A new model of fuzzy reasoning
The paper presents a new model of reasoning in presence of fuzzy premises. For antecedents \(ant_ i\) as well as a new fact \(A_ 0\) available, the consequence \(B_ 0\) is to be determined. The approach studied in this paper involves rules in which Y is expressed as a union of weighted \(B_ i's\). It means that for the i-th rule we obtain, \[ ant_ i:\;\text{ if X is \(A_ i\) then } Y=\lambda_{i1}/B_ 1+\lambda_{i2}/B_ 2+...+\lambda_{iN}/B_ N \] with the right-hand side of the expression denoting a union of \(B_ j\)'s activated at levels \(\lambda_{ij}\). From a formal standpoint \(``+''\) can be viewed as maximum. Then the entire construct specifies a fuzzy set defined over a family of the reference fuzzy sets formed by \(B_ j's\) [see also \textit{W. Pedrycz}, Fuzzy control and fuzzy systems, Research Studies Press (J. Wiley, 1989), where the same structure was discussed along with efficient numerical procedures enabling to determine the respective levels of activation \(\lambda_{ij}\) indicated in the above scheme of reasoning]. Relevant algorithmic (execution time, accuracy) and applicational issues are also thoroughly addressed in the context of linguistic synthesis.
scientific article; zbMATH DE number 4168400
scientific article