Theoretical analysis reveals new inequality relations among intuitionistic fuzzy aggregation operators and values, providing a rigorous mathematical foundation for fuzzy decision operations.
Intuitionistic fuzzy sets, characterized by membership degree μ μ , non-membership degree υ υ and hesitation degree π π , are a meaningful extension of fuzzy set. Inequalities on intuitionistic fuzzy sets/values are very important in solving real problems. In this paper, some inequalities on intuitionistic fuzzy sets are derived from operations. Moreover, three unweighted intuitionistic fuzzy aggregation operators, including unweighted intuitionistic fuzzy Square, unweighted intuitionistic fuzzy Arithmetic and unweighted intuitionistic fuzzy Geometric, are developed. Later, some corresponding inequality relations on them are deeply explored. Finally, some inequalities on intuitionistic fuzzy value are constructed by equality μ +υ +π =1 μ + υ + π = 1 in critical definition and proved by some existing famous inequalities, which provide a novel basis for the intuitionistic fuzzy inequalities in operations and aggregation operators.
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Peng et al. (2022) studied this question.
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