Probabilistic multiplicative unbalanced linguistic game using linguistic cloud model.

In many game theoretic environments, the precise crisp values of payoffs are not always easy to gather as real-life decision-making problems are not inevitably precise and symmetrically distributed in nature. Hence, there is a need to explore matrix games having unbalanced probabilistic linguistic information. To fill this research gap, this study proposes a concept of probabilistic multiplicative unbalanced linguistic (PM-UL) game in which the players express their responses in terms of PM-UL term. This type of PM-UL game is a useful technique for multiple criteria analysis. Further, to thoroughly capture the uncertainty involved in payoffs of such games, they are converted to probabilistic unbalanced linguistic clouds (PULCs) that describe the uncertainties of qualitative payoffs by implementing the uncertain transformation between PM-UL payoffs and quantitative values. The PULCs are represented by three numerical characteristics, i.e. expectation, entropy and hyperentropy. Hence, this model overcomes the inherent limitation of existing linguistic games where only the fuzziness of concepts is evaluated, by providing a PULC strategy and PULC value of the game. This procedure overcomes the loss of information occurring in the process of transformation of payoff values into quantitative ones. The defined methodology is implemented on a real-life working problem to demonstrate the effect and applicability in decision-making circumstances. [ABSTRACT FROM AUTHOR]