Garmendia Salvador, LuisSalvador Alcaide, AdelaMontero De Juan, Francisco Javier2023-06-202023-06-202009Garmendia, L., Salvador, A., Montero, J.: Computing a T-transitive lower approximation or opening of a proximity relation. Fuzzy Sets and Systems. 160, 2097-2105 (2009). https://doi.org/10.1016/j.fss.2009.01.0150165-011410.1016/j.fss.2009.01.015https://hdl.handle.net/20.500.14352/50075Since transitivity is quite often violated even by decision makers that accept transitivity in their preferences as a condition for consistency, a standard approach to deal with intransitive preference elicitations is the search for a close enough transitive preference relation, assuming that such a violation is mainly due to decision maker estimation errors. In some way, the higher the number of elicitations, the more probable is inconsistency. This is mostly the case within a fuzzy framework, even when the number of alternatives or objects to be classified is relatively small. In this paper, we propose a fast method to compute a T-indistinguishability from a reflexive and symmetric fuzzy relation, T being any left-continuous t-norm. The computed approximation we propose will have O(n3) time complexity, where n is the number of elements under consideration, and is expected to produce a T-transitive opening. To the authors’ knowledge, there is no other proposed algorithm that computes T-transitive lower approximations or openings while preserving the reflexivity and symmetry properties.engjournal articlehttps//doi.org/10.1016/j.fss.2009.01.015http://www.sciencedirect.com/science/article/pii/S0165011409000554restricted access510.64Fuzzy relationFuzzy proximity relationT-transitive relationfuzzy similarityT-indistinguishabilityT-transitive lower approximationT-transitive openingLógica simbólica y matemática (Matemáticas)1102.14 Lógica Simbólica