Publication Date



Technical Report: UTEP-CS-13-30a

To appear in Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics IEEE SMC'2013, Manchester, UK, October 13-16, 2013.


In many practical situations, we encounter physical quantities like time for which there is no fixed starting point for measurements: physical properties do not change if we simply change (shift) the starting point. To describe knowledge about such properties, it is desirable to select membership functions which are similarly shift-invariant. We show that while we cannot require that each membership function is shift-invariant, we can require that the linear space of all linear combinations of given membership functions is shift-invariant. We describe all such shift-invariant families of membership functions, and we show that they are naturally related to the corresponding formulas of chemical kinetics.

tr13-30.pdf (65 kB)
Original file: UTEP-CS-13-30