Pappis, C. P.; Adamopoulos, G. I. A computer algorithm for the solution of the inverse problem of fuzzy systems. (English) Zbl 0727.93029 Fuzzy Sets Syst. 39, No. 3, 279-290 (1991). The paper presents a computer algorithm for the solution of the so-called “inverse problem”. Given a fuzzy relation \(R\subset U\times V\) and a fuzzy subset \(B\subset V\), this algorithm produces the solution semilattice formed by the fuzzy subsets \(A\subset U\) satisfying the fuzzy relational equation \(A\circ R=B\), where \(\circ\) denotes maxmin composition. The program, while written in ZBasic, runs also in less powerful versions of Basic. Some examples are included to show the output format. Perhaps a portable FORTRAN or Pascal version would be more performant and more profitable. The algorithm is applicable to the optimization and control problems of fuzzy systems for which the maxmin rule of composition is acceptable as an inference mechanism. Reviewer: O.Pastravanu (Iaşi) Cited in 15 Documents MSC: 93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems) 93-04 Software, source code, etc. for problems pertaining to systems and control theory 93C42 Fuzzy control/observation systems Keywords:computer algorithm; fuzzy relational equation PDFBibTeX XMLCite \textit{C. P. Pappis} and \textit{G. I. Adamopoulos}, Fuzzy Sets Syst. 39, No. 3, 279--290 (1991; Zbl 0727.93029) Full Text: DOI References: [1] Pappis, C. P., Multi-input multi-output fuzzy systems and the Inverse Problem, European J. Oper. Res., 28, 228-230 (1987) [2] Pappis, C. P., Resolution of Cartesian products of fuzzy sets, Fuzzy Sets and Systems, 26, 387-391 (1988) · Zbl 0664.04005 [3] Pappis, C. P.; Sugeno, M., Fuzzy relational equations and the inverse problem, Fuzzy Sets and Systems, 15, 79-90 (1985) · Zbl 0561.04003 [4] Sanchez, E., Resolution of composite fuzzy relation equations, Inform. and Control, 30, 38-48 (1976) · Zbl 0326.02048 [5] (Sugeno, M., Industrial Applications of Fuzzy Control (1985), North-Holland: North-Holland Amsterdam) · Zbl 0586.93053 [6] Zadeh, L. A., Outline of a new approach to the analysis of complex systems and decision processes, IEEE Trans. Systems Man Cybernet., 3, 28-44 (1973) · Zbl 0273.93002 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.