The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Poset-valued preference relations

Vladimír Janiš; Susana Montes; Branimir Šešelja; Andreja Tepavčević

Kybernetika (2015)

  • Volume: 51, Issue: 5, page 747-764
  • ISSN: 0023-5954

Abstract

top
In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.

How to cite

top

Janiš, Vladimír, et al. "Poset-valued preference relations." Kybernetika 51.5 (2015): 747-764. <http://eudml.org/doc/276117>.

@article{Janiš2015,
abstract = {In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.},
author = {Janiš, Vladimír, Montes, Susana, Šešelja, Branimir, Tepavčević, Andreja},
journal = {Kybernetika},
keywords = {relation; poset; order reversing involutions; weakly orthogonal poset; transitivity},
language = {eng},
number = {5},
pages = {747-764},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Poset-valued preference relations},
url = {http://eudml.org/doc/276117},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Janiš, Vladimír
AU - Montes, Susana
AU - Šešelja, Branimir
AU - Tepavčević, Andreja
TI - Poset-valued preference relations
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 5
SP - 747
EP - 764
AB - In decision processes some objects may not be comparable with respect to a preference relation, especially if several criteria are considered. To provide a model for such cases a poset valued preference relation is introduced as a fuzzy relation on a set of alternatives with membership values in a partially ordered set. We analyze its properties and prove the representation theorem in terms of particular order reversing involution on the co-domain poset. We prove that for every set of alternatives there is a poset valued preference whose cut relations are all relations on this domain. We also deal with particular transitivity of such preferences.
LA - eng
KW - relation; poset; order reversing involutions; weakly orthogonal poset; transitivity
UR - http://eudml.org/doc/276117
ER -

References

top
  1. Bezdek, J., Spillman, B., Spillman, R., 10.1016/0165-0114(78)90017-9, Fuzzy Sets Systems 1 (1978), 255-268. Zbl0398.90009MR0508976DOI10.1016/0165-0114(78)90017-9
  2. Birkhoff, G., Lattice Theory. (Third edition., AMS Colloquium Publications, Vol. XXV, 1967. MR0227053
  3. Chajda, I., 10.1007/s00500-013-1047-1, Soft Computing 18 (2013), 1, 1-4). DOI10.1007/s00500-013-1047-1
  4. Cignoli, R., Esteva, F., 10.1016/j.apal.2009.05.008, Annals of Pure and Applied Logic 161 (2009), 2, 150-160. Zbl1181.03061MR2552735DOI10.1016/j.apal.2009.05.008
  5. Dasgupta, M., Deb, R., 10.1007/bf00187373, Soc. Choice Welfare 8 (1991), 2, 171-182. Zbl0717.90004MR1115895DOI10.1007/bf00187373
  6. David, H., The Method of Paired Comparisons., Griffin's Statistical Monographs and Courses, Vol. 12, Charles Griffin and D. Ltd., 1963. Zbl0665.62075MR0174105
  7. Baets, B. De, Meyer, H. De, Transitivity frameworks for reciprocal relations: cycle-transitivity versus FG-transitivity., Fuzzy Sets and Systems 152 (2005), 2, 249-270. Zbl1114.91031MR2138509
  8. Baets, B. De, Meyer, H. De, Schuymer, B. De, 10.1016/j.fss.2004.11.002, Social Choice and Welfare 26 (2006), 217-238. Zbl1158.91338MR2226508DOI10.1016/j.fss.2004.11.002
  9. Doignon, J.-P., Monjardet, B., Roubens, M., Vincke, Ph., 10.1016/0022-2496(86)90020-9, J. Math. Psych. 30 (1986), 435-480. Zbl0612.92020MR0868774DOI10.1016/0022-2496(86)90020-9
  10. Dutta, B., Laslier, J.F., 10.1007/s003550050158, Soc. Choice Welfare 16 (1999), 513-532. Zbl1066.91535MR1713186DOI10.1007/s003550050158
  11. Fan, Z.-P., X, X. Chen, 10.1007/11539506_16, Lecture Notes in Artificial Intelligence, Springer-Verlag 3613 (2005), 130-139. DOI10.1007/11539506_16
  12. Fan, Z.-P., Jiang, Y. P., A judgment method for the satisfying consistency of linguistic judgment matrix., Control and Decision 19 (2004), 903-906. 
  13. Fishburn, P. C., 10.1016/0022-2496(73)90021-7, J. Math. Psychology 10 (1973), 327-352. Zbl0277.92008MR0327330DOI10.1016/0022-2496(73)90021-7
  14. Flachsmeyer, J., Note on orthocomplemented posets II., In: Proc. 10th Winter School on Abstract Analysis (Z. Frolík, ed.), Circolo Matematico di Palermo, Palermo 1982. pp. 67-74. Zbl0535.06003MR0683769
  15. Fodor, J., Roubens, M., 10.1007/978-94-017-1648-2, Kluwer Academic Publishers 1994. Zbl0827.90002DOI10.1007/978-94-017-1648-2
  16. García-Lapresta, J., Llamazares, B., 10.1007/s003550000048, Soc. Choice Welfare 17 (2000), 673-690. Zbl1069.91518MR1778698DOI10.1007/s003550000048
  17. García-Lapresta, J., Llamazares, B., 10.1016/s0304-4068(01)00055-6, J. Math. Economics 35 (2001), 463-481. Zbl0987.91022MR1838607DOI10.1016/s0304-4068(01)00055-6
  18. Goguen, J. A., 10.1016/0022-247x(67)90189-8, J. Math. Anal. Appl. 18 (1967), 145-174. Zbl0145.24404MR0224391DOI10.1016/0022-247x(67)90189-8
  19. Herrera, F., 10.1016/0020-0255(95)00025-k, Inform. Sci. 85 (1995), 223-239. DOI10.1016/0020-0255(95)00025-k
  20. Herrera, F., Herrera-Viedma, E., 10.1016/s0165-0114(99)00024-x, Fuzzy Sets and Systems 115 (2000), 67-82. Zbl1073.91528MR1776304DOI10.1016/s0165-0114(99)00024-x
  21. Herrera, F., Martínez, L., 10.1109/91.890332, IEEE Transactions on Fuzzy Systems 8 (2000), 746-752. MR1784646DOI10.1109/91.890332
  22. Herrera, F., Herrera-Viedma, E., Mart{í}nez, L., 10.1016/s0165-0114(98)00093-1, Fuzzy Sets and Systems 114 (2000), 43-58. MR1776304DOI10.1016/s0165-0114(98)00093-1
  23. Herrera, F., Herrera-Viedma, E., Verdegay, J. L., 10.1016/0165-0114(95)00107-7, Fuzzy Sets and Systems 78 (1996), 73-87. MR1376216DOI10.1016/0165-0114(95)00107-7
  24. Herrera, F., Herrera-Viedma, E., Verdegay, J. L., 10.1016/0165-0114(95)00162-x, Fuzzy Sets and Systems 79 (1996), 175-190. Zbl0870.90007MR1388390DOI10.1016/0165-0114(95)00162-x
  25. Herrera-Viedma, E., Herrera, F., Chiclana, F., 10.1109/tsmca.2002.802821, IEEE Trans. Systems, Man and Cybernetics 32 (2002), 394-402. DOI10.1109/tsmca.2002.802821
  26. Kacprzyk, J., Fedrizzi, M., Nurmi, H., 10.1016/0165-0114(92)90107-f, Fuzzy Sets and Systems 49 (1992), 21-31. Zbl0768.90003MR1177944DOI10.1016/0165-0114(92)90107-f
  27. Kacprzyk, J., Nurmi, H., (eds.), M. Fedrizzi, Consensus under Fuzziness., Kluwer Academic Publishers, Boston 1996. Zbl0882.00024
  28. Klement, E. P., Mesiar, R., Pap, E., 10.1007/978-94-015-9540-7, Kluwer Academic Publishers, Boston - London - Dordrecht 2000. Zbl1087.20041MR1790096DOI10.1007/978-94-015-9540-7
  29. Lahiri, S., 10.1016/s0165-0114(01)00240-8, Fuzzy Sets and Systems 132 (2002), 77-82. Zbl1042.91016MR1936216DOI10.1016/s0165-0114(01)00240-8
  30. Menger, K., 10.1073/pnas.37.3.178, Proc. Nat. Acad. Sci. (Math.) 37 (1951), 178-180. Zbl0042.37103MR0042080DOI10.1073/pnas.37.3.178
  31. Monjardet, B., 10.1007/978-3-642-51711-2_3, In: Non-conventional Preference Relations in Decision Making (J. Kacprzyk and M. Roubens, eds.), Lecture Notes in Economics and Mathematical Systems, Vol. 301, Springer-Verlag, 1988. MR1133647DOI10.1007/978-3-642-51711-2_3
  32. Nurmi, H., 10.1016/0165-0114(81)90003-8, Fuzzy Sets Systems 6 (1981), 249-259. Zbl0465.90006MR0635346DOI10.1016/0165-0114(81)90003-8
  33. Nurmi, H., 10.1007/978-94-009-3985-1, Reidel, Dordrecht 1987. DOI10.1007/978-94-009-3985-1
  34. Ovchinnikov, S., 10.1016/0165-0114(91)90048-u, Fuzzy Sets and Systems 40 (1991), 1, 107-126. Zbl0725.04003MR1103658DOI10.1016/0165-0114(91)90048-u
  35. Pták, P., Pulmannová, P., Orthomodular Structures as Quantum Logics., Kluwer Academic Publishers, Dordrecht 1991. Zbl0743.03039MR1176314
  36. Roberts, F., 10.1016/0022-2496(71)90016-2, J. Math. Psych. 8 (1971), 248-263. Zbl0223.92017MR0292534DOI10.1016/0022-2496(71)90016-2
  37. Roubens, M., Vincke, Ph., 10.1007/978-3-642-46550-5, Springer-Verlag, Berlin 1985. Zbl0612.92020MR0809182DOI10.1007/978-3-642-46550-5
  38. Šešelja, B., Tepavčević, A., On a construction of codes by P -fuzzy sets., Review of Research, Fac. of Sci., Univ. of Novi Sad, Math. Ser. 20 2 (1990), 71-80. Zbl0749.94027MR1158427
  39. Šešelja, B., Tepavčević, A., 10.1016/0165-0114(94)00352-8, Fuzzy Sets and Systems 72 (1995), 2, 205-213. Zbl0844.04008MR1335535DOI10.1016/0165-0114(94)00352-8
  40. Šešelja, B., Tepavčević, A., 10.1016/s0165-0114(02)00365-2, Fuzzy Sets and Systems 136 (2003), 1-19. Zbl1020.06005MR1978466DOI10.1016/s0165-0114(02)00365-2
  41. Šeselja, B., Tepavčević, A., 10.1016/s0165-0114(02)00366-4, Fuzzy Sets and Systems 136 (2003), 21-39. Zbl1026.03039MR1978467DOI10.1016/s0165-0114(02)00366-4
  42. Switalski, Z., 10.1016/s0165-0114(97)00313-8, Fuzzy Sets and Systems 107 (1999), 187-190. Zbl0938.91019MR1702851DOI10.1016/s0165-0114(97)00313-8
  43. Yager, R. R., 10.1016/0888-613x(94)00035-2, Int. J. Approx. Reasoning 12 (1995), 237-261. Zbl0870.68137MR1327857DOI10.1016/0888-613x(94)00035-2
  44. Zadeh, L. A., 10.1016/s0019-9958(65)90241-x, Information and Control 8 (1965), 338-353. Zbl0942.00007MR0219427DOI10.1016/s0019-9958(65)90241-x

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.