Operations on Z-numbers with acceptable degree of specificity

Abstract

Basically, the concept of a Z-number relates to the issue of reliability of information. Existing studies on operations over Z-numbers are based on classical interval and fuzzy arithmetic. Operation over a set of Z-numbers produces a Z-number with a very lengthy supports of its components. This result some times is practically unsuitable for users. The second limitation here is that some fundamental properties of operations over real numbers are lost. All the existing works on computation of Z-numbers are characterized by increasing of entropy. In particular, these approaches are not able to account for informativeness of computation results. An importance of informativeness of Z-numbers was first mentioned by Zadeh. This paper describes some preliminary investigations on informativeness of Z-number calculus by using concept of specifity and concept of horizontal membership functions. We propose a strategy for optimizing informativeness of Z-number operations with desired degree of specificity. Validity of the proposed approach is illustrated in an examples.