On some logical connectives for fuzzy sets theory. (English) Zbl 0522.03012


03B50 Many-valued logic
03E72 Theory of fuzzy sets, etc.
Full Text: DOI


[1] Aczél, J., Lectures on Functional Equations and Their Applications (1969), Academic Press: Academic Press New York
[2] Bellman, R.; Giertz, M., On the analytic formalism of the theory of fuzzy sets, Inform. Sci., 5, 149-156 (1973) · Zbl 0251.02059
[3] Cignoli, R., Boolean elements in Luckasiewicz algebras I, (Proc. Japan Acad. Ser. A, 41 (1965)), 670-675 · Zbl 0168.00601
[4] Dubois, D.; Prade, H., New results about properties and semantics of fuzzy settheoretic operators, (First Symposium on Policy Analysis and Information Systems. First Symposium on Policy Analysis and Information Systems, Durham, North Carolina (1979))
[5] Frank, M. J., On the simultaneous associativity of \(F(x, y)\) and \(x + y − F(x, y)\), Aequationes Math., 19, 194-226 (1979) · Zbl 0444.39003
[6] Haack, S., Philosophy of Logic (1978), Cambridge Univ. Press: Cambridge Univ. Press London/New York
[7] Hamacher, H., On logical connectives of fuzzy statements and their affiliated truth function, (Proc. Third European Meeting Cyberneties and Systems Res.. Proc. Third European Meeting Cyberneties and Systems Res., Vienna, Austria (1976))
[8] de Fériet, J. Kampé, Mesure de l’information fournie par un événement, (Colloq. Internat. CNRS, 186 (1969)), 191-212 · Zbl 0233.94009
[9] Ling, C. H., Representation of associative functions, Publ. Math. Debrecen, 12, 182-212 (1965) · Zbl 0137.26401
[10] Lowen, R., On fuzzy complements, Inform. Sci., 14, 107-113 (1978) · Zbl 0416.03047
[11] Mostered, P. S.; Shields, A. L., On the structure of semigroups on a compact manifold with boundary, Ann. of Math. (2), 65, 117-143 (1957)
[12] de Miranda, A. B.Paalman, Topological semigroups, (Mathematical Centre Tracts, No. 11 (1970), Mathematisch Centrum: Mathematisch Centrum Amsterdam) · Zbl 0242.22003
[13] Schweizer, B.; Sklar, A., Statistical metric spaces, Pacific J. Math., 10, 313-334 (1960) · Zbl 0091.29801
[14] Silvert, W., Symmetric summation: a class of operations on fuzzy sets, IEEE Trans. Systems Man Cybernet. (1979) · Zbl 0424.04003
[15] Trillas, E., Sobre funciones de negación en la teoria de conjuntos difusos, Stochastica, III-1, 47-60 (1979)
[16] Trillas, E.; Domingo, X.; Valverde, L., Pushing Luckasiewicz-Tarski implication a little farther, (Proc. of 11th Internat. Symposium of Multiple-Valued Logic. Proc. of 11th Internat. Symposium of Multiple-Valued Logic, Oklahoma (1981)), 232-234 · Zbl 0564.03022
[17] Yager, R. R., Generalized “and/or” operators for multivalued and fuzzy logic, (Proceedings of Tenth Symposium of Multiple-Valued Logic. Proceedings of Tenth Symposium of Multiple-Valued Logic, Evanston, Illinois (1980)), 214-218 · Zbl 0539.03010
[18] Zadeh, L. A., A fuzzy-algorithmic approach to the definition of complex or imprecise concepts, Internat. J. Man-Mach. Stud., 8, 249-291 (1976) · Zbl 0332.68068
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.