Linguistic Neutrosophic Cubic Numbers and Their Multiple Attribute Decision-Making Method

Jun Ye

doi:10.3390/info8030110

Abstract

To describe both certain linguistic neutrosophic information and uncertain linguistic neutrosophic information simultaneously in the real world, this paper originally proposes the concept of a linguistic neutrosophic cubic number (LNCN), including an internal LNCN and external LNCN. In LNCN, its uncertain linguistic neutrosophic number consists of the truth, indeterminacy, and falsity uncertain linguistic variables, and its linguistic neutrosophic number consists of the truth, indeterminacy, and falsity linguistic variables to express their hybrid information. Then, we present the operational laws of LNCNs and the score, accuracy, and certain functions of LNCN for comparing/ranking LNCNs. Next, we propose a LNCN weighted arithmetic averaging (LNCNWAA) operator and a LNCN weighted geometric averaging (LNCNWGA) operator to aggregate linguistic neutrosophic cubic information and discuss their properties. Further, a multiple attribute decision-making method based on the LNCNWAA or LNCNWGA operator is developed under a linguistic neutrosophic cubic environment. Finally, an illustrative example is provided to indicate the application of the developed method.

Highlights

In terms of complex objective aspects of real life, human preference judgments may use linguistic expression, instead of numerical value expression, in order to be more suitable for people’s thinking habits
This study presents a new concept of a linguistic neutrosophic cubic number (LNCN), where the uncertain linguistic neutrosophic number corresponding to its first part is composed of the truth, indeterminacy, and falsity uncertain linguistic variables and the linguistic neutrosophic number corresponding to its second part is composed of the truth, indeterminacy, and falsity linguistic variables
Based on the operational laws of linguistic intuitionistic fuzzy numbers and linguistic neutrosophic numbers introduced in the existing literature [12,13,14,16,17], we propose the following operational laws of LNCNs

Summary

Introduction

In terms of complex objective aspects of real life, human preference judgments may use linguistic expression, instead of numerical value expression, in order to be more suitable for people’s thinking habits. We develop a decision-making method based on the LNCNWAA or LNCNWGA operator and the score, accuracy, and certain functions to solve decision-making problems with the hybrid information of both certain linguistic neutrosophic numbers and uncertain linguistic neutrosophic numbers under linguistic environments. Let two LNCNs be h1 = (h[s Ta1 , s Tb1 ], [s Ia1 , s Ib1 ], [s Fa1 , s Fb1 ]i, hs T1 , s I1 , s F1 i) and h2 = (h[s Ta2 , s Tb2 ], [s Ia2 , s Ib2 ], [s Fa2 , s Fb2 ]i, hs T2 , s I2 , s F2 i) Their ranking method based on their score, accuracy, and certain functions are defined as follows: If S(h1 ) > S(h2 ), h1 h2 ; If S(h1 ) = S(h2 ) and H(h1 ) > H(h2 ), h1 h2 ;. According to the ranking method of Definition 5, their ranking order is h3 h1 h2

Two Weighted Aggregation Operators of LNCNs

Faj w j

LNCNWGA Operator

Illustrative Example

Conclusions