Analysis of systems under probabilistic and fuzzy uncertainty using multi-valued logic

Abstract

This paper introduces a special class of functions characterised by two interrelated mappings—logical and probabilistic. This formal theory is implemented by means of input–output sets of data from real multi-factor, multi-stage, non-stationary processes operating under stochastic and fuzzy uncertainty of the environment. It is shown how incorrect data can be successfully processed for prediction and control purposes by applying interpolation, composition and extrapolation procedures to these functions.

Keywords:

• Probability theory
• fuzzy sets
• probabilistic-fuzzy uncertainty
• multi-valued logical probabilities
• probabilistic-fuzzy functions

Notes

Alexander Gegov obtained a BSc degree in Automatics and an MSc degree in Robotics from the Technical University of Sofia, Bulgaria, in 1987 and 1989. In 1992 and 1997, he obtained a Ph.D. degree in Control Systems and a DSc degree in Intelligent Systems from the Bulgarian Academy of Sciences. He has been a visiting researcher at the Universities of Duisburg and Wuppertal, Germany, and the Delft University of Technology, Holland. He is currently a Senior Lecturer in Computer Science at the University of Portsmouth, UK. His research interests are in the theory and applications of computational intelligence techniques such as fuzzy logic, neural networks and evolutionary algorithms.

Daniela Parashkevova obtained a BSc degree in Information and Control Systems from the University of Mining and Geology, Bulgaria, in 1996. She is currently a PhD student in the Department of Process Control at the same university. Her research interests are in the areas of industrial automation and control systems.

Krum Ljubenov obtained a BSc degree in Control Systems from the Technical University of Sofia, Bulgaria, in 1973. He has worked in a number of research engineering institutes. He is currently an Associate Professor in Process Automation at the University of Mining and Geology, Sofia, Bulgaria. His research interests are in the area of industrial control systems.

^† E-mail: [email protected]

^‡ E-mail: [email protected]