Approximate Reasoning Based on Similarity of Z-numbers

Document Type : Research Paper

Authors

1 ASOIU

2 Department of Electrical & Computer Engineering, University of Alberta, Edmonton

3 Department of Computer-Aided Control Systems, Azerbaijan State Oil Academy, 20 Azadlig Ave., AZ1010 Baku, Azerbaijan

4 Research Laboratory of Intelligent Control and Decision Making Systems in Industry and Economics, Azerbaijan State Oil and Industry University, 20 Azadlig Ave., AZ1010, Baku, Azerbaijan

5 DEPARTMENT OF COMPUTER-AIDED CONTROL SYSTEMS, AZERBAIJAN STATE OIL ACADEMY, BAKU, AZERBAIJAN

Abstract

The concept of Z-number was introduced by Zadeh in order to deal with partial reliability of information. This concept
describes a fusion of fuzzy and probabilistic types of uncertainty. In turn, one of the main fields of dealing with imperfect
information 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 and
computational complexity. In this work, we develop an approach to reasoning with such kind of rules. The original
approach proposed here allows to deal with sparse rule base and is characterized by relatively low computational
complexity. The new concept of similarity of Z-numbers based on Jaccard similarity index and measure of divergence
of probability distributions is introduced. Based on similarity degrees of current input Z-numbers and Z-numbers
located in rule antecedents, weights of linear combination of Z-numbers in rule consequents are determined. The linear
combination is based on operations with Z-numbers proposed by authors. Applications of the proposed approach to
evaluation of economic development level for a country and control problem are considered.

Keywords

Main Subjects

References

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Iranian Journal of Fuzzy Systems
Volume 21, Issue 1
January and February 2024
Pages 159-172

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