Using New Version of Extended t -Norms and s -Norms for Aggregating Interval Linguistic Labels

The aim of this paper is to develop some closed algebra operational laws for interval linguistic labels based on extended t-norms and s-norms. We discuss the properties of these operational laws, such as commutative law, associative law, and distribution law. Different kinds of extended t-norms and s-norms, such as the extended algebraic, extended Einstein, extended Hamacher, and extended Frank t-norms and s-norms, have been investigated to produce different operational laws. As an application of such operational laws, we propose some extended t-norms and s-norms based interval linguistic weighted power average operators. We also study some basic properties of such aggregation functions. The cross-entropy of interval linguistic information is proposed and applied to obtain the weights of attributes. An approach to multiple attributes decision making with interval linguistic information is proposed. Finally, two cases of practical decision issues are illustrated to show the application of the proposed method.