Approximate Reasoning Based on Similarity of Z-numbers

The concept of Z-number was introduced by Zadeh in order to deal with partial reliability of information. This conceptdescribes a fusion of fuzzy and probabilistic types of uncertainty. In turn, one of the main fields of dealing with imperfectinformation is approximate reasoning. For the case of pure fuzzy information this field is well-developed. In contrast,existing studies on reasoning with Z-valued “if-then” rules are scarce. One of the main reasons is high analytical andcomputational complexity. In this work, we develop an approach to reasoning with such kind of rules. The originalapproach proposed here allows to deal with sparse rule base and is characterized by relatively low computationalcomplexity. The new concept of similarity of Z-numbers based on Jaccard similarity index and measure of divergenceof probability distributions is introduced. Based on similarity degrees of current input Z-numbers and Z-numberslocated in rule antecedents, weights of linear combination of Z-numbers in rule consequents are determined. The linearcombination is based on operations with Z-numbers proposed by authors. Applications of the proposed approach toevaluation of economic development level for a country and control problem are considered.

Keywords:

IF-THEN rules , Fuzzy number , Probability density function , reliability