Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables
Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human t...
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doaj-5c3a7c77f957466d9db076b705013e5d2020-11-25T00:47:18ZengMDPI AGAlgorithms1999-48932018-09-0111913510.3390/a11090135a11090135Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant VariablesJun Ye0Wenhua Cui1Department of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaDepartment of Electrical Engineering and Automation, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, ChinaLinguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches.http://www.mdpi.com/1999-4893/11/9/135linguistic cubic hesitant variableleast common multiple numberweighted aggregation operatorlinguistic score functiondecision making |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jun Ye Wenhua Cui |
spellingShingle |
Jun Ye Wenhua Cui Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables Algorithms linguistic cubic hesitant variable least common multiple number weighted aggregation operator linguistic score function decision making |
author_facet |
Jun Ye Wenhua Cui |
author_sort |
Jun Ye |
title |
Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables |
title_short |
Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables |
title_full |
Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables |
title_fullStr |
Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables |
title_full_unstemmed |
Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables |
title_sort |
multiple attribute decision-making method using linguistic cubic hesitant variables |
publisher |
MDPI AG |
series |
Algorithms |
issn |
1999-4893 |
publishDate |
2018-09-01 |
description |
Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches. |
topic |
linguistic cubic hesitant variable least common multiple number weighted aggregation operator linguistic score function decision making |
url |
http://www.mdpi.com/1999-4893/11/9/135 |
work_keys_str_mv |
AT junye multipleattributedecisionmakingmethodusinglinguisticcubichesitantvariables AT wenhuacui multipleattributedecisionmakingmethodusinglinguisticcubichesitantvariables |
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