Available online at www.sciencedirect.com Fuzzy Sets and Systems 201 (2012) 86 – 104 www.elsevier.com/locate/fss Signatures: Definitions, operators and applications to fuzzy modelling Claudiu Pozna a , b , Nicu¸ sor Minculete c , Radu-Emil Precup d , ∗ , László T. Kóczy e , f , Áron Ballagi g a Department of Informatics, Széchenyi István University, Egyetem tér 1, 9026 Gyõr, Hungary b Department of Product Design and Robotics, Transilvania University of Brasov, Bd. Eroilor 28, 500036 Brasov, Romania c Faculty of International Economic Relations, “Dimitrie Cantemir” University of Brasov, Str. Bisericii Romane 107, 500068 Brasov, Romania d Department of Automation and Applied Informatics, “Politehnica” University of Timisoara, Bd. V. Parvan 2, 300223 Timisoara, Romania e Faculty of Engineering Sciences, Széchenyi István University, Egyetem tér1, 9026 Gyõr, Hungary f Department of Telecommunications and Media Informatics, Budapest University of Technology and Economics, Magyar tudósok krt. 2, 1117 Budapest, Hungary g Department of Automation, Széchenyi István University, Egyetem tér 1, 9026 Gyõr, Hungary Received 24 November 2010; received in revised form 23 December 2011; accepted 26 December 2011 Available online 18 January 2012 Abstract This paper presents a new framework for the symbolic representation of data which is referred to as signatures. The definitions of signatures and of signature trees are first given. Original operators on signatures are next presented, i.e., contraction, extension, pruning, addition, multiplication, and grafting. Attractive applications of signatures related to the modelling of fuzzy inference systems are suggested and discussed. An example is included to accompany the theoretical results. © 2012 Elsevier B.V. All rights reserved. Keywords: Fuzzy inference systems; Fuzzy signatures; Operators; Signatures; Symbolic representation 1. Introduction The modelling of complex systems needs various ways to handle the complexity and the uncertainty [1–4]. Several modelling issues from engineering points of view are addressed in [1]. Tools and applications related to linguistic decision making are overviewed in [2]. A combination of prediction and classification is discussed in [3] and expressed as an optimal adaptive voting strategy. A prototype-based rule inference system that incorporates linear functions is proposed in [4]. Fuzzy logic and fuzzy modelling have gained widespread applications in the context of uncertainty modelling in complex systems [5–8]. Multidimensional generalized fuzzy integrals and applications to the definitions of indices are ∗ Corresponding author. Tel.: +40 2564032 29, +40 2564032 30, +40 2564032 40 (lab), +40 2564032 26 (office); fax: +40 256403214. E-mail address: radu.precup@aut.upt.ro (R.-E. Precup). 0165-0114/$-see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.fss.2011.12.016