Hukuhara difference of Z-numbers

Real-world problems in decision analysis, economics, optimization and other fields are characterized by fuzzy and partially reliable information. In this regard, Prof. Zadeh suggested the concept of a Z-number, as an ordered pair Z = (A, B) of fuzzy numbers A and B, the first of which describes a linguistic value, and the second one is a fuzzy value of probability measure of the first one, playing a role of reliability of information. Construction of mathematical models to handle Z-number-based information is a new challenge which requires development of Z-number-valued analysis including Z-number-valued equations, Z-number-valued derivative and integral and other concepts. One of the basic concepts in this realm is an inverse of addition operation. In the existing literature devoted to set-valued arithmetic and fuzzy arithmetic this operation is referred to as Hukuhara difference. For interval numbers and fuzzy numbers, the existence conditions of Hukuhara difference are derived. Unfortunately, the concept of Hukuhara difference for Z-numbers is not developed. In this work for the first time we suggest a fundamental approach for development of the concept of Hukuhara difference of Z-numbers. Examples are provided in the paper to show validity of the suggested approach.