The bag model in language statistics F. Criado a, * , T. Gachechiladze b , H. Meladze b , G. Tsertsradze b a Facultad de Ciencias, Campus de Teatinos, Universidad de M alaga, 29071 M alaga, Spain b Department of Applied Mathematics and Computer Science, Tbilisi State University, 1, chavchavadze Ave, Tbilisi 380028, Georgia Received 8 May 2000; received in revised form 3 November 2001; accepted 30 January 2002 Abstract In this paper, fuzzy quantitative models of language statistics are constructed. All suggested models are based on the assumption about a superposition of two kinds of uncertainties: probabilistic and possibilistic. The realization of this superposition in statistical distributions is achieved by the probability measure splitting procedure. In this way, the fuzzy versions of generalized binomial, Fucks and Zipf–MandelbrotÕs distributions are constructed describing the probabilistic and possibilistic organization of language at any level: morphological, syntactic or phonological. The main problem when constructing the quantitative model of some fuzzy linear structure is finding the corresponding linguistic spectrum, which is reduced to the solution of algebraic or transcendental equation systems by inverse spline-interpolation. In the final section, the general linear mathematical model of language structures is then described briefly, as well as bag statistics for consonantal structures of languages. Ó 2002 Elsevier Science Inc. All rights reserved. Keywords: Fuzzy sets; Membership functions; Probability theory; Linguistic modeling Information Sciences 147 (2002) 13–44 www.elsevier.com/locate/ins * Corresponding author. E-mail address: f_criado@uma.es (F. Criado). 0020-0255/02/$ - see front matter Ó 2002 Elsevier Science Inc. All rights reserved. PII:S0020-0255(02)00201-3