The use of the concept of vague environment in approximate fuzzy reasoning

Rok, strany: 1997, 169 - 181

Using the concept of vague environment described by scaling functions [F. Klawonn: Fuzzy sets and vague environments, Fuzzy Sets and Systems 66 (1994), 207–221] instead of the linguistic terms of the fuzzy partition gives a simple way for fuzzy approximate reasoning. Widely used way of fuzzy approximate reasoning is based on similarity measures described by distance measure of fuzzy sets [I. B. Turksen, Z. Zhond: An approximate analogical reasoning schema based on similarity measures and interval-valued fuzzy sets Fuzzy Sets and Systems 34 (1990), 323–346]. The approximate fuzzy reasoning needs a lot of computational efforts, because the difficult way of calculating the distances of the fuzzy sets [L. T. Kóczy, K. Hirota: Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases, Inform. Sci 71 (1992), 169–201]. In most of the practical applications, the universes of the fuzzy partitions (used as primary sets of the fuzzy rulebase) can be described by vague environments (based on the familarity or indistinguishability of the elements [F. Klawonn: Fuzzy sets and vague environments, Fuzzy Sets and Systems 66 (1994), 207–221). The similarity relations in a vague environment can be defined by a scaling function. Comparing a description of a universe given by a fuzzy partition with the way of using the concept of vague environment we can say, that the linguistic terms of the fuzzy partition are points in the vague environment, while the shape of the fuzzy sets is described by the scaling function. So the similarity measure of fuzzy sets needed for approximate reasoning can be calculated as vague distance of points. In this case the primary fuzzy sets of the antecedent and the consequent parts of the fuzzy rules are points in their vague environments, so the fuzzy rules themselves are points in their vague environment too (in the vague environment of the fuzzy rulebase). It means, that the question of approximate fuzzy reasoning can be reduced to the problem of interpolation of the rule points in the vague environment of the fuzzy rulebase relation [Sz. Kovács, L. T. Kóczy: Fuzzy Rule Interpolation in Vague Environment, in: Proceedings of the 3rd. European Congress on Intelligent Techniques and Soft Computing, Aachen, Germany, 1995, pp. 95–98], [Sz. Kovács: {it New Aspects of Interpolative Reasoning}, in:  Proceedings of the 6th. International Conference on Information Processing and Management of Uncertainty in Knowledge-Based Systems, Granada, Spain, 1996, pp. 477–482].

ISO 690:

Kovács, S., Kóczy, L. 1997. The use of the concept of vague environment in approximate fuzzy reasoning. In Tatra Mountains Mathematical Publications, vol. 12, no.3, pp. 169-181. 1210-3195.

APA:

Kovács, S., Kóczy, L. (1997). The use of the concept of vague environment in approximate fuzzy reasoning. Tatra Mountains Mathematical Publications, 12(3), 169-181. 1210-3195.