APPROXIMATE RECONSTRUCTION OF MAPPING FUNCTIONS FROM LINGUISTIC DESCRIPTIONS IN PROBLEMS OF FUZZY LOGIC APPLIED TO SYSTEM CONTROL
G.P. Rao, D.A. Rutherford · Cybernetics & Systems · 1981
This paper discusses some aspects of approximate reconstruction of mapping functions from their linguistic descriptions. Linguistic description of the input-output characteristic of a control element is relevant to the treatment of fuzziness in real world control problems. It would normally be in the form of a set of statements. Zadeh's fuzzy set theory becomes a useful tool in the inference, interpretation and implementation of the fuzzy algorithm containing the fuzzy statements. The process of inference and interpretation may be online or offline. Offline interpretation involves the generation of either a fixed look up table (discrete) or the nonfuzzy input-output control characteristic (continuous) incorporating the input-output relation for the defined conditions. This paper concentrates on some important aspects of reconstructing the mapping function in an approximate form for decisive implementation in practical control problems. Interpretation of the fuzzy statement with the min-max logic leads to certain important questions discussed in the paper. The idea of smoothing is suggested to fuzzy relations as an approach to the problem of reconstructing the mapping function for convenience of implementation.