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- MakaleYalnız künye2023Scopus SJRQ1Correlation coefficients of simplified neutrosophic multiplicative sets and their applications in clustering analysis
Köseoğlu, Ali; Şahin, Rıdvan
The use of fuzzy sets, intuitionistic fuzzy sets and neutrosophic sets can often handle with real-life problems that contain incomplete and uncertain information. The 0–1 scale is used to deal with such information which is graded symmetrically and uniformly but, some problems consist of unsymmetrical and non-uniform information. Although intuitionistic multiplicative set (IMS) is a powerful tool to deal with this kind of problems, due to the dependence of hesitant information to the membership and non-membership functions in IMS, it brings a restriction to decision-makers while working on the real-life problems such as applications of correlation coefficients and clustering. In this study, we propose novel correlation coefficients (CCs) of simplified neutrosophic multiplicative sets (SNMSs) which is defined recently by removing the shortages of IMSs. Firstly, we give SNMS-based operations, fulfil the deficiencies in the theoretical background of IMS and establish a theoretical structure for the SNMS. Then, we propose novel correlation coefficients (CC) of SNMS and show some of their important properties. Finally, we apply the CCs to a clustering problem to confirm the efficiency of the proposed SNMS and its correlation coefficients.
AtıfScopus5WoS4OpenAlex6
İncele - MakaleYalnız künye2020Scopus SJRQ2A simplified neutrosophic multiplicative set-based TODIM using water-filling algorithm for the determination of weights
Köseoğlu, Ali; Şahin, Rıdvan; Merdan, Mehmet
Due to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real-life problems contain nonsymmetrical and non-uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real-life problems. However, IMSs cannot handle real-life problems completely because indeterminate information depends on membership and non-membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set-based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water-filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative-TODIM method.
AtıfScopus27WoS22OpenAlex30İncele