A Symmetry-Based Approach to Selecting Membership Functions and Its Relation to Chemical Kinetics

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.