Citation: | YU Peng, “Quantitative Method Based on Cotangent Similarity Degree in Three-Valued Ł ukasiewicz Logic,” Chinese Journal of Electronics, vol. 30, no. 1, pp. 134-144, 2021, doi: 10.1049/cje.2020.11.011 |
[1] |
Roser J. B and Turquette A. R, Many-valued Logic, Amsterdam: North-Holland, 1952.
|
[2] |
Pavelka J, "On fuzzy logic: Ⅰ", Zeitschrift für Mathematische Logik und Grundlagen Mathematik, Vol. 25, No. 2, pp.45-52, 1979.
|
[3] |
Adam E W, A Primer of Probability Logic, Stanford: CSLI Publications, pp.11-34, 1998.
|
[4] |
Mundici D, "Averaging truth value in Łukasizewicz logic", Studia Logica, Vol. 55, No. 1, pp.113-127, 1995. doi: 10.1007/BF01053035
|
[5] |
Flaminio T and Godol, "A logic for reasoning about the probability of fuzzy events", Fuzzy Sets and Systems, Vol. 158, No. 6, pp.625-638, 2007. doi: 10.1016/j.fss.2006.11.008
|
[6] |
X. Li and B.D. Liu, "Foundation of credibilistic logic", Fuzzy Optimization and Decision Making, Vol. 8, No. 1, pp.91-102, 2009. doi: 10.1007/s10700-009-9053-6
|
[7] |
Faginr, Halpernjy and Megiddon, "A logic for reasoning about probabilities", Information and Computation, Vol. 87, No. 12, pp.78-128, 1990. doi: 10.1109/LICS.1988.5138
|
[8] |
G.J. Wang and H.J. Zhou, "Quantitative logic", Information Science, Vol. 179, No. 3, pp.226-247, 2009. doi: 10.1016/j.ins.2008.09.008
|
[9] |
G.J. Wang and L. Fu and J.S. Song, "Theory of truth degrees of propositions in two-valued logic", Science in China(Series A), Vol. 45, No. 9, pp.1106-1116, 2002. doi: 10.1360/02ys9122
|
[10] |
H.J. Zhou and G.J. Wang, "Borel probabilistic and quantitative logic", Science China: Information Sciences, Vol. 54, No. 9, pp.1843-1854, 2011. doi: 10.1007/s11432-011-4268-x
|
[11] |
L. Cheng, H. W Liu and G.J. Wang, "Correction and improvement on several results in quantitative logic", Information Sciences, Vol. 278, pp.555-558, 2014. doi: 10.1016/j.ins.2014.03.073
|
[12] |
G.J. Wang, "A unified integrated method for evaluating goodness of propositions in several propositional logic systems and its applications", Chinese Journal of Electronics, Vol. 21, No. 2, pp.195-201, 2012. http://cje.ejournal.org.cn/en/article/id/3516
|
[13] |
H.B. Wu, "The generalized truth degree of quantitative logic in the logic system $L. {*}_{n}$(n-valued NM-logic system)", Computers & Mathematics with Applications, Vol. 59, No. 8, pp.2587-2596. http://www.ams.org/mathscinet-getitem?mr=2607962
|
[14] |
Y.H. She, G.J. Wang and X.L. He, "Topological characterization of consistency of logic theories in n-valued Ł ukasizewicz logic Ł uk(n)", Chinese Journal of Eletronics, Vol. 19, No. 3, pp.427-430, 2009. http://www.zhangqiaokeyan.com/academic-journal-cn_electronic-journal-english_thesis/0201268501098.html
|
[15] |
G.J. Wang, "Theory of logic metric spaces", Acta Mathematica Sinica, Chinese Series, Vol. 44, No. 1, pp.159-168, 2001.
|
[16] |
G.J. Wang and Y.H. She, "A topological characterization of consistency of logic theories in propositional logic", Mathematical Logic Quarterly, Vol. 52, pp.470-477, 2006. doi: 10.1002/malq.200610007
|
[17] |
Y.H. She and X.L. He, "A quantitative approach to reasoning about incomplete knowledge", Information Sciences, Vol. 451, pp.100-111, 2018. http://smartsearch.nstl.gov.cn/paper_detail.html?id=e703a536c793af12df4cc1321a9f4e88
|
[18] |
J. Li and F. G Deng, "Unified theory of truth degrees in n-valueds MTL propositionan logic", Acta Electronica Sinica, Vol. 39, No. 8, pp.1864-1868, 2011.
|
[19] |
J. Li and J.T. Yao, "Theory of integral truth degrees if formulas in SMTL propositongal logic", Acta Electronica Sinica, Vol. 41, No. 5, pp.878-883, 2013. http://www.researchgate.net/publication/287163397_Theory_of_integral_truth_degrees_of_formula_in_SMTL_propositional_logic
|
[20] |
W.B. Zuo, "Probability truth degrees of formulas in MTL-algebras semantics", Acta Electronica Sinica, Vol. 43, No. 2, pp.293-298, 2015. http://en.cnki.com.cn/Article_en/CJFDTotal-DZXU201502014.htm
|
[21] |
S.L. Cheng, J.G. Li and X.G. Wang, Fuzzy Set Theory and Its Application, Beijing: Science Press, 2005.
|
[22] |
X.H. Zhang and Y. Zheng, "Linguistic quantifiers modeled by interval-valued intuitionistic Sugeno integrals", Journal of Intelligent & Fuzzy Systems, Vol. 29, No. 2, pp.583-592, 2015. http://www.researchgate.net/publication/282900004_Linguistic_quantifiers_modeled_by_interval-valued_intuitionistic_Sugeno_integrals1
|
[23] |
J. Ye, "Single-valued neutrosophic similarity measures based on cotangent function and their application in the fault diagnosis of steam turbine", Soft Computing, Vol. 21, pp.817-825, 2017. doi: 10.1007/s00500-015-1818-y
|
[24] |
P. Yu and B. Zhao, "The Hamming distance representation and decomposition theorem of formula's TruthDegree", Journal of Software, Vol. 29, No. 10, pp.3091-3110, 2018. http://www.zhangqiaokeyan.com/academic-journal-cn_journal-software_thesis/0201271020749.html
|
[25] |
B. Zhao and P. Yu, "A kind of quantitative method Based on camberra fuzzy distance in multiple-valued logic", Acta Electronica Sinica, Vol. 46, No. 10, pp.2305-2315, 2018. http://en.cnki.com.cn/Article_en/CJFDTotal-DZXU201810001.htm
|
[26] |
M.K. Chakraborty, Use of Fuzzy Set Theory in Introducducing Grade Consequence in Multiple-valued Logic, in Fuzzy Logic in Knowledge-based systems, Decision and Aontrol, North-Holled, pp.247-257, 1998. http://www.researchgate.net/publication/265347970_Use_of_fuzzy_set_theory_in_introducing_graded_consequence_in_multiple_valued_logic
|
[27] |
M.K. Chakraborty and Sanjukta Basu, "Graded consequence and Some Metalogical Notions Generalized", Fundamenta Informaticae, Vol. 32, pp.299-311, 1997. doi: 10.3233/FI-1997-323405
|