Incomplete Complex Intuitionistic Fuzzy System: Preference Relations, Expert Weight Determination, Group Decision-Making and Their Calculation Algorithms

Abstract

As is well known, complex intuitionistic fuzzy preference relation can describe the fuzzy characters of things in more detail and comprehensively and is very useful in dealing with decision-making problems that include periodic or recurring phenomena. However, sometimes, a decision-maker may provide incomplete judgments in a complex intuitionistic fuzzy preference relation because of a lack of knowledge, time pressure, and the decision-makers’ limited expertise related to the problem domain. In such cases, it would be sensible not to force the expert to express “false” preferences over these objects. Consequently, how to define incomplete complex intuitionistic fuzzy preference relations and to estimate their missing elements in an incomplete complex intuitionistic fuzzy preference relation becomes a necessary step in a decision-making process. In this paper, the concept of incomplete complex intuitionistic fuzzy preference relation is introduced and its properties are discussed. Meanwhile, the multiplicative consistent incomplete complex intuitionistic fuzzy preference relations are defined. Secondly, estimating algorithms are developed to estimate the missing elements in the acceptable incomplete complex intuitionistic fuzzy preference relations. Finally, an expert weight determination algorithm and the group decision-making algorithms based on incomplete complex intuitionistic fuzzy preference relations are established. The solving process of the algorithms is illustrated by an example, the practicability of the algorithms is verified, the advantages and disadvantages of two group decision-making algorithms are compared and analyzed, and the simulation verification of incomplete complex intuitionistic fuzzy system is carried out by MATLAB software. The framework proposed in this paper effectively generalizes and enriches the previous works and has a good application prospect.