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Intuitionistic Fuzzy Set Characteristic Analysis with Lexicographical Vector Lattice Structure

Sanghyuk Lee, Youpeng Yang

Abstract



The similarity measure design for the different patterns has been proposed based on the information characteristic analysis and the distance measure. Analysis of fuzzy sets (FSs), intuitionistic fuzzy sets (IFSs), and Pythagorean fuzzy sets (PFSs) and characteristics comparison between them also have been carried out with membership and non-membership degrees. Each degree of FSs, IFSs and PFSs is illustrated through figures, and its characteristics are analyzed. The existing similarity measures are also explained and compared for each fuzzy set. The proposed similarity can be applied to all membership and non-membership points satisfying 0≤μ(x)≤1 and 0≤nu(x)≤1. Similarity measure has been designed for the membership and non-membership degree separately, and it constitutes a 2-dimensional component Together with two degrees, it is emphasized that the hesitation has relation with the similarity design. With the consideration of membership and non-membership degree, each similarity measure component is integrated as the ordered sets. Similarity measure integration with two measures provides several analysis outcomes; magnitude, 1-norm, and inner product with respect to 〖45〗^∘ line. The obtained results can be included in the ordered set, and a lattice structure is proposed on the similarity measure. Additionally, the Cartesian product structure is organized for two similarity measures with the help of vector lattice structure. With the illustrative example, it is shown that the relevant result comparison is carried out with the existing result.

Keywords


Intuitionistic Fuzzy Sets, Similarity Measure, Distance Measure, Membership Degree, Non-membership Degree, Lattice.

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