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A two-parameter generalization of Shannon-Khinchin axioms and the uniqueness theorem. (English) Zbl 1209.94027
Summary: Based on the one-parameter generalization of Shannon-Khinchin (SK) axioms presented by one of the authors, and utilizing a tree-graphical representation, we have developed for the first time a two-parameter generalization of the SK axioms in accordance with the two-parameter entropy introduced by Sharma, Taneja, and Mittal. The corresponding unique theorem is also proved. It is found that our two-parameter generalization of Shannon additivity is a natural consequence from the Leibniz product rule of the two-parameter Chakrabarti-Jagannathan difference operator.
##### MSC:
 94A17 Measures of information, entropy 39A70 Difference operators