A NOTE ON THE SUPER-ADDITIVE AND SUB-ADDITIVE TRANSFORMATIONS OF AGGREGATION FUNCTIONS: THE MULTI-DIMENSIONAL CASE

作者：Kouchakinejad Fateme^*; Siposova Alexandra

来源：Kybernetika, 2017, 53(1): 129-136.

DOI：10.14736/kyb-2017-1-0129

• aggregation function
• overrunning and underrunning property
• sub-additive and super-additive transformation

For an aggregation function A we know that it is bounded by A* and A(*) which are its super-additive and sub-additive transformations, respectively. Also, it is known that if A* is directionally convex, then A = A* and A(*) is linear; similarly, if A(*) is directionally concave, then A = A(*) and A* is linear. We generalize these results replacing the directional convexity and concavity conditions by the weaker assumptions of overrunning a super-additive function and underrunning a sub-additive function, respectively.

• 出版日期2017