Fuzzy Optim Decis Making (2011) 10:287–309 DOI 10.1007/s10700-011-9106-5 Possibility-theoretic extension of derivation operators in formal concept analysis over fuzzy lattices Yassine Djouadi · Henri Prade Received: 29 July 2009 / Accepted: 4 August 2011 / Published online: 21 August 2011 © Springer Science+Business Media, LLC 2011 Abstract Formal concept analysis (FCA) associates a binary relation between a set of objects and a set of properties to a lattice of formal concepts defined through a Galois connection. This relation is called a formal context, and a formal concept is then defined by a pair made of a subset of objects and a subset of properties that are put in mutual correspondence by the connection. Several fuzzy logic approaches have been proposed for inducing fuzzy formal concepts from L -contexts based on antitone L-Galois connections. Besides, a possibility-theoretic reading of FCA which has been recently proposed allows us to consider four derivation powerset operators, namely sufficiency, possibility, necessity and dual sufficiency (rather than one in standard FCA). Classically, fuzzy FCA uses a residuated algebra for maintaining the closure property of the composition of sufficiency operators. In this paper, we enlarge this framework and provide sound minimal requirements of a fuzzy algebra w.r.t. the clo- sure and opening properties of antitone L-Galois connections as well as the closure and opening properties of isotone L-Galois connections. We apply these results to particular compositions of the four derivation operators. We also give some noticeable properties which may be useful for building the corresponding associated lattices. Keywords Formal concept analysis · Fuzzy relations · Possibility theory · Fuzzy sets connectives · Antitone and isotone Galois connections · Closure and interior operators Y. Djouadi (B ) Department of Computer Science, University of Tizi-Ouzou, BP 17 RP, Tizi-Ouzou, Algeria e-mail: ydjouadi@mail.ummto.dz H. Prade IRIT, Université Paul Sabatier, 118 Route de Narbonne, 31062 Toulouse Cedex 09, France e-mail: prade@irit.fr 123