A CONSISTENT IMPUTATION GENERATION METHOD FOR LINGUISTIC COOPERATIVE GAMES AND ITS APPLICATION TO RISK AVERSION

Abstract

Cooperative game theory is very useful to risk aversion problems in economics and management systems. The existing methods only focus on the situation payoffs take the form of numerical values, ones take the form of linguistic labels are seldom discussed. The aim of this study is to propose the consistent imputation for cooperative games under a linguistic environment. To support risk aversion, a 2-tuple linguistic representation is employed to obtain the valid results and avoid the loss of linguistic information. This paper firstly defines some concepts for linguistic cooperative games, such as linguistic imputation, carrier, core and null player. A set of their desirable properties are also discussed. The linguistic Shapley value is then presented based on three axioms. Moreover, the existence and uniqueness of the linguistic Shapley value are discussed in detail. To adjust the linguistic imputation in accordance with the cardinality of a given original linguistic label set, an adjustment algorithm for generating consistent imputation is proposed. Finally, we give the application of linguistic imputation in solving risk aversion problems to illustrate the validity of the consistent imputation generation (CIG) method.