System with probabilistic fuzzy knowledge base and parametric inference operators in risk assessment of innovative projects

This paper presents the properties, identification issues and utilisation of a new concept of probabilistic fuzzy system for the innovative project risk assessment. This system constitutes the extension of Mamdani probabilistic fuzzy system. For this purpose, a group of risk factors, which influence risk variables, has been chosen. Linguistic risk variables are inputs to the innovation risk assessment system. The structure of fuzzy sets for linguistic values takes into account knowledge of a number of experts. Knowledge is presented as fuzzy IF-THEN rules together with probability measures of fuzzy events occurrence in the antecedent and conclusion of rules. The paper presents a new method of identification of the analysed system. The method uses parametric family of triangular t-norms, which facilitates inference parameters optimisation, enables flexible adjustment of a system to empirical data and makes the system more precise. The modified FP-Growth algorithm to create probabilistic fuzzy rule base is used. Using assumption of the minimal support of rules enables decreasing of knowledge base complexity while preserving the level of identification quality, comparable to the system with full marginal and conditional probability distributions. The results of the system inference have been compared with regression model and Mamdani fuzzy inference system. Finally, the numerical experiments show more precision of system inference than the compared method. The example of analytical use of created probabilistic fuzzy knowledge base in the context of technical innovation risk assessment is also presented. The constructed expert system has an identification character and it can be develop as a tool to help the assessment of applications for funding the implementation of innovative projects by the institutions established for this purpose. (C) 2015 Elsevier Ltd. All rights reserved.