Fundamental Properties With Respect to the Completeness of Intuitionistic Fuzzy Partially Ordered Set

Intuitionistic fuzzy set (A-IFS), originally introduced by Atanassov in 1983, is a generalization of a fuzzy set. The basic elements of an A-IFS are intuitionistic fuzzy values (IFVs), based on which the intuitionistic fuzzy calculus (IFC) has been proposed recently. To avoid relying too much upon the classical calculus and make the IFC to be an independent subject, it is necessary to develop the limit theory of the IFC. In this paper, we first define the concepts of the supremum and the infimum with respect to IFVs, and investigate their properties in detail. Then, we reveal the relationships among them and four types of limits, and finally, we give a series of fundamental theorems with respect to the completeness of intuitionistic fuzzy partially ordered set.

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