TODIM and TOPSIS with Z-numbers

Renato A. KROHLING; André G. C. PACHECO; Guilherme A. dos SANTOS

doi:10.1631/FITEE.1700434

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TODIM and TOPSIS with Z-numbers

Regular Papers | Updated：2022-05-19

- TODIM and TOPSIS with Z-numbers
- 基于Z数的TODIM与TOPSIS方法
- Frontiers of Information Technology & Electronic Engineering Vol. 20, Issue 2, Pages: 283-291(2019)
- Affiliations：
  
  Department of Production Engineering, Federal University of Espirito Santo, Vitória, ES, CEP 29075-910, Brazil
  Graduate Program in Computer Science, Federal University of Espirito Santo, Vitória, ES, CEP 29075-910, Brazil
- Author bio：
  
  Renato A. KROHLING, E-mail: krohling.renato@gmail.com
  [ "André G. C. PACHECO, E-mail: pacheco.comp@gmail.com" ]
  [ "Guilherme A. dos SANTOS, E-mail: guilherme.artem@gmail.com" ]
- Funds：
- DOI：10.1631/FITEE.1700434
  CLC： O212.5
- Received：29 June 2017，
  
  Revised：2019-;2-15，
  
  Published：2019-02
- Accepted：
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Renato A. KROHLING, André G. C. PACHECO, Guilherme A. dos SANTOS. TODIM and TOPSIS with Z-numbers[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(2): 283-291.
DOI：

Renato A. KROHLING, André G. C. PACHECO, Guilherme A. dos SANTOS. TODIM and TOPSIS with Z-numbers[J]. Frontiers of Information Technology & Electronic Engineering, 2019, 20(2): 283-291. DOI： 10.1631/FITEE.1700434.

摘要

提出一种针对多标准决策问题处理Z数的方法。使用模糊数

和B的有序对Z=(

)定义Z数，其中

是兴趣变量的语言值，

是

的概率测度语言值。人类通过自然语言进行交流，使用这样的句子如"从家到大学大约需要半小时"。将Z数转化为模糊数，Z-TODIM和Z-TOPSIS分别是模糊TODIM和模糊TOPSIS的直接扩展。将提出的方法应用于两个案例并与使用精确数的标准方法比较，结果证明其可行。

Abstract

In this paper

we present an approach that can handle Z-numbers in the context of multi-criteria decision-making problems. The concept of Z-number as an ordered pair

) of fuzzy numbers

and

is used

where

is a linguistic value of a variable of interest and

is a linguistic value of the probability measure of

. As human beings

we communicate with each other by means of natural language using sentences like "the journey from home to university most likely takes about half an hour." The Z-numbers are converted to fuzzy numbers. Then the Z-TODIM and Z-TOPSIS are presented as a direct extension of the fuzzy TODIM and fuzzy TOPSIS

respectively. The proposed methods are applied to two case studies and compared with the standard approach using crisp values. The results obtained show the feasibility of the approach.

关键词

Keywords

references

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