C. Langrand, V. Kreinovich, and H. T. Nguyen, "Two-dimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, Vol. 1, pp. 221--224, 1995. 12 Home/Search Document Details and Download
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Research on Advanced Soft Computing and Its Applications - Novák, Perfilieva.. (2002) (Correct)
....is a qualitative difference between different pairs of degrees. A natural way to describe this difference in continuous case is to use the approach of non standard analysis, with the actual infinitesimal elements ( lexicographic ordering) The optimal selection of such logics is described in [18, 37]. Eventually, we plan to combine these two directions. 9 Analyzing Possible Non Associative Operations Since A B and B A mean the same thing, it is natural to require that our degree of belief in A B be the same as our degree of belief in B A, i.e. that the and operation is commutative. ....
C. Langrand, V. Kreinovich, and H. T. Nguyen, "Two-dimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, Vol. 1, pp. 221--224, 1995. 12
Interval Mathematics for Analysis of Multi-Level Granularity - Kreinovich, Aló (2001) Self-citation (Kreinovich) (Correct)
....there is a qualitative difference between different pairs of degrees. A natural way to describe this difference in continuous case is to use the approach of nonstandard analysis, with the actual infinitesimal elements ( lexicographic ordering) The optimal selection of such logics is described in [39], 56] Conclusion A natural way to analyze complex systems is to apply granulation. Granulation simplifies the analysis of the system and thus makes this analysis feasible, but it also makes the results of this analysis less accurate. To combine feasibility and accuracy, we must supplement the ....
C. Langrand, V. Kreinovich, and H. T. Nguyen, "Twodimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, Vol. 1, pp. 221--224, 1995.
On Efficient Representation of Expert Knowledge by Fuzzy.. - Nguyen, Kreinovich (2001) Self-citation (Kreinovich Nguyen) (Correct)
....value is a reasonable way of describing the uncertainty of a single expert. However, the confidence strongly depends on the consensus between different experts. We may want to use additional dimensions to describe how many expert share the original expert s opinion, and to what degree; see, e.g. [25,43]. ffl Different experts may strongly disagree. To describe the degree of this disagreement, we also need additional numerical characteristics, which make the resulting logic multi D; see, e.g. 41] In all these cases, we need a multi D logic to adequately describe expert s degree of ....
Langrand, G., Kreinovich, V., Nguyen, H. T. (1995) Two-dimensional fuzzy logic for expert systems, Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, 1 221--224. Hung T. Nguyen and Vladik Kreinovich
Interval Mathematics for Analysis of Multiresolutional Systems - Kreinovich, Aló (2001) Self-citation (Kreinovich) (Correct)
....there is a qualitative difference between different pairs of degrees. A natural way to describe this difference in continuous case is to use the approach of nonstandard analysis, with the actual infinitesimal elements ( lexicographic ordering) The optimal selection of such logics is described in [37], 54] Conclusion Interval mathematics is very helpful in the analysis of multiresolutional systems. Acknowledgments This work was supported in part by NASA under cooperative agreement NCC5 209 and grant NCC 2 1232, by the Future Aerospace Science and Technology Program (FAST) Center for ....
C. Langrand, V. Kreinovich, and H. T. Nguyen, "Twodimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, Vol. 1, pp. 221--224, 1995.
Why Unary and Binary Operations in Logic: General Result.. - Nguyen, Kreinovich (2001) (1 citation) Self-citation (Kreinovich Nguyen) (Correct)
....is a reqsonable way of describing the uncertainty of a single expert. However, the confidence strongly depends on the it consensus between different experts. We may want to use additional dimensions to describe how many expert share the original expert s opinion, and to what degree; see, e.g. [13, 23]. ffl Different experts may strongly disagree. To describe the dgeree of this disagreement, we also need additional numerical characteristics, which make the resulting logic multi D; see, e.g. 21] In all these cases, we need a multi D logic to adequately describe expert s degree of ....
C. Langrand, V. Kreinovich, and H.T. Nguyen, "Two-dimensional fuzzy logic for expert systems ", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22-- 28, 1995, Vol. 1, pp. 221--224.
On Efficient Representation of Expert Knowledge by Fuzzy Logic - Nguyen, Kreinovich (2001) Self-citation (Kreinovich Nguyen) (Correct)
....value is a reasonable way of describing the uncertainty of a single expert. However, the confidence strongly depends on the consensus between different experts. We may want to use additional dimensions to describe how many expert share the original expert s opinion, and to what degree; see, e.g. [30, 50]. Different experts may strongly disagree. To describe the degree of this disagreement, we also need additional numerical characteristics, which make the resulting logic multi D; see, e.g. 48] In all these cases, we need a multi D logic to adequately describe expert s degree of ....
Langrand, G., Kreinovich, V., Nguyen, H.T.: Two-dimensional fuzzy logic for expert systems, Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, 1995, 1 221--224.
Fuzzy/Probability ~ Fractal/Smooth - Nguyen, al. (1999) Self-citation (Nguyen) (Correct)
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C. Langrand, V. Kreinovich and H. T. Nguyen, "Two-dimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress (San Paulo, Brazil, July 22--28, 1995) 1 221--224.
Possible New Directions in Mathematical Foundations of.. - Nguyen, Kreinovich (1998) Self-citation (Kreinovich Nguyen) (Correct)
....is a non negative integer, and ff, fi and are real numbers. Comments. ffl This result (to be more precise, the appearance of sin) explains the above described oscillating behavior of Y (N; A) ffl As shown in [42] for n = 1, the only possible families are fC 1 Delta N ff g considered in [34, 41]. For ff = 1, we get functions corresponding to a probability approach; in [34, 41] we also give an interpretation for families corresponding to ff 6= 1. ffl For n = 2, we already have a possibility of an oscillating function f(N ) C 1 Delta N C 2 Delta N Delta sin(fi Delta ln(N ) ....
.... (to be more precise, the appearance of sin) explains the above described oscillating behavior of Y (N; A) ffl As shown in [42] for n = 1, the only possible families are fC 1 Delta N ff g considered in [34, 41] For ff = 1, we get functions corresponding to a probability approach; in [34, 41], we also give an interpretation for families corresponding to ff 6= 1. ffl For n = 2, we already have a possibility of an oscillating function f(N ) C 1 Delta N C 2 Delta N Delta sin(fi Delta ln(N ) For this function, as sin oscillates between Gamma1 and 1, the ratio dN (A) f(N ) N ....
C. Langrand, V. Kreinovich and H. T. Nguyen, "Two-dimensional fuzzy logic for expert systems", Sixth International Fuzzy Systems Association World Congress, San Paulo, Brazil, July 22--28, 1995, Vol. 1, pp. 221--224.
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