Abstract
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.
Highlights
Fuzzy set theory was introduced by Zadeh [1] in 1965 with the help of the concept of membership function that is used as an effective tool to overcome uncertainty in science, and it has applications in many different fields such as economics, engineering, decision-making, management, and medicine [2,3,4]. ere are many generalizations of the concept of the fuzzy set in the literature, and their applications to several areas such as decision-making and medical diagnosis are studied to model uncertain data that is encountered in science often
Motivated from this, we propose a new concept which is called consistency fuzzy set (CFS). is concept is expressed as an ordered pair whose components are the average value and the consistency degree of the sequence, respectively
We introduce a correlation coefficient and a cosine similarity measure between CFSs, and we give the multiperiod medical diagnosis approaches by using the proposed correlation coefficient and cosine similarity measure to show the efficiency of these new concepts
Summary
Fuzzy set theory was introduced by Zadeh [1] in 1965 with the help of the concept of membership (truth) function that is used as an effective tool to overcome uncertainty in science, and it has applications in many different fields such as economics, engineering, decision-making, management, and medicine [2,3,4]. ere are many generalizations of the concept of the fuzzy set in the literature, and their applications to several areas such as decision-making and medical diagnosis are studied to model uncertain data that is encountered in science often. A HFS can model uncertain data better than a fuzzy set, thanks to its handy structure, so it has been frequently preferred by researchers to solve multicriteria (group) decision-making or multiperiod medical diagnosis problems [9,10,11,12]. We introduce a correlation coefficient and a cosine similarity measure between CFSs, and we give the multiperiod medical diagnosis approaches by using the proposed correlation coefficient and cosine similarity measure to show the efficiency of these new concepts. (v) e proposed correlation coefficient and cosine similarity measure between CFSs provide useful ranking method, and they are beneficial mathematical tools for multiperiod medical diagnosis and multicriteria group decision-making problems in the FMS environment.
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