Gomez, D.Montero, JavierYáñez, JavierWang, P.P.2023-06-202023-06-202003[1] B. Dushnik and E.W. Miller: Partially ordered sets. American Journal of Mathematics 63 (1941), 600{610. [2] J. Gonzalez-Pachon, D.Gomez, J.Montero and J.Yañez: Searching for the dimension of binary valued preference relations. Int. J. Approximate Reasoning (to appear). [3] J. Gonzalez-Pachon, D.Gomez, J.Montero and J.Yañez: Soft dimension theory. Fuzzy Sets and Systems (to appear). [4] J. Montero and J. Tejada: Some problems on the denition of fuzzy preference relation. Fuzzy Sets and Systems 20 (1986), 45-53. [5] P.K. Pattanaik: Voting and Collective Choice.Cambridge U.P., London, 1971. [6] A.K. Sen: Collective Choice and Social Welfare. Holden-Day, San Francisco, 1970. [7] W.T. Trotter: Combinatorics and Partially Ordered Sets. Dimension Theory. The Johns Hopkins University Press, Baltimore and London (1992). [8] M. Yannakakis: On the complexity of the partial order dimension problem. SIAM Journal of Algebra and Discrete Mathematics 3 (1982), 351-358. [9] J. Yañez and J. Montero: A poset dimension algorithm. Journal of Algorithms 30 (1999), 185-208.0970789025https://hdl.handle.net/20.500.14352/60928Decision making based upon valued preference relations is assuming that each decision maker is able to consistently manage intensity values for preferences, but this is indeed a di±cult task, even when dealing with few alternatives. Representation tools will therefore play a key role in order to help decision makers to understand their preference structure. This paper introduces a particular representation based upon classical crisp dimension theory,addressing some associated computational complexity problems, which will hopefully be useful within a valued framework.engbook partopen access510.64Lógica simbólica y matemática (Matemáticas)1102.14 Lógica Simbólica