Article
Full entry |
PDF
(0.4 MB)
Feedback
PDF
(0.4 MB)
Feedback
Keywords:
t-norm; t-conorm; ordinal sum; bounded lattice
t-norm; t-conorm; ordinal sum; bounded lattice
Summary:
Recently, the topic related to the construction of triangular norms and triangular conorms on bounded lattices using ordinal sums has been extensively studied. In this paper, we introduce a new ordinal sum construction of triangular norms and triangular conorms on an appropriate bounded lattice. Also, we give some illustrative examples for clarity. Then, we show that a new construction method can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on an appropriate bounded lattice, respectively. And we provide some illustrative examples.
References:
[1] Aşıcı, E.: An extension of the ordering based on nullnorms. Kybernetika 55 (2019), 217-232. DOI | MR 4014584
[2] Aşıcı, E.: The equivalence of uninorms induced by the $ U $-partial order. Hacet. J. Math. Stat. 357 (2019), 2-26. DOI | MR 3974553
[3] Aşıcı, E., Mesiar, R.: New constructions of triangular norms and triangular conorms on an arbitrary bounded lattice. Int. J. Gen. Systems 49 (2020), 143-160. DOI | MR 4074092
[4] Aşıcı, E., Mesiar, R.: Alternative approaches to obtain t-norms and t-conorms on bounded lattices. Iran. J. Fuzzy Syst. 17 (2020), 121-138. DOI | MR 4155854
[5] Aşıcı, E., Mesiar, R.: On the construction of uninorms on bounded lattices. Fuzzy Sets Syst. 408 (2021), 65-85. DOI | MR 4210984
[6] Aşıcı, E., Karaçal, F.: On the T-partial order and properties. Inform. Sci. 267 (2014), 323-333. DOI | MR 3177320
[7] Bedregal, B., Reiser, R., Bustince, H., Lopez-Molina, C., Torra, V.: Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Inform. Sci. 255 (2014), 1, 82-99. DOI | MR 3117131
[8] Birkhoff, G.: Lattice Theory. Third edition. Providence, 1967. MR 0227053
[9] Clifford, A.: Naturally totally ordered commutative semigroups. Amer. J. Math. 76 (1954), 631-646. DOI | MR 0062118
[10] Çaylı, G. D.: Construction methods for idempotent nullnorms on bounded lattices. Appl. Math. Comput. 366 (2020). DOI | MR 4011595
[11] Çaylı, G. D.: Some methods to obtain t-norms and t-conorms on bounded lattices. Kybernetika 55 (2019), 273-294. DOI | MR 4014587
[12] Çaylı, G. D.: Alternative approaches for generating uninorms on bounded lattices. Inform. Sci. 488 (2019), 111-139. DOI | MR 3924420
[13] Çaylı, G. D.: On a new class of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. 332 (2018), 129-143. DOI | MR 3732255
[14] Dan, Y., Hu, B. Q., Qiao, J.: New construction of t-norms and t-conorms on bounded lattices. Fuzzy Sets Syst. 395 (2020), 40-70. DOI | MR 4109061
[15] Dvořák, A., Holčapek, M.: New construction of an ordinal sum of t-norms and t-conorms on bounded lattices. Inform. Sci. 515 (2020), 116-131. DOI | MR 4042588
[16] Ertuğrul, Ü., Karaçal, F., Mesiar, R.: Modified ordinal sums of triangular norms and triangular conorms on bounded lattices. Int. J. Intell. Syst. 30 (2015), 807-817. DOI
[17] Goguen, J. A.: L-fuzzy sets. J. Math. Anal. Appl. 18 (1967), 145-174. DOI | MR 0224391
[18] İnce, M. A., Karaçal, F., Mesiar, R.: Medians and nullnorms on bounded lattices. Fuzzy Sets Syst. 289 (2016), 74-81. DOI | MR 3454462
[19] Karaçal, F., İnce, M. A., Mesiar, R.: Nullnorms on bounded lattices. Inform. Sci. 325 (2015), 227-235. DOI | MR 3392300
[20] Klement, E. P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Academic Publishers, Dordrecht 2000. MR 1790096 | Zbl 1087.20041
[21] Medina, J.: Characterizing when an ordinal sum of t-norms is a t-norm on bounded lattices. Fuzzy Sets Syst. 202 (2012), 75-88. DOI | MR 2934787
[22] Mostert, P. S., Shields, A. L.: On the Structure of Semigroups on a Compact Manifold With Boundary. Ann. Math., II. Ser. 65 (1957), 117-143. DOI | MR 0084103
[23] Ouyang, Y., Zhang, H-P., Baets, B. D.: Ordinal sums of triangular norms on a bounded lattice. Fuzzy Sets Syst. 408 (2021), 1-12. DOI | MR 4210979
[24] Rodriguez, R. M., Martinez, L., Herrera, F.: Fuzzy linguistic term sets for decision making. IEEE Trans. Fuzzy Syst. 20 (2012), 2, 109-119. DOI
[25] Rodriguez, R. M., Martinez, L., Herrera, F.: A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets. Inform. Sci. 241 (2013), 28-42. DOI | MR 3064113
[26] Rodriguez, R. M., Martinez, L., Torra, V., Xu, Z. S., Herrera, F.: Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. 29 (2014), 6, 495-524. DOI
[27] Saminger, S.: On ordinal sums of triangular norms on bounded lattices. Fuzzy Sets Syst. 325 (2006), 1403-1416. MR 2226983 | Zbl 1099.06004
[28] Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10 (1960), 313-334. DOI | MR 0115153 | Zbl 0136.39301
[29] Torra, V.: Hesitant fuzzy sets. Int. J. Intell. Syst. 25 (2010), 529-539. DOI
Search
Partner of
