# zbMATH — the first resource for mathematics

Solutions of composite fuzzy relational equations with triangular norms. (English) Zbl 0582.94031
This paper contains several results on fuzzy relational equations. Some of them are used for fuzzy inference.
Reviewer: N.Ţăndăreanu

##### MSC:
 94D05 Fuzzy sets and logic (in connection with information, communication, or circuits theory) 03E20 Other classical set theory (including functions, relations, and set algebra)
Full Text:
##### References:
 [1] Birkhoff, G.D., (), AMS Colloquium Publications Vol. 25 [2] Czoga£a, E.; Drewniak, J.; Pedrycz, W., Fuzzy relation equations on a finite set, Fuzzy sets and systems, 7, 89-101, (1982) · Zbl 0483.04001 [3] De Luca, A.; Termini, S., Algebraic properties of fuzzy sets, J. math. anal. appl., 40, 373-396, (1972) · Zbl 0211.31002 [4] Di Nola, A.; Sessa, S., On the set of solutions of composite fuzzy relation equations, Fuzzy sets and systems, 9, 275-285, (1983) · Zbl 0514.94027 [5] Di Nola, A.; Sessa, S., On the fuzziness of solutions of σ-fuzzy relation equations of finite spaces, Fuzzy sets and systems, 11, 65-77, (1983) · Zbl 0523.04002 [6] Drewniak, J., Note of fuzzy relation equations, Busefal, 12, 50-51, (1982) [7] Goguen, J.A., L-fuzzy sets, J. math. anal. appl., 18, 145-174, (1976) · Zbl 0145.24404 [8] Frank, M.J., On the simultaneous associativity of F(x, y) and x+y−F(x, y), Acquationes mathematicae, 19, 194-226, (1979) · Zbl 0444.39003 [9] Fukami, S.; Mizumoto, M.; Tanaka, K., Some considerations of fuzzy conditional inference, Fuzzy sets and systems, 4, 243-273, (1980) · Zbl 0453.03022 [10] Izumi, K.; Tanaka, H.; Asai, K., Duality of fuzzy systems based on the intuitionistic logical system, Trans. I.E.C.E. Japan J66-D, 10, 1114-1121, (1983), (in Japanese) [11] Klement, E.P., Operations of fuzzy sets: an axiomatic approach, Information sciences, 27, 221-232, (1982) · Zbl 0515.03036 [12] Klement, E.P., Construction of fuzzy σ-algebra using triangular norms, J. math. anal. appl., 85, 543-565, (1982) · Zbl 0491.28003 [13] Miyakoshi, M.; Sato, Y.; Kawaguchi, M., A fuzzy-fuzzy relation and its application to the clustering technique, Behaviormetrika, 8, 15-22, (1980) [14] Miyakoshi, M.; Shimbo, M., Composite fuzzy relations with T-norms, Trans. I.E.C.E. Japan, J67-D, 4, 391-398, (1984), (in Japanese) · Zbl 0554.60004 [15] Mizumoto, M.; Zimmermann, H.-J., Comparison of fuzzy reasoning methods, Fuzzy sets and systems, 8, 253-283, (1982) · Zbl 0501.03013 [16] Negoita, C.V.; Ralescu, D.A., () [17] Ovchinnikov, S.V., Structure of fuzzy binary relations, Fuzzy sets and systems, 6, 169-195, (1981) · Zbl 0464.04004 [18] Pedrycz, W., Fuzzy relational equations with triangular norms and their resolutions, Busefal, 11, 24-32, (1982) · Zbl 0498.04004 [19] Pedrycz, W., Fuzzy relational equations with generalized connectives and their applications, Fuzzy sets and systems, 10, 185-201, (1983) · Zbl 0525.04004 [20] Pedrycz, W., Numerical and applicational aspects of fuzzy relational equations, Fuzzy sets and systems, 11, 1-18, (1983) · Zbl 0517.93001 [21] Pedrycz, W., Fuzzy relational equations with triangular norms in modelling of decision-making processes, (), 269-274 [22] Prévot, M., Algorithm for the solution of fuzzy relations, Fuzzy sets and systems, 5, 319-322, (1981) · Zbl 0451.04004 [23] Sanchez, E., Resolution of composite relation equations, Information and control, 30, 38-48, (1976) · Zbl 0326.02048 [24] Sanchez, E., Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic, (), 221-234 [25] Sanchez, E., Eigen fuzzy sets and fuzzy relations, J. math. anal. appl., 81, 399-421, (1981) · Zbl 0466.04003 [26] Schweizer, B.; Sklar, A., Operations on distribution functions not derivable from operations on random variables, Studia Mathematica, 52, 43-52, (1974) · Zbl 0292.60035 [27] Tamura, S.; Higuchi, S.; Tanaka, K., Pattern classification based on fuzzy relations, IEEE trans. systems man cybernet., 1, 1, 61-66, (1976) · Zbl 0224.68012 [28] Tong, R.M., Analysis of fuzzy control algorithms using the relation matrix, Internat. J. man-machine studies, 8, 679-686, (1976) · Zbl 0355.93022 [29] Weber, S., A general concept of fuzzy connectives, negations and implications based on t-norms and t-conorms, Fuzzy sets and systems, 11, 115-134, (1983) · Zbl 0543.03013 [30] Yager, R.R., On a general class of fuzzy connectives, Fuzzy sets and systems, 4, 235-242, (1980) · Zbl 0443.04008 [31] Zadeh, L.A., Fuzzy sets, Information and control, 8, 338-353, (1965) · Zbl 0139.24606
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.