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Probabilistic multiplicative unbalanced linguistic term set and its application in matrix games

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Abstract

Probabilistic linguistic term sets (PLTSs) are suitable for enunciating evaluators’ complex linguistic perceptions more accurately within the intricate qualitative setting. Usually, the PLTS is based on a balanced concept and does not serve as a good information representation for an unbalanced qualitative concept. Therefore, to reflect experts’ distinct preferences and uncertainties, this paper proposes a new PLTS called the probabilistic multiplicative unbalanced linguistic term set (PM-ULTS), where both probabilities and non-uniform spacing of the linguistic labels are considered simultaneously. Afterwards, we put forward specific operational laws for the newly constructed PLTS to preserve the resultant linguistic labels and corresponding probability information. Some elementary aggregation operators beneficial in aggregating probabilistic linguistic information in decision-making problems are also constructed, and their excellent properties are addressed. Furthermore, based on the proposed concept, this study initiates the design of a unified two-person linguistic matrix game model with the new PLTS as a parameter. It addresses the imprecise information by the information measure function. Such a two-player probabilistic unbalanced linguistic matrix game is considered a convenient technique for multiple decision scenarios. Additionally, the proposed game model involves a re-translation process to convert the output back into the original probabilistic unbalanced linguistic domain without information loss, thereby escalating the interpretability of the game model compared with other existing uncertain matrix game methodologies. Finally, we discuss the significance of the proposed methodology and concept to question its validity and usefulness by presenting suitable examples.

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  1. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Tanya Malhotra & Anjana Gupta

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  1. Tanya Malhotra
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  2. Anjana Gupta
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Correspondence to Anjana Gupta.

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Malhotra, T., Gupta, A. Probabilistic multiplicative unbalanced linguistic term set and its application in matrix games. Int. J. Mach. Learn. & Cyber. 14, 1253–1283 (2023). https://doi.org/10.1007/s13042-022-01697-2

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