A linguistic truth set in which each element is a linguistic truth value is discussed. Ranking linguistic truth values based on Graded Mean Integration Representation method is discussed also. We then give a decreasing linguistic truth set and an increasing linguistic truth set by using the above ranking method, and present a Not function of linguistic truth value combined by the above decreasing linguistic truth set and the increasing linguistic truth set. A minimum function and a maximum function based on representations of linguistic truth values are introduced. In addition, some natural operations of linguistic logic combined by minimum function and maximum function, and Not function are presented. Some properties of our presented natural operations are presented, and are proved. Furthermore, some application examples of linguistic logical statements are discussed finally.
Linguistic truth, linguistic logic, Graded Mean Integration Representation, rank, order, natural operation, linguistic logical statement
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