Expert group information formalization based on Z-numbers

Abstract

A model for formalizing expert group information with a given level of reliability was developed in the paper. To formalize the information Z-numbers were used, components of which are formalizations (fuzzy numbers) of terms of Full Orthogonal Semantic Scopes (linguistic variables with the properties of completeness and orthogonality). If experts evaluate a characteristic X of objects, then individual expert criteria for evaluating this characteristic are represented as a set of Z-numbers, the first components of which are formalizations of the terms of Full Orthogonal Semantic Scope with the title X, and the second component are formalizations of the terms of Full Orthogonal Semantic Scope with the title “Reliability”. The group expert criterion is also determined in the form of a set of Z-numbers, first components of which satisfy the Pareto condition. For Z-numbers, aggregation segments are determined, which are used to determine the distance between two Z-numbers and to recognize the reliability of the group expert criterion. Reliability recognition and identification with one of the linguistic terms (and, accordingly, with the fuzzy number formalizing this term) of the semantic scope “Reliability” is based on a comparative analysis of the distances between Z-number belonging to the group criterion and Z-numbers, the first component of which coincides with the first component of Z-number from the group criterion, and the second components are formalizations of the terms of semantic scope “Reliability”. The reliability of expert group evaluation (the second component of Z-number from the group criterion) is determined by the linguistic value (and, accordingly the fuzzy number formalizing this value) that corresponds to the minimum distance.