Probabilistic fuzzy logic and probabilistic fuzzy systems

Abstract

A novel concept of probabilistic f u w logic is introduced as a way of representing and/or modeling existing randomness in many real world systems and natural language propositions. The approach is actually based on combining both the concepts of probability of truth and degree of truth in a unique framework. This combination is carried out in both the fuzzy sets and fuzzy rules resulting in the new concepts of probabilistic fiw sets and probabilistic fuzzy rules, respectively. Having one of these probabilistic elements, a probabilistic fuzqv system is then introduced as a fuzzy-probabilistic model of a complex nondeterministic system. In a simple example, human skepticism about the optimal fuzzy rule base is modeled through substituting a probabilistic fuzzy rule base for a conventional one. The closed loop response of the resulting controller for tank level control is shown through simulation and is compared with a conventional fuzzy controller,

Probabilistic Fuzzy Reasoning in a Coherent Setting

“…A relevant problem in literature is the managing of fuzzy IF-THEN rules based systems: they are essentially composed by a collection of rules of the form "IF A THEN B, with a given probability", where either premise A and consequence B of the rule can be fuzzy subsets [4,31,32,39,41,46,49]. Here we study this problem by adopting the interpretation of fuzzy sets in terms of coherent conditional probabilities introduced in [7,8,9] (and developed in [40,6,14,15]) whose main concepts are recalled in Appendix A.…”

“…One of the main objectives is to jointly handle probability and vagueness [3,4,6,8,9,11,14,15,16,21,22,23,31,32,39,40,41,46,43,44,47,48,49]. For this task it is suitable to have a general framework in which it is possible to handle uncertainty encoding the different aspect by maintaining consistency with the model of reference: this is crucial to ensure a sound inference.…”

Fuzzy Rule Base Design With Probabilistic Weights

“…Some approaches aim to develop hybrid systems for the treatment of uncertainty as in [2] and [3]. However, these are not the first results joining both theories.…”

“…There is an extensive discussion about the theme in the literature: some authors agree with such combination [2,3], while others limit themselves to just compare the two theories [4,5].…”

Modeling and control of an unstable system using probabilistic fuzzy inference system

“…Therefore to overcome the shortcomings of conventional FIS, a new concept of Probabilistic Fuzzy Inference System (PFIS) is introduced by integrating fuzzy theory and probability theory, which has been discussed in [1][2][3]5,6,9,10], but these works present only the relationship of randomness and fuzziness, and are not applied to process control engineering applications. In this PFIS, the MFs of the antecedent and consequent are Probabilistic Fuzzy Sets (PFS), whose membership grades for each element of this set is a fuzzy number in (0,1), hence useful for incorporating uncertainties [13].…”