Deschrijver, Glad; Kerre, Etienne E. On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision. (English) Zbl 1121.03074 Inf. Sci. 177, No. 8, 1860-1866 (2007). The paper offers a concise and focused view at intuitionistic fuzzy sets cast in the framework of various formalisms used to model uncertainty. In a nutshell, intuitionistic sets are useful in capturing concepts where a degree of membership of a certain point, \(A(x)\), taken along with a degree of non-membership, \(A^\sim(x)\), satisfy the relationship \(A(x)+A^\sim(x)\leq 1\). This concept is compared vis-à-vis some other commonly encountered models of uncertainty, in particular interval-valued fuzzy sets, \(L\)-fuzzy sets, soft sets and a number of interesting linkages between them and intuitionistic fuzzy sets are revealed. The study offers an interesting diagram summarizing the main dependencies between all these constructions. Reviewer: Witold Pedrycz (Edmonton) Cited in 64 Documents MSC: 03E72 Theory of fuzzy sets, etc. 68T37 Reasoning under uncertainty in the context of artificial intelligence Keywords:interval-valued fuzzy set; intuitionistic fuzzy set; \(L\)-fuzzy set; probabilistic set; soft set; taxonomy; vagueness; comparative analysis; models of uncertainty PDFBibTeX XMLCite \textit{G. Deschrijver} and \textit{E. E. Kerre}, Inf. Sci. 177, No. 8, 1860--1866 (2007; Zbl 1121.03074) Full Text: DOI References: [1] K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), 1983 (in Bulgarian).; K.T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia (deposed in Central Science-Technical Library of Bulgarian Academy of Science, 1697/84), 1983 (in Bulgarian). [2] Atanassov, K. T., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87-96 (1986) · Zbl 0631.03040 [3] Atanassov, K. T., Intuitionistic Fuzzy Sets (1999), Physica-Verlag: Physica-Verlag Heidelberg/New York · Zbl 0939.03057 [4] Basu, K.; Deb, R.; Pattanaik, P. K., Soft sets: an ordinal formulation of vagueness with some applications to the theory of choice, Fuzzy Sets and Systems, 45, 45-58 (1992) · Zbl 0749.90006 [5] Bustince, H.; Burillo, P., Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, 79, 403-405 (1996) · Zbl 0871.04006 [6] Deng, J. L., Introduction to grey system theory, Journal of Grey Systems, 1, 1-24 (1989) · Zbl 0701.90057 [7] Deschrijver, G.; Kerre, E. E., On the relationship between intuitionistic fuzzy sets and some other extensions of fuzzy set theory, Journal of Fuzzy Mathematics, 10, 3, 711-724 (2002) · Zbl 1013.03066 [8] Deschrijver, G.; Kerre, E. E., On the relationship between some extensions of fuzzy set theory, Fuzzy Sets and Systems, 133, 2, 227-235 (2003) · Zbl 1013.03065 [9] Dubois, D.; Ostasiewicz, W.; Prade, H., Fuzzy sets: history and basic notions, (Dubois, D.; Prade, H., Fundamentals of Fuzzy Sets (2000), Kluwer Academic Publishers: Kluwer Academic Publishers Dordrecht), 80-93 [10] Gau, W. L.; Buehrer, D. J., Vague sets, IEEE Transcations on Systems Man and Cybernetics, 23, 2, 610-614 (1993) · Zbl 0782.04008 [11] Goguen, J., L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18, 145-174 (1967) · Zbl 0145.24404 [12] Hirota, K., Concepts of probabilistic sets, Fuzzy Sets and Systems, 5, 31-46 (1981) · Zbl 0442.60008 [13] Nikolova, M.; Nikolov, N.; Cornelis, C.; Deschrijver, G., Survey of the research on intuitionistic fuzzy sets, Advanced Studies in Contemporary Mathematics, 4, 2, 127-157 (2002) · Zbl 1008.03036 [14] R. Sambuc, Fonctions Φ;; R. Sambuc, Fonctions Φ; [15] Zadeh, L. A., Fuzzy sets, Information and Control, 8, 338-353 (1965) · Zbl 0139.24606 [16] Zadeh, L. A., The concept of a linguistic variable and its application to approximate reasoning, Information Sciences, 8, 199-249 (1975) · Zbl 0397.68071 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.