| Title:
|
Extensions of fuzzy connectives on ACDL (English) |
| Author:
|
Liu, Hui |
| Author:
|
Zhao, Bin |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
55 |
| Issue:
|
3 |
| Year:
|
2019 |
| Pages:
|
472-494 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications and also make a study on the behaviors of $R$-implication and reciprocal implication. Finally, we construct two classes of infinitely $\bigvee$-distributive uninorms and infinitely $\bigwedge$-distributive uninorms. (English) |
| Keyword:
|
extensions |
| Keyword:
|
algebraic completely distributive lattices |
| Keyword:
|
fuzzy connectives |
| MSC:
|
03B52 |
| MSC:
|
03E72 |
| MSC:
|
06D10 |
| idZBL:
|
Zbl 07144949 |
| idMR:
|
MR4015994 |
| DOI:
|
10.14736/kyb-2019-3-0472 |
| . |
| Date available:
|
2019-11-14T08:35:42Z |
| Last updated:
|
2020-04-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147870 |
| . |
| Reference:
|
[1] Baczyński, M., Jayaram, B.: Fuzzy Implications..Studies in Fuzziness and Soft Computing, Springer-Verlag, Berlin Heidelberg 2008. Zbl 1293.03012, MR 2428086 |
| Reference:
|
[2] Çaylı, G. D.: On a new class of t-norms and t-conorms on bounded lattices..Fuzzy Sets Syst. 332 (2018), 129-143. MR 3732255, 10.1016/j.fss.2017.07.015 |
| Reference:
|
[3] Çaylı, G. D., Drygaś, P.: Some properties of idempotent uninorms on a special class of bounded lattices..Inform. Sci. 422 (2018), 352-363. MR 3709474, 10.1016/j.ins.2017.09.018 |
| Reference:
|
[4] Çaylı, G. D., Karaçal, F.: Construction of uninorms on bounded lattices..Kybernetika 53 (2017), 394-417. MR 3684677, 10.14736/kyb-2017-3-0394 |
| Reference:
|
[5] Çaylı, G. D., Karaçal, F., Mesiar, R.: On a new class of uninorms on bounded lattices..Inform. Sci. 367-368 (2016), 221-231. MR 3684677, 10.1016/j.ins.2016.05.036 |
| Reference:
|
[6] Davey, B. A., Priestley, H. A.: Introduction to lattices and Order..Cambridge University Press, Cambridge 1990. MR 1058437 |
| Reference:
|
[7] Baets, B. De, Mesiar, R.: Triangular norms on product lattices..Fuzzy Sets Syst. 104 (1999), 61-75. Zbl 0935.03060, MR 1685810, 10.1016/s0165-0114(98)00259-0 |
| Reference:
|
[8] Deschrijver, G.: Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory..Inform. Sci. 244 (2013), 48-59. MR 3068360, 10.1016/j.ins.2013.04.033 |
| Reference:
|
[9] Jenei, S., Baets, B. De: On the direct decomposability of t-norms on product lattices..Fuzzy Sets Syst. 139 (2003), 699-707. MR 2015162, 10.1016/s0165-0114(03)00125-8 |
| Reference:
|
[10] Karaçal, F., Ertuğrul, Ü., Mesiar, R.: Characterization of uninorms on bounded lattices..Fuzzy Sets Syst. 308 (2017), 54-71. MR 3579154, 10.1016/j.fss.2016.05.014 |
| Reference:
|
[11] Karaçal, F., Mesiar, R.: Uninorms on bounded lattices..Fuzzy Sets Syst. 261 (2015), 33-43. MR 3291484, 10.1016/j.fss.2014.05.001 |
| Reference:
|
[12] Karaçal, F., Sağiroğlu, Y.: Infinitely $\bigvee$-distributive t-norms on complete lattices and pseudo-complements..Fuzzy Sets Syst. 160 (2009), 32-43. MR 2469428, 10.1016/j.fss.2008.03.022 |
| Reference:
|
[13] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms..Kluwer Academic Publishers, Dordrecht 2000. Zbl 1087.20041, MR 1790096 |
| Reference:
|
[14] Palmeira, E. S., Bedregal, B. C.: Extensions of fuzzy logic operators defined on bounded lattices via retraction..Comput. Math. Appl. 63 (2012), 1026-1038. MR 2892746, 10.1016/j.camwa.2011.12.007 |
| Reference:
|
[15] Palmeira, E. S., Bedregal, B. C.: On the extension of lattice-valued implications via retractions..Fuzzy Sets Syst. 240 (2014), 66-85. MR 3167513, 10.1016/j.fss.2013.07.023 |
| Reference:
|
[16] Palmeira, E. S., Bedregal, B. C., Mesiar, R., Fernandez, J.: A new way to extend t-norms, t-conorms and negations..Fuzzy Sets Syst. 240 (2014), 1-21. MR 3167509, 10.1016/j.fss.2013.05.008 |
| Reference:
|
[17] Saminger-Platz, S.: On ordinal sums of triangular norms on bounded lattices..Fuzzy Sets Syst. 157 (2006), 1403-1416. MR 2226983, 10.1016/j.fss.2005.12.021 |
| Reference:
|
[18] Saminger-Platz, S., Klement, E. P., Mesiar, R.: On extensions of triangular norms on bounded lattices..Indag. Math. 19 (2008), 1, 135-150. MR 2466398, 10.1016/s0019-3577(08)80019-5 |
| Reference:
|
[19] Wang, Z. D., Fang, J. X: On the direct decomposability of pseudo-t-norms, t-norms and implication operators on product lattices..Fuzzy Sets Syst. 158 (2007), 2494-2503. MR 2361663, 10.1016/j.fss.2007.06.011 |
| Reference:
|
[20] Wang, Z. D., Yu, Y. D: Pseudo-t-norms and implication operators on a complete Brouwerian lattice..Fuzzy Sets Syst. 132 (2002), 113-124. MR 1936220, 10.1016/s0165-0114(01)00210-x |
| Reference:
|
[21] Yılmaz, Ş., Kazancı, O.: Constructions of triangular norms on lattices by means of irreducible elements..Inform. Sci. 397-398 (2017), 110-117. 10.1016/j.ins.2017.02.041 |
| . |
