Bustince, H.; Calderón, M.; Mohedano, V. Some considerations about a least squares model for fuzzy rules of inference. (English) Zbl 0930.03025 Fuzzy Sets Syst. 97, No. 3, 315-336 (1998). Summary: The method of least squares is applied to fuzzy inference rules. We study conditions under which we can build a fuzzy set from another one through the method of least squares. Then we apply this technique in order to evaluate the conclusions of the generalized modus ponens and the generalized modus tollens. We present different theorems and examples that demonstrate the fundamental advantages of the method studied. We conclude presenting a method for obtaining the conclusion when working with fuzzy conditional propositions that contain two fuzzy propositions joined by the connective “and”. Cited in 1 Document MSC: 03B52 Fuzzy logic; logic of vagueness 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:approximate reasoning; least squares model; fuzzy logic; power function; fuzzy inference rules; generalized modus ponens; generalized modus tollens; fuzzy conditional propositions PDFBibTeX XMLCite \textit{H. Bustince} et al., Fuzzy Sets Syst. 97, No. 3, 315--336 (1998; Zbl 0930.03025) Full Text: DOI References: [1] Baldwin, J. F.; Guild, N. C.F., Feasible algorithms for approximate reasoning using fuzzy logic, Fuzzy Sets and Systems, 3, 225-251 (1980) · Zbl 0435.03019 [2] Chang, T. C.; Hasegawa, K.; Ibbs, C. W., The effects of membership function on fuzzy reasoning, Fuzzy Sets and Systems, 44, 169-186 (1991) · Zbl 0735.68073 [3] Ezawa, Y.; Kandel, A., Robust fuzzy inference, Internat. J. Intelligent Systems, 6, 185-197 (1991) · Zbl 0728.03022 [4] Fukami, S.; Mizumoto, M.; Tanaka, K., Some considerations on fuzzy conditional inference, Fuzzy Sets and Systems, 4, 243-273 (1980) · Zbl 0453.03022 [5] Gorzalczany, M. B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems, 21, 1-17 (1987) · Zbl 0635.68103 [6] Mizumoto, M., Extended fuzzy reasoning, (Gupta; Kandel; Blander; Kiszka, Reasoning in Expert Systems (1985), North-Holland: North-Holland Amsterdam), 71-85 [7] Mizumoto, M.; Zimmermann, H.-J., Comparison of fuzzy reasoning methods, Fuzzy Sets and Systems, 8, 253-283 (1982) · Zbl 0501.03013 [8] Nafarieh, A., A new approach to inference in approximate reasoning and its application to computer vision, (Ph.D. Dissertation (1988), University of Missouri: University of Missouri Columbia) [9] Park, D.; Cao, Z.; Kandel, A., Investigations on the applicability of fuzzy inference, Fuzzy Sets and Systems, 49, 151-169 (1992) [10] Pham, T. D.; Valliappan, S., A least squares model for fuzzy rules of inference, Fuzzy Sets and Systems, 64, 207-212 (1994) · Zbl 0845.03009 [11] Raha, S.; Ray, K. S., Analogy between approximate reasoning and the method of interpolation, Fuzzy Sets and Systems, 51, 259-266 (1992) [12] Ray, K. S.; Ghoshal, J., Approximate reasoning to pattern recognition, Fuzzy Sets and Systems, 77, 125-150 (1996) [13] Zadeh, L. A., A fuzzy-sets theoretic interpretation of linguistic hedges, J. Cybernetics, 2, 4-34 (1972) [14] Zadeh, L. A., The concept of a linguistic variable, and its application to the approximate reasoning. Part III, Inform. Sci., 8, 43-80 (1975) · Zbl 0404.68075 [15] Zadeh, L. A., The concept of a linguistic variable, and its application to the approximate reasoning. Part II, Inform. Sci., 8, 301-357 (1975) · Zbl 0404.68074 [16] Zadeh, L. A., Fuzzy logic, IEEE Computer, 83-93 (April 1988) 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.