| تعداد نشریات | 31 |
| تعداد شمارهها | 834 |
| تعداد مقالات | 8,015 |
| تعداد مشاهده مقاله | 14,854,475 |
| تعداد دریافت فایل اصل مقاله | 9,587,528 |
A NEW WAY TO EXTEND FUZZY IMPLICATIONS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 15، شماره 3، مرداد و شهریور 2018، صفحه 79-97 اصل مقاله (360.96 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2018.3951 | ||
| نویسندگان | ||
| Yuan-Liang Han* 1؛ Fu-gui Shi2 | ||
| 1School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China and College of Science, North China Institute of Science and Technology, Langfang 065201, P.R.China | ||
| 2School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China | ||
| چکیده | ||
| The main purpose of this paper is to use a new way to extend fuzzy implications $I$ from a generalized sublattice $M$ to a bounded lattice $L$, such that the extended implications preserve many of the considered properties of fuzzy implications on $M$. Furthermore, as a special case, we investigate the extension of $(S,N)-$implications. Results indicate that the extended implications preserve many of the considered properties of $(S,N)$-implications. | ||
| کلیدواژهها | ||
| Extension-sublattice؛ Fuzzy implications؛ E-operator؛ Retraction | ||
| مراجع | ||
|
[1] M. Baczynski and B. Jayaram, Fuzzy Implications, Studies in Fuzziness and Soft Computing, Springer, Berlin, 231 (2008). [2] M. Baczynski and B. Jayaram, (S;N)- and R-implications: A state-of-the-art survey, Fuzzy Sets Syst., 159 (2008), 1836{1859. [3] M. Baczynski and B. Jayaram, On the characterization of (S;N)-implications, Fuzzy Sets Syst., 158 (2007), 1713{1737. [4] B. C. Bedregal, H. S. Santos and R. Callejas-Bedregal, T-norms on bounded lattices: t-norm morphisms and operators, in: IEEE International Conference on Fuzzy Systems, (2006), 22{28. [5] B. C. Bedregal, G. Beliakov, H. Bustince, J. Fernandez, A. Pradera and R. Reiser, Advances in fuzzy implication functions, in: M. Baczynski, et al.(Eds.), (S;N)-Implications on Bounded Lattices, Studies in Fuzziness and Soft Computing, Springer, Berlin, 300(3) (2013), 769{777. [6] B. C. Bedregal and A. Takahashi, The best interval representations of t-norms and automor- phisms, Fuzzy Sets Syst., 157 (2006), 3220{3230. [7] G. Birkho, Lattice Theory, American Mathematical Society, Providence, RI, 1973. [8] G. Chen and T. T. Pham, Fuzzy Sets, Fuzzy Logic and Fuzzy Control Systems, CRC Press, Boca Raton, 2001. [9] A. Cruz, B. Bedregal and R. Santiago, On the Boolean-like law I(x; I(y; x)) = 1, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 22(2) (2014), 205{215. [10] C. G. Da Costa, B. R. C. Bedregal and A. D. Doria Neto, Relating De Morgan triples with Atanassov's intuitionistic De Morgan triples via automorphisms, Int. J. Approx. Reason., 52(4) (2011), 473{487. [11] B. A. Davey and H. A. Priestley, Introduction to Lattices and Order, 2nd ed., Cambridge University Press, Cambridge, 2002. [12] J. Fodor, On fuzzy implication operators, Fuzzy Sets Syst., 42 (1991), 293{300. [13] Y. L. Han, Study on the extension method of fuzzy implications on generalized sublattices, Journal of North China Institute of Science and Technology, 12(3) (2015), 111{115. [14] A. K. Hans-Peter and L. B. Shapiro, On simultaneous extension of continuous partial func- tions, Proc. Am. Math. Soc., 125(6) (1997), 1853{1859. [15] K. Horiuchi and H. Murakami, Extension of the concept of mappings using fuzzy sets, Fuzzy Sets Syst., 56 (1) (1993), 79{88. [16] B. Jayaram, On the law of importation (x^y)!z(x!(y!z)) in fuzzy logic, IEEE Trans- actions on Fuzzy Systems, 16(1) (2008), 130{144. [17] S. Kasahara, A remark on the contraction principle, Proc. Jpn. Acad., 44(1) (1968), 1009{ 1012. [18] E. P. Klement, R. Mesiar and E. Pap, Triangular Norms, Kluwer Academic Publishers, Dordrecht, 2000. [19] H. W. Liu, Semi-uninorms and implications on a complete lattice, Fuzzy Sets Syst., 191 (2012), 72{82. [20] S. Massanet and J. Torrens, The law of importation versus the exchange principle on fuzzy implications, Fuzzy Sets Syst., 168 (2011), 47{69. [21] E. S. Palmeira, B. C. Bedregal, R. Mesiar and J. Fernandez, A new way to extend t-norms, t-conorms and negations, Fuzzy Sets Syst., 240 (2014), 1{21. [22] E. S. Palmeira, B. C. Bedregal, J. Fernandez and A. Jurio, On the extension of lattice valued implications via retractions, Fuzzy Sets Syst., 240 (2014), 66{85. [23] E. S. Palmeira and B. C. Bedregal, Extension of fuzzy logic operators defined on bounded lattices via retractions, Comput. Math. Appl., 63 (2012), 1026{1038. [24] S. Saminger-Platz, E. P. Klement and R. Mesiar, On extension of triangular norms on bounded lattices, Indag. Math., 19(1) (2008), 135{150. [25] Y. Shi, D. Ruan and E. E. Kerre, On the characterizations of fuzzy implications satisfying I(x; y) = I(x; I(x; y)), Information Sci., 177 (2007), 2954{2970. [26] Y. Su and Z. Wang, Pseudo-uninorms and coimplications on a complete lattice, Fuzzy Sets Syst., 224 (2013), 53{62. [27] Z. D. Wang and Y. D. Yu, Pseudo t-norms and implication operators on a complete Brouw- erian lattice, Fuzzy Sets Syst., 132 (2002), 113{124. | ||
|
آمار تعداد مشاهده مقاله: 1,400 تعداد دریافت فایل اصل مقاله: 652 |
||