain/interval linguistic arguments and confident linguistic arguments in the decision making process by a linguistic form, this study first presents the concept of a single-valued linguistic neutrosophic interval linguistic number (SVLN-ILN), which is comprehensively composed of its uncertain/interval linguistic number (determinate linguistic argument part) and its single-valued linguistic neutrosophic number (confident linguistic argument part), and its basic operations. Then, the score function of SVLN-ILN based on the attitude index and confident degree/level is presented for ranking SVLN-ILNs. After that, SVLN-ILN weighted arithmetic averaging (SVLN-ILNWAA) and SVLN-ILN weighted geometric averaging (SVLN-ILNWGA) operators are proposed to aggregate SVLN-ILN information and their properties are investigated. Further, a multi-attribute decision-making (MADM) method based on the proposed SVLN-ILNWAA or SVLN-ILNWGA operator and the score function is established under consideration of decision makers’ preference attitudes (pessimist, moderate, and optimist). Lastly, an actual example is given to show the applicability of the established MADM approach with decision makers’ attitudes.

Highlights

Multi-attribute decision-making (MADM) explicitly evaluates multiple conflicting attributes in decision making to help people make optimal decisions [1,2,3,4]
This study proposed the SVLN-interval linguistic numbers (ILNs) concept to express the hybrid information of both a single-valued linguistic neutrosophic numbers (LNNs) and an ILN, the operational laws of SVLN-ILNs, and the score function of SVLN-ILN, along with the attitude index and confident degree for ranking SVLN-ILNs
The SVLN-ILNWAA and SVLN-ILNWGA operators were presented in order to aggregate SVLN-ILN. Information, and their advantage is that all the linguistic terms (LTs) values in their aggregated SVLN-ILN can still belong to the predefined LT set, rather than beyond the LT set in some linguistic operations [8,9]

Summary

Introduction

Multi-attribute decision-making (MADM) explicitly evaluates multiple conflicting attributes in decision making to help people make optimal decisions [1,2,3,4]. There usually exists uncertainty and vagueness in MADM problems. In this situation, it may prove difficult for decision makers (DMs) to express their evaluation values of attributes, especially qualitative attributes, by numerical values. The expression of linguistic terms (LTs) is very fit for human thinking and expressing habits. When the quality of some product is evaluated by LTs, we use LTs “good”,. Linguistic decision making methods have been wildly used for MADM problems with linguistic information. Zadeh [5] presented the concept of a linguistic variable (LV) for its fuzzy reasoning application. Herrera et al [6]

Methods

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Conclusion