Some more properties of lists and fuzzy lists B.K. Tripathy a, * , S.S. Gantayat b a Department of Computer Science, Berhampur University, Berhampur 760 007, Orissa, India b Hi-Tech Institute of Information Technology, Jeypore 764 002, Orissa, India Received 20 February 2003; received in revised form 20 June 2003; accepted 20 October 2003 Abstract In this article we introduce the map operator on a list, define list indexing the cons operator and establish their properties. Parallel notions and properties for fuzzy lists are also considered. Ó 2003 Elsevier Inc. All rights reserved. Keywords: List; Fuzzy list; Take; Drop; Map; Indexing; Cons 1. Introduction The concept of lists [1] is a generalization of the notion of bags [6], which is itself a generalization of the concept of sets. In fact the number of occurrences of an element and their order of occurrence is significant in a list, which are unimportant in the setting of sets. Jena et al. redefined the notion of list very recently [2]. Some of the well- known operations on lists were also defined from the new direction and properties of these operations were established. This study was further carried out by Tripathy and Pattnaik [4,5] by the introduction and study of the operators ‘take’ and ‘drop’ on a list. In this paper we establish one more property of the ‘take’ and ‘drop’ operator; define the notions of ‘map’, ‘list indexing’, ‘interval of natural * Corresponding author. E-mail addresses: tripathybk@rediffmail.com (B.K. Tripathy), sgantayat67@rediffmail.com (S.S. Gantayat). 0020-0255/$ - see front matter Ó 2003 Elsevier Inc. All rights reserved. doi:10.1016/j.ins.2003.10.014 Information Sciences 166 (2004) 167–179 www.elsevier.com/locate/ins