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

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.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

“…Then, Turkarslan et al [16] introduced the concept of CFS in terms of the average value and consistency degree (complement of standard deviation) of a fuzzy sequence in FMS and proposed GDM methods using the weighted correlation coefficient and weighted cosine similarity measure of CFSs. However, existing methods [15,16] cannot be applied to the two actual cases because we cannot find a desired/ideal STO/CFS T * i in current clinical applications and existing literature and use the correlation coefficient or cosine similarity measure between the STO T i and the desired CFS T * i . Obviously, our GDM model without considering the ideal STO/CFS can solve the STO problem and reflect its superiority over the existing methods in clinical applications.…”

“…Obviously, our GDM model without considering the ideal STO/CFS can solve the STO problem and reflect its superiority over the existing methods in clinical applications. In addition, the conversion method using the complement of the standard deviation (degree of consistency) [16] is generally only suitable for the normal distribution, which shows its limitations, then we can make up for this gap by using the normalized entropy conversion method. Therefore, our model reflects its highlighting merits in the information expression of EFS, flexible aggregation operations, and the GDM method of STOs in the case of FMSs.…”

“…Since fuzzy multi-sets (FMSs) [14] can occur more than once with the different and/or identical membership values, El-Azab et al [15] proposed correlation measures of FMSs and used them for medical diagnosis problems. Then, Turkarslan et al [16] introduced a conversion method for transforming FMS into a consistency fuzzy set (CFS) based on the mean and consistency level (complement of standard deviation) of a fuzzy sequence in FMS, then they proposed the correlation coefficient and cosine similarity measure of CFSs and applied it to medical diagnosis problems in the setting of FMSs.…”

“…Then, the FMS information is very suitable for the information expression of the GDM problem of STOs. In a GDM problem, the consistency level can be reflected by the complement of standard deviation of group evaluation values [16]. Since there is a certain degree of approximately linear relationship between the standard deviation and Shannon/probability entropy [20], the larger the standard deviation, the smaller the Shannon/probability entropy value.…”

An information measure based extended VIKOR method in intuitionistic fuzzy valued neutrosophic value setting for multi-criteria group decision making

“…These extensions have been widely used by the researchers to address the problems such as multi-criteria decision making (MCDM), multi-criteria group decision making (MCGDM), classification and pattern recognition etc. (see, e.g., [8][9][10][11][12][13][14][15][16][17][18]).…”