Direct clustering analysis based on intuitionistic fuzzy implication

• Propose an intuitionistic fuzzy implication operator.
• Propose an intuitionistic fuzzy triangle product and an intuitionistic fuzzy square product.
• Develop a direct method for intuitionistic fuzzy clustering analysis.

In this paper, we investigate the technique for clustering analysis under intuitionistic fuzzy environment. We first develop an intuitionistic fuzzy implication operator and extend the Lukasiewicz implication operator to intuitionistic fuzzy environment, and then we define an intuitionistic fuzzy triangle product and an intuitionistic fuzzy square product. Furthermore, we apply the intuitionistic fuzzy triangle product to compare the alternatives in multiple attribute decision making with intuitionistic fuzzy information, and use the intuitionistic fuzzy square product to construct an intuitionistic fuzzy similarity matrix, based on which we develop a direct method for intuitionistic fuzzy clustering analysis. Some numerical examples are also given to illustrate and verify our results.

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