Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis | Zendy

Ezgi Türkarslan | Zendy; Jun Ye | Zendy; Mehmet Ünver | Zendy; Murat Olgun | Zendy

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Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis

Author(s) -

Ezgi Türkarslan,

Jun Ye,

Mehmet Ünver,

Murat Olgun

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/9975983

Subject(s) - multiset , measure (data warehouse) , mathematics , consistency (knowledge bases) , sequence (biology) , cosine similarity , fuzzy logic , similarity (geometry) , fuzzy set , set (abstract data type) , degree (music) , data mining , algorithm , discrete mathematics , artificial intelligence , pattern recognition (psychology) , computer science , physics , biology , acoustics , image (mathematics) , genetics , programming language

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set 0,1 2 . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.

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