In this paper, we review the definition and basic properties of the different types of fuzzy sets that have appeared up to now in the literature. We also analyze the relationships between them and enumerate some of the applications in which they have been used.

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A Historical Account of Types of Fuzzy Sets and Their Relationships

The cloud model, which can implement uncertain transformation between a qualitative concept and its quantitative instantiations, has attracted great attention in multicriteria decision-making problems with linguistic information. This paper proposes some operations and a possibility degree of trapezium clouds, as well as several new aggregation operators: the trapezium cloud weighted arithmetic averaging operator, the trapezium cloud ordered weighted arithmetic averaging operator, and the trapezium cloud hybrid arithmetic operator. Moreover, a method with Atanassov's interval-valued intuitionistic linguistic numbers (AIVILNs) based on trapezium clouds is presented, which can provide solutions to multicriteria group decision-making problems with Atanassov's interval-valued intuitionistic linguistic information. In this method, AIVILNs are first converted into trapezium clouds and aggregated by trapezium cloud aggregation operators. Then, the ranking of alternatives is determined by the possibility degree matrix of trapezium clouds. Finally, an illustrative example confirming the validity and feasibility of the proposed method is given.

Atanassov's Interval-Valued Intuitionistic Linguistic Multicriteria Group Decision-Making Method Based on the Trapezium Cloud Model

Interval-valued intuitionistic fuzzy QUALIFLEX method with a likelihood-based comparison approach for multiple criteria decision analysis

Intuitionistic fuzzy sets (IFSs) are successful to handle the uncertain situations of data. Distance measures of IFSs are important in the evaluation of IFSs relationships. In this paper, we analyzed the disadvantages of existing distance measures of IFSs and proposed a new distance measure called H-max of IFSs. We continued to point out some new results on intuitionistic t-norms and intuitionistic t-conorms and evaluated distance measure between two IFSs which are basically structured from these operations. Further, we combined the classification of t-representable intuitionistic fuzzy t-norms and t-conorms with the proposed distance measure to study some interesting properties. Moreover, we studied De Morgan triplets of IFSs based on the proposed distance measure. Finally, we applied the proposed distance measure to medical diagnosis problem examples and experimental validation on real-world datasets to check the applicability and effectiveness.

D. P. Goswami

Papers

Uncertainties with Atanassov's intuitionistic fuzzy sets: Fuzziness and lack of knowledge