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Symmetry 2018, 10(9), 392; https://doi.org/10.3390/sym10090392

Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making

1
Department of IT, AGI Education, Auckland 1051, New Zealand
2
Department of Information Technology, Otago Polytechnic, Auckland International Campus, Auckland 1141, New Zealand
3
Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan
4
Department of Mathematics, University of Management and Technology, Lahore 54770, Pakistan
*
Author to whom correspondence should be addressed.
Received: 22 July 2018 / Revised: 31 August 2018 / Accepted: 3 September 2018 / Published: 10 September 2018
(This article belongs to the Special Issue Fuzzy Techniques for Decision Making 2018)
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Abstract

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. View Full-Text
Keywords: hesitant intuitionistic fuzzy linguistic term set; probabilistic hesitant intuitionistic linguistic term set; multi-attribute group decision making; aggregation operators; TOPSIS hesitant intuitionistic fuzzy linguistic term set; probabilistic hesitant intuitionistic linguistic term set; multi-attribute group decision making; aggregation operators; TOPSIS
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Malik, M.G.A.; Bashir, Z.; Rashid, T.; Ali, J. Probabilistic Hesitant Intuitionistic Linguistic Term Sets in Multi-Attribute Group Decision Making. Symmetry 2018, 10, 392.

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