Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making
Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their cor...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-09-01
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| Series: | Symmetry |
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| Online Access: | http://www.mdpi.com/2073-8994/10/9/392 |
| _version_ | 1811263999515295744 |
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| author | M. G. Abbas Malik Zia Bashir Tabasam Rashid Jawad Ali |
| author_facet | M. G. Abbas Malik Zia Bashir Tabasam Rashid Jawad Ali |
| author_sort | M. G. Abbas Malik |
| collection | DOAJ |
| description | Decision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models. |
| first_indexed | 2024-04-12T19:55:16Z |
| format | Article |
| id | doaj.art-2a23bf40a7bf4bdc9bb3d4332a8bc362 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-12T19:55:16Z |
| publishDate | 2018-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-2a23bf40a7bf4bdc9bb3d4332a8bc3622022-12-22T03:18:41ZengMDPI AGSymmetry2073-89942018-09-0110939210.3390/sym10090392sym10090392Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision MakingM. G. Abbas Malik0Zia Bashir1Tabasam Rashid2Jawad Ali3Department of IT, AGI Education, Auckland 1051, New ZealandDepartment of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDepartment of Mathematics, University of Management and Technology, Lahore 54770, PakistanDepartment of Mathematics, Quaid-i-Azam University, Islamabad 45320, PakistanDecision making is the key component of people’s daily life, from choosing a mobile phone to engaging in a war. To model the real world more accurately, probabilistic linguistic term sets (PLTSs) were proposed to manage a situation in which several possible linguistic terms along their corresponding probabilities are considered at the same time. Previously, in linguistic term sets, the probabilities of all linguistic term sets are considered to be equal which is unrealistic. In the process of decision making, due to the vagueness and complexity of real life, an expert usually hesitates and unable to express its opinion in a single term, thus making it difficult to reach a final agreement. To handle real life scenarios of a more complex nature, only membership linguistic decision making is unfruitful; thus, some mechanism is needed to express non-membership linguistic term set to deal with imprecise and uncertain information in more efficient manner. In this article, a novel notion called probabilistic hesitant intuitionistic linguistic term set (PHILTS) is designed, which is composed of membership PLTSs and non-membership PLTSs describing the opinions of decision makers (DMs). In the theme of PHILTS, the probabilities of membership linguistic terms and non-membership linguistic terms are considered to be independent. Then, basic operations, some governing operational laws, the aggregation operators, normalization process and comparison method are studied for PHILTSs. Thereafter, two practical decision making models: aggregation based model and the extended TOPSIS model for PHILTS are designed to classify the alternatives from the best to worst, as an application of PHILTS to multi-attribute group decision making. In the end, a practical problem of real life about the selection of the best alternative is solved to illustrate the applicability and effectiveness of our proposed set and models.http://www.mdpi.com/2073-8994/10/9/392hesitant intuitionistic fuzzy linguistic term setprobabilistic hesitant intuitionistic linguistic term setmulti-attribute group decision makingaggregation operatorsTOPSIS |
| spellingShingle | M. G. Abbas Malik Zia Bashir Tabasam Rashid Jawad Ali Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making Symmetry hesitant intuitionistic fuzzy linguistic term set probabilistic hesitant intuitionistic linguistic term set multi-attribute group decision making aggregation operators TOPSIS |
| title | Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making |
| title_full | Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making |
| title_fullStr | Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making |
| title_full_unstemmed | Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making |
| title_short | Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making |
| title_sort | probabilistic hesitant intuitionistic linguistic term sets in multi attribute group decision making |
| topic | hesitant intuitionistic fuzzy linguistic term set probabilistic hesitant intuitionistic linguistic term set multi-attribute group decision making aggregation operators TOPSIS |
| url | http://www.mdpi.com/2073-8994/10/9/392 |
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