Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems

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.

show abstract

“…where f is a monotone increasing function, [0, 1] i . Now, we introduce two kinds of LSFs (Peng & Wang, 2016):…”

Section: Linguistic Term Set and Linguistic Scale Functionmentioning

confidence: 99%

“…To begin; we translate LNNs into SVNNs. There are two conversion methods by LSF in Peng and Wang (2016). For example, when f f s…”

Section: Tablementioning

confidence: 99%

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

Лю

You

2019

Computers & Industrial Engineering

View full text Add to dashboard Cite

show abstract

“…As analyzed in Peng and Wang, by applying diverse approaches, the rankings are

u_{4} ≻ u_{3} ≻ u_{1} ≻ u_{2}, u_{3} ≻ u_{4} ≻ u_{2} ≻ u_{1}

and

u_{4} ≻ u_{1} ≻ u_{3} ≻ u_{2}

, respectively. While the ranking given by Peng and Wang is

u_{3} ≻ u_{2} ≻ u_{1} ≻ u_{4}

.…”

Section: Illustrative Examplementioning

confidence: 99%

Linguistic Z‐number fuzzy soft sets and its application on multiple attribute group decision making problems

et al. 2019

View full text Add to dashboard Cite

In this study, the concept of linguistic Z-number fuzzy soft set (LZnFSS) is proposed to describe multiple uncertainties in practical decision making problems. LZnFSS combines the concepts of fuzzy soft set, linguistic Z-number, and soft set, which could reflect both of the uncertainty in structure and the uncertainty in detailed evaluations. As an initial idea, the set operations on LZnFSSs are put forward, the properties of such operations are also discussed. With traditional soft set based decision procedure and fuzzy soft set based decision procedure, a novel linguistic Z-number fuzzy soft set based group decision procedure is developed to solve multiattribute group decision making with linguistic Z-numbers. Wherein an extended technique for order preference by similarity to ideal solution is also developed. Finally, a numerical example is shown to illustrate the practicality and effectiveness of the given method. K E Y W O R D S linguistic Z-number, linguistic Z-number fuzzy soft set, multiattribute group decision making, soft set, TOPSIS

show abstract

“…Definition 1. [34] Let S t = {s i |i = 1, 2, ⋯ , 2t} be a discrete LTS, s i , be an LT. There exists a numerical value i ∈ [0, 1], then the LSF is a mapping from s i to i (i = 0, 1, ⋯ , 2t), and it can be defined as follows:…”

Section: Lts and Linguistic Scale Functionmentioning

confidence: 99%

“…There are several methods to translate LNNs into SVNNs. We use two LSFs−f 1 (s i ) and f 2 (s i ) from Reference [34] to achieve the transformation. Specifically, when f = f 1 (s i ), the evaluation value y 12 = (s 3 , s 4 , s 2 ) is converted into (0.375,0.5,0.25); when f = f 2 (s i ) (r = 1.37), the evaluation value y 12 is converted into (0.427,0.5,0.326).…”

Section: Ranking Ordersmentioning

confidence: 99%

Improved TODIM Method Based on Linguistic Neutrosophic Numbers for Multicriteria Group Decision-Making

Лю¹,

You²

2019

IJCIS

View full text Add to dashboard Cite

A B S T R A C TThe TODIM (an acronym in Portuguese for interactive multicriteria decision-making) method can consider the decisionmakers' (DMs') psychological behavior. However, the classical TODIM method has been unable to address fuzzy information such as the linguistic neutrosophic number (LNN), which is an effective tool to represent uncertainty. In this paper, an extended TODIM method is proposed to solve multicriteria group decision-making (MCGDM) problems in a linguistic neutrosophic environment. First, the definitions and characteristics of the classical TODIM and the LNNs are introduced. Then, an improved score function (SF) of LNNs is proposed. Furthermore, we obtain the combined weights of the criteria and aggregate individual decision matrices into a group decision matrix. The classical TODIM method is extended to address MCGDM problems with LNNs, and specific decision steps are provided. Finally, several examples are given to verify the effectiveness and superiority of the proposed approach by comparison with some existing methods. Rashno et al. utilized [11] NSs and graph algorithms to present a fully automated algorithm in the healthcare industry. Fan et al.proposed [12] a neutrosophic Hough transform (NHT) method to improve the track initiation monitoring capacity in an uncertain environment.In practice, people are used to giving their opinions in qualitative terms, such as "excellent, " "fair, " and "worse. " At this point, Zadeh defined [13] linguistic variables (LVs) to describe words or sentences in natural language. Since then, many studies on linguistic decision-making problems have been conducted. Wu et al. put forward [14] the maximum support degree model to guarantee the accuracy of group opinion based on linguistic distributions. Zhang et al. established [15] a new decision support model with 2-tuple linguistic terms that provided a basis for emergency decision-making. Furthermore, there are many extensions of LVs to accurately express evaluation information. Based on the FS model, Rodríguez et al. proposed [16] the concept of a hesitant fuzzy linguistic term set (HFLTS) in which a DM may hesitate among several LVs to define the TM. Analogously, Chen and Liu defined [17] the linguistic intuitionistic fuzzy numbers (LIFNs) that represent the TM and FM by LVs. However, the above linguistic forms reflect only the TM (and FM), and thus they are insufficient to accommodate uncertain and inconsistent information. Therefore, Fang and Ye introduced [18] the concept of linguistic neutrosophic numbers (LNNs) based on NS, which is characterized by describing the TM, IM, and FM of each element in a universe using three LVs.For MCGDM problems, there are two common methods to help DMs select the optimal proposal from a variety of alternatives. One method uses aggregation operators that integrate the evaluation Pdf_Folio:1

show abstract

Hesitant Uncertain Linguistic Z-Numbers and Their Application in Multi-criteria Group Decision-Making Problems

Cited by 106 publications

References 43 publications

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

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

Linguistic Z‐number fuzzy soft sets and its application on multiple attribute group decision making problems

Improved TODIM Method Based on Linguistic Neutrosophic Numbers for Multicriteria Group Decision-Making

Contact Info

Product

Resources

About