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

Authors

Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Jorge Y. Cabrera, The University of Texas at El PasoFollow
Mario Gutierrez, The University of Texas at El PasoFollow
Thavatchai Ngamsantivong, King Mongkut's Institute of Technology North BangkokFollow

Publication Date

2013

Comments

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.

Abstract

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.