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Computing a T-transitive lower approximation or opening of a proximity relation Garmendia Salvador, Luis Salvador Alcaide, Adela Montero De Juan, Francisco Javier 510.64 Fuzzy relation Fuzzy proximity relation T-transitive relation fuzzy similarity T-indistinguishability T-transitive lower approximation T-transitive opening Lógica simbólica y matemática (Matemáticas) 1102.14 Lógica Simbólica Since 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. Depto. de Estadística e Investigación Operativa Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T09:37:57Z 2023-06-20T09:37:57Z 2009 journal article https://hdl.handle.net/20.500.14352/50075 0165-0114 10.1016/j.fss.2009.01.015 eng Garmendia, 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.2009.01.015 restricted access application/pdf Elsevier Science Bv