×

A method of inference in approximate reasoning based on interval-valued fuzzy sets. (English) Zbl 0635.68103

This paper introduces and discusses a method of approximate inference which operates on the extension of the concept of a fuzzy set by the concept of an interval-valued fuzzy set. This method allows a formal, fuzzy representation to be built for verbal decision algorithms. Furthermore, it can have an effective computer representation. An example showing how this method operates is provided.

MSC:

68T99 Artificial intelligence
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Baldwin, J.F.; Pilsworth, B.W., A model of fuzzy reasoning through multi-valued logic and set theory, Internat. J. man-machine stud., 11, 351-380, (1979) · Zbl 0413.03015
[2] Czogala, E., On distribution function description of probabilistic sets and its application in decision making, Fuzzy sets and systems, 10, 21-29, (1983) · Zbl 0535.62011
[3] Czogała, E.; Pedrycz, W., On the concept of fuzzy probabilistic controllers, Fuzzy sets and systems, 10, 109-121, (1983) · Zbl 0544.93003
[4] Dubois, D.; Prade, H., Operations in a fuzzy-valued logic, Inform. and control, 43, 224-240, (1979) · Zbl 0434.03020
[5] A. Dziech and M.B. Gorzałczany, Effectiveness evaluation of the interval-valued fuzzy decisional rule in some decisionmaking problems of signal transmission, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish).
[6] Dziech, A.; Gorzałczany, M.B., Application of interval-valued fuzzy sets in signal transmission problems, (), 77-82
[7] Gorzalczany, M.B.; Stachowicz, M.S., On certain ideas of designing fuzzy controllers, (), 167-188, (in Polish)
[8] Gorzalczany, M.B.; Kiszka, J.B.; Stachowicz, M.S., Some problems of studying adequacy of fuzzy models, (), 14-34
[9] M.B. Gorzałczany, Interval-valued fuzzy formalisation method of verbal decisional rules taking into consideration the hierarchy of their importance, Zeszyty Kieleckiego Towarzystwa Naukowego “Studia Kieleckie” (to appear) (in Polish).
[10] Gorzałczany, M.B., Approximate inference with interval-valued fuzzy sets - an outline, (), 89-95
[11] Gorzałczany, M.B., Interval-valued fuzzy method of approximate inference and its application to the problems of signal transmission and construction of control algorithms, (), (in Polish)
[12] Hirota, K., Concept of probabilistic sets, Fuzzy sets and systems, 5, 31-46, (1981)
[13] Kania, A.A.; Kiszka, J.B.; Gorzałczany, M.B.; Maj, J.R.; Stachowicz, M.S., On stability of formal fuzziness systems, Inform. sci., 22, 51-68, (1980) · Zbl 0464.93005
[14] Zadeh, L.A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE trans. systems man cybernet., 1, 28-44, (1973) · Zbl 0273.93002
[15] Zadeh, L.A., The concept of a linguistic variable and its application to approximate reasoning - I, Inform. sci., 8, 199-249, (1975) · Zbl 0397.68071
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.