Bustince, H.; Burillo, P. Perturbation of intuitionistic fuzzy relations. (English) Zbl 1113.03334 Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 9, No. 1, 81-103 (2001). Summary: In this paper we present a way of perturbing reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relations, thus obtaining the perturbation of another reflexive, symmetric, antisymmetric, perfect antisymmetric, transitive and partially included intuitionistic fuzzy relation. To do so we study the main properties of an operator that allows us to go from an intuitionistic fuzzy set to another intuitionistic fuzzy set, we then apply this operator to intuitionistic fuzzy relations with different properties and we study the conditions that must be fulfilled by the new intuitionistic fuzzy relation to maintain the original properties. Cited in 4 Documents MSC: 03E72 Theory of fuzzy sets, etc. Keywords:intuitionistic fuzzy relation; composition of intuitionistic fuzzy relations; Atanassov’s operator PDFBibTeX XMLCite \textit{H. Bustince} and \textit{P. Burillo}, Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 9, No. 1, 81--103 (2001; Zbl 1113.03334) Full Text: DOI References: [1] Atanassov K., VII ITKR’s Session, Deposed in Central Sci. Techn. Library of Bulg. Acd. of Set, Sofia pp 1684– (1983) [2] DOI: 10.1016/S0165-0114(86)80034-3 · Zbl 0631.03040 [3] DOI: 10.1016/0165-0114(89)90215-7 · Zbl 0685.03037 [4] DOI: 10.1016/0165-0114(96)84611-2 · Zbl 0872.94061 [5] Atanassov K., FUBEST94, Sofia, Bulgaria pp 43– (1994) [6] Atanassov K., Proc. Polish Symp. Interval and Fuzzy Mathematics, Poznan pp 4– (1986) [7] Szmidt E., Notes on IFS 2 pp 15– (1996) [8] Atanassov K., First Scientific Session of the Mathematical Foundations Artificial Intelligence, Sofia IM-MFAIS pp 1– (1989) [9] Burillo P., Mathware and Soft Computing 2 pp 5– (1995) [10] Bustince H., Mathware and Soft Computing 2 pp 117– (1995) [11] DOI: 10.1016/0165-0114(96)84610-0 · Zbl 0875.04006 [12] Burillo P., Notes on IFS 1 pp 93– (1995) [13] DOI: 10.1109/TSMC.1973.5408575 · Zbl 0273.93002 [14] DOI: 10.1016/0165-0114(95)00313-4 · Zbl 0903.04001 [15] Zadeh L. A., U. K. pp 149– (1970) 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.