Computational Complexity and Feasibility of Fuzzy Data Processing: Why Fuzzy Numbers, Which Fuzzy Numbers, Which Operations with Fuzzy Numbers

Authors

Hung T. Nguyen
Misha Kosheleva
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Radko Mesiar

Publication Date

3-1998

Comments

Technical Report: UTEP-CS-97-28a

Published in the Proceedings of the International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems (IPMU'98), Paris, France, July 6-10, 1998, pp. 273-280.

Abstract

In many real-life situations, we cannot directly measure or estimate the desired quantity r. In these situations, we measure or estimate other quantities r1,...,rn related to r, and then reconstruct r from the estimates for r_i. This reconstruction is called data processing.

Often, we only have fuzzy information about ri. In such cases, we have fuzzy data processing. Fuzzy data means that instead of a single number ri, we have several numbers that describes the fuzzy knowledge about the corresponding quantity. Since we need to process more numbers, the computation time for fuzzy data processing is often much larger than for the usual non-fuzzy one. It it, therefore, desirable to select representations and processing algorithms that minimize this increase and thus, make fuzzy data processing feasible.

In this paper, we show that the necessity to minimize computation time explains why we use fuzzy numbers, and describes what operations we should use.