*Corresponding author. Robotics and Computer-Integrated Manufacturing 14 (1998) 465 — 474 Fuzzy methods for analysing fuzzy production environment G. Perrone *, S. Noto La Diega DIFA-University of Basillcata — Potenza, Italy DTPM-University of Palermo, Italy Abstract Very recently, in production management research literature, the necessity to extend production systems analysis techniques, such as queue theory, Mean Value Analysis (MVA) and discrete simulation, to Fuzzy Production Environments, i.e. to those production situations in which data are vague, has emerged. Fuzzy set theory is a powerful tool to model vagueness and, therefore, fuzzy mathematics can be used to extend classical production system analysis techniques. This paper proposes a methodology based on fuzzy relation algebra to extend classical MVA and discrete event simulation.  1998 Elsevier Science Ltd. All rights reserved Keywords: Fuzzy; Production systems analysis techniques; Discrete simulation 1. Introduction Statistics has always been the main tool to model uncertainty in production system design and analysis. For this reason, several analysis techniques involving statistical methods are available to model production systems. Mean Value Analysis (MVA) [1] and Discrete Event Simulation are the most used techniques to analyse pro- duction systems [2]. Recently, it has been highlighted how it is often im- possible to lead back production environment uncertain- ty to statistical basis. This happens when uncertainty takes the form of vagueness. Vagueness is a kind of uncertainty related to event definition and knowledge. Examples of vagueness in manufacturing have been reported by  Ishii [3] and Ishibuchi [4]. In the paper the authors stress that due date is not a simple number, but is a concept, more precisely an agreement among customers and suppliers. Agreements are subject to human imprecision, therefore concepts such as due dates are more properly described by using fuzzy linguistic variables.  Inuiguishi [5], Kuroda [6], Perrone [7]. In the paper the authors generalise the vagueness concept in production systems stating that it can concern data such as service times, job availability, etc., and require- ments or constraints, such as cost requirements, due dates, production volumes. The data vagueness is due to the approximate knowledge of the process especially when humans are involved. Service times, especially in small and medium enterprises, are an example of vagueness concern- ing data. In such environments data such as processing times and job availability are more easily expressed through approximate expression such as ‘‘about X units of time’’, or ‘‘the job will be available in approximately ½ units of time’’. Such vague concepts can be easily turned into fuzzy numbers and treated by using fuzzy algebraic oper- ators. Moreover, requirement and constraints are often the result of a human decision process. Due dates are the result of an agreement; production quantities are the result of a trade-off among marketing requirements and production resources availability; cost requirements are the result of a decision process involving budget consid- eration and production resources utilisation. The result of human decision processes is never a crisp requirement, because it is human in nature, then vague. Such vague- ness is usually linguistically expressed. More generally, Young et al. [8] have located at least three kinds of vagueness in engineering processes:  Relationship imprecision, that is when process para- meters are related through vague relations; 0736-5845/98/$19.00  1998 Elsevier Science Ltd. All rights reserved. PII: S0736-5845(98)00021-0