References
- B. De Baets. A. Markova-Stupnanova, "Analytical expressions for the addition of fuzzy intervals," Fuzzy Sets and Systems. vol. 91. pp. 203-213. 1997. https://doi.org/10.1016/S0165-0114(97)00141-3
- M. Delgado. M. Vila. W. Voxman, "On a canonical representation for fuzzy numbers." Fuzzy Sets and Systems. vol. 93. pp. 125-135. 1998. https://doi.org/10.1016/S0165-0114(96)00144-3
- W. Dong, H. C. Shah, "Vertex method for computing functions of fuzzy variables." Fuzzy Sets and Systems. vol. 24. pp. 65-78, 1987. https://doi.org/10.1016/0165-0114(87)90114-X
- D. Dubois. H. Prade. Fuzzy Sets and Systems Theory and Applications, Academic Press, New York, 1980.
- D. Dubois, H. Prade. "Additions of interactive fuzzy numbers," IEEE Trans. Automat. Control, vol. 26. no. 4. pp. 926-936, 1981. https://doi.org/10.1109/TAC.1981.1102744
- D. Dubois, H. Prade, Fuzzy Information. CRS Press, Boca Raton, FL, 1987, pp. 112-148.
- D. Dubois, H. Prade, "The mean value of a fuzzy number," Fuzzy Sets and Systems, vol. 24, pp. 279-300, 1987. https://doi.org/10.1016/0165-0114(87)90028-5
- D. Dubois, H. Prade. "Logique floue, interpolation et commande," J. Eur. des Systemes Automatises, vol. 30, pp. 607-644, 1996.
- D. Dubois, E. Kerre, R. Mesiar, H. Prade, Fuzzy interval analysis, in: D. pubois, H. Prade (Eds,) , Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Dordecht, 2000, pp. 483-582.
- D. Filev, R. R. Yager, "Generalized defuzzification method via BADD distribution," Internat. J. Intell. Systems, vol. 6, pp. 687-697, 1991. https://doi.org/10.1002/int.4550060702
- D. Filev, R. R. Yager, "An adaptive approach to defuzzification based on level sets," Fuzzy Sets and Systems, vol. 54, pp. 355-360, 1993. https://doi.org/10.1016/0165-0114(93)90383-S
- P. Fortemps, M. Roubens, "Ranking and defuzzification methods based on area compensation," Fuzzy Sets and Systems, vol. 82, pp. 319-330, 1996. https://doi.org/10.1016/0165-0114(95)00273-1
- R. Fuller and T. Keresztfalvi, "t-norm-based addition of fuzzy intervals," Fuzzy Sets and Systems, vol. 51, pp. 155-159, 1992. https://doi.org/10.1016/0165-0114(92)90188-A
- R. Fuller and H.-J. Zimmermann, "On computation of the compositional rule of inference under triangular norms," Fuzzy Sets and Systems, vol. 51, pp. 267-275, 1992. https://doi.org/10.1016/0165-0114(92)90017-X
- D. H. Hong and S. Y. Hwang, "The convergence of T-product of fuzzy numbers," Fuzzy Sets and Systems, vol. 85, pp. 373-378, 1997. https://doi.org/10.1016/0165-0114(95)00333-9
- D. H. Hong, "A note on t-norm-based addition of fuzzy intervals," Fuzzy Sets and Systems, vol. 75, pp. 73-76, 1995. https://doi.org/10.1016/0165-0114(94)00329-6
-
D. H. Hong and H. Y. Do, "Fuzzy system reliability analysis by the use of
$T_{w}$ (the weakest t-norm) on fuzzy number arithmetic operations," Fuzzy Sets and Systems, vol. 90, pp. 307-316, 1997. https://doi.org/10.1016/S0165-0114(96)00125-X - D. H. Hong and C. Hwang, "A T-sum bound of LR-fuzzy numbers," Fuzzy Sets and Systems, vol. 91, pp. 239-252, 1997. https://doi.org/10.1016/S0165-0114(97)00144-9
- D. H. Hong and H. Kim, "A note to the sum of fuzzy variables," Fuzzy Sets and Systems, vol. 93, pp. 121-124, 1998. https://doi.org/10.1016/S0165-0114(96)00233-3
- D. H. Hong and S. Y. Hwang, "On the compositional rule of inference under triangular norms," Fuzzy Sets and Systems, vol. 66, pp. 25-38, 1994. https://doi.org/10.1016/0165-0114(94)90299-2
- D. H. Hong, "Shape preserving multiplications of fuzzy intervals," Fuzzy Sets and Systems, vol. 123, pp. 93-96, 2001. https://doi.org/10.1016/S0165-0114(00)00074-9
- D. H. Hong, "Some results on the addition of fuzzy intervals," Fuzzy Sets and Systems, vol. 122, pp. 349-352, 2001. https://doi.org/10.1016/S0165-0114(00)00005-1
- D. H. Hong, S. Lee and H. Y. Do, "Fuzzy linear regression analysis for fuzzy input-output data using shape-preserving operations," Fuzzy Sets and Systems, vol. 122, pp. 513-526, 2001. https://doi.org/10.1016/S0165-0114(00)00003-8
- D. H. Hong, "On shape-preserving additions of fuzzy interval," J. Math. Anal. Appl., vol. 267, pp. 369-376, 2002. https://doi.org/10.1006/jmaa.2001.7788
- T. Keresztfalvi and M. Kovocs, "g, p-fuzzification of arithmetic operations," Tatra Mt. Math. Publ. vol. 1, pp. 65-71, 1992.
- E. P. Klement, R. Mesiar, and E. Pap, "A characterization of the ordering of continuous t-norms," Fuzzy Sets and Systems, vol. 86, pp. 189-195, 1997. https://doi.org/10.1016/0165-0114(95)00407-6
- A. Kolesarova, "Triangular norm-based addition preserving linearity of t-sums of fuzzy intervals," Mathware Soft Comput. vol. 5, pp. 97-98, 1998.
- A. Kolesarova, "Triangular norm-based addition of linear fuzzy numbers," Tatra Mt. Math. Publ. vol. 6, pp. 75-82, 1995.
- J. J. Lee, D. H. Hong, and S. Y. Hwang, "A learning algorithm of fuzzy neural networks using a shape preserving operation," J. Electr. Engrg: Inform. Sci., vol. 3, pp. 131-138, 1998.
- A. Markova, "T-sum of L-R-fuzzy numbers", Fuzzy Sets and Systems, vol. 85, pp. 379-384, 1996.
- A. Markova, "A note to the addition of fuzzy numbers based on a continuous Archimedean T-norm," Fuzzy Sets and Systems, vol. 91, pp. 253-258, 1997. https://doi.org/10.1016/S0165-0114(97)00145-0
- R. Mesiar, LR-fuzzy numbers, in "Proceedings of IPMU'96, Granada, 1996," pp. 337-342.
- R. Mesiar, "A note on the T-sum of LR fuzzy numbers," Fuzzy Sets and Systems, vol. 79, pp. 259-261, 1996. https://doi.org/10.1016/0165-0114(95)00178-6
- R. Mesiar, "Shape preserving additions of fuzzy intervals," Fuzzy Sets and Systems, vol. 86, pp. , 1997.
- R. Mesiar, "Triangular-norm based addition on fuzzy intervals," Fuzzy Sets and Systems, vol. 91, pp. 231-237, 1997. https://doi.org/10.1016/S0165-0114(97)00143-7
- M. Oussalah, "On the compatibility between defuzzification and fuzzy arithmetic operations," Fuzzy Sets and Systems, vol. 128, pp. 247-260, 2002. https://doi.org/10.1016/S0165-0114(01)00125-7
- B. Schweizer and A. Sklar, "Associative functions and abstract semigroups," Publ. Math. Debrecen, vol. 10, pp. 69-81, 1963.
- W. Van Leekwijck, E. Kerre, "Defuzzification: criteria and classification," Fuzzy Sets and Systems, vol. 108, pp. 159-178, 1999. https://doi.org/10.1016/S0165-0114(97)00337-0
- R. R. Yager, D. P. Filev, "SLIDE: a simple adaptive defuzzification method," IEEE Trans. Fuzzy Systems, vol. 1, no. 1, pp. 69-78, 1993. https://doi.org/10.1109/TFUZZ.1993.390286
- L. A. Zadeh, "The concept of linguistic variable and its application to approximate reasoning," Inform. Sic., Part 1, vol. 8, pp. 199-249, Part 2, pp. 301-357, Part 3, vol. 9, pp. 43-80, 1975.
- R. Zhao, R. Govind, "Defuzzification of fuzzy intervals," Fuzzy Sets and Systems, vol. 43, pp. 45-56, 1991. https://doi.org/10.1016/0165-0114(91)90020-Q