5. SUMMARY
There is very little absolute knowledge in the real world. Inquiry must be a process of removal of doubt and skepticism or representing it properly. One of the main aspects of this skepticism has been identified as fuzziness, which is well represented with conventional fuzzy logic. Another aspect of the existing skepticism is uncertainty about the future of random processes and probabilistic events. Many of the real world systems, although may not have a random nature, may seem random to us due to insufficient knowledge and should be modeled accordingly. Although these two aspects have, up until now, been studied separately, the new concept of probabilistic fuzzy logic tries to merge them in a unifying framework. Probabilistic Jiczzy logic is a new approach for incorporating probability in fuzzy logic in order to better represent non-deterministic real world systems. It has not only the advantages of the approximate reasoning property of fuzzy systems, but also can be regarded as an extension to conventional one in the sense that the latter is a special case of the former with zero degree of randomness. The existing randomness in a probabilistic fuzzy system can be interpreted as: 1. Probabilistic nature in some of the natural language propositions and human reasoning as well as the statistical differences and variety of different human experts’ knowledge. 2. Existing randomness in many of the real world systems, which is required to be modeled, including human skepticism in defining the filzn knowledge base.
