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A note on the idempotent functions with respect to pseudo-convolution. (English) Zbl 0953.28012

Summary: A general notion of pseudo-convolution based on pseudo-arithmetical operations is recalled. The idempotents with respect to pseudo-convolutions are investigated. Complete characterization of idempotents with respect to pseudo-convolutions based on the generalized Sugeno integral is given. Several other cases based on the idempotent pseudo-additions are studied.

MSC:

28E10 Fuzzy measure theory
26E50 Fuzzy real analysis
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[1] Bertoluzza, K., On the distributivity between t-norms and tconorms, (2nd IEEE Conf. on Fuzzy Systems. 2nd IEEE Conf. on Fuzzy Systems, San Francisco (1993)), 140-147
[2] Golan, J. S., The Theory of Semirings with Applications in Mathematics and Theoretical Computer Sciences, (Pitman Monographs and Surveys in Pure and Applied Mathematics, vol. 54 (1992), Longman: Longman New York) · Zbl 0584.16015
[3] Kolesárová, A., Similarity preserving t-norm-based additions of fuzzy numbers, Fuzzy Sets and Systems, 91, 215-229 (1997) · Zbl 0920.04009
[4] Kolesárová, A., Triangular norm-based addition of similar fuzzy numbers and preserving similarity, Busefal, 69, 43-54 (1997)
[5] Marková, A., Idempotents of the T-addition of fuzzy numbers, Tatra Mount. Math. Publ., 12, 65-72 (1997) · Zbl 0954.03059
[6] Marková-Stupňanová, A., Pseudo-convolutions and their idempotents, (Proc. IFSA’97. Proc. IFSA’97, Praha (1997)), 484-487
[7] Marková-Stupňanová, A., T-sum idempotents, (Proc. EUFIT’97. Proc. EUFIT’97, Aachen (1997)), 24-28
[8] Mesiar, R., Possibility measures based integrals — theory and applications, (Proc. FAPT’95. Proc. FAPT’95, Gent (1995)), 99-107 · Zbl 0895.28009
[9] Mesiar, R., Shape preserving additions of fuzzy intervals, Fuzzy Sets and Systems, 86, 73-78 (1997) · Zbl 0921.04002
[10] Pap, E., Null-Additive Preserved by Given PseudoConvolution ∗ Set Functions (1995), Ister Science & Kluwer Academic Publishers: Ister Science & Kluwer Academic Publishers Dordrecht · Zbl 0856.28001
[11] Pap, E., Decomposable measures and nonlinear equations, Fuzzy Sets and Systems, 92, 205-221 (1997) · Zbl 0934.28015
[12] E. Pap, N. Ralević, Pseudo-Laplace transform, Nonlinear Anal. Theory Meth. Appl., to appear.; E. Pap, N. Ralević, Pseudo-Laplace transform, Nonlinear Anal. Theory Meth. Appl., to appear. · Zbl 0931.44001
[13] Pap, E.; Štajner, I., Pseudo-convolution in the theory of optimization, probabilistic metric spaces, information, fuzzy numbers, system theory, (Proc. IFSA’97. Proc. IFSA’97, Praha (1997)), 491-495
[14] E. Pap, N. Teofanov, Pseudo-delta sequences, Yugoslav. J. Oper. Res., to appear.; E. Pap, N. Teofanov, Pseudo-delta sequences, Yugoslav. J. Oper. Res., to appear. · Zbl 0946.28014
[15] Sugeno, M., Theory of fuzzy integrals and its applications, (Ph.D. Thesis (1974), Tokyo Institute of Technology) · Zbl 0316.60005
[16] Wang, Z.; Klir, G., Fuzzy Measure Theory (1992), Plenum Press: Plenum Press New York · Zbl 0812.28010
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