Multicriteria Decision-Making Method Based on Similarity Measures under Single-Valued Neutrosophic Refined and Interval Neutrosophic Refined Environments

Abstract

In this paper, we propose three similarity measure methods for single‐valued neutrosophic refined (SVNR) sets and interval neutrosophic refined (INR) sets based on Jaccard, Dice, and Cosine similarity measures of SVN‐sets and interval neutrosophic sets. Furthermore, we suggest two multicriteria decision‐making (MCDM) methods under SVNR environment and INR environment, and give applications of proposed MCDM methods. Finally, we suggest a consistency analysis method for proposed similarity measures between INR‐sets and give an application to demonstrate process of the method.

RETRACTED ARTICLE: Extentions of neutrosophic cubic sets via complex fuzzy sets with application

“…Neutrosophic cubic sets (NCSs) which are the generalized form of fuzzy sets, cubic sets andņeutrosophic sets. Different researchers used the fuzzy sets and extended version such as neutrosophic set, single-valued neutrosophic sets neutrosophic soft sets and neutrosophic refined sets in decision making problems with the help of aggregation operators for detail see [10][11][12][13][14][15].…”

The Projection Model with Unknown Weight Information under Interval Neutrosophic Environment and Its Application to Software Quality-in-Use Evaluation

“…A common approach is to assume that decision makers are risk conservatives, who tend to avoid risk. If decision makers are conservative and pessimistic, then according to equations (20) and (21), the positive and negative ideal solutions can be defined as follows: (9) and 10, we rank the attribute values from big to small. Here, we can set the value of φ. e value of φ represents the attitude to the indeterminacy information.…”

“…(3) If decision makers are conservative and pessimistic, the common approach is adopted. According to equations (20) and (21), determine the positive and negative ideal solutions:…”

“…e other is to combine new concepts with more mature MCDM methods and further innovate and apply these methods. Among them, the research on the single value neutrosophic set mainly includes basic concepts, operational rules, similarity measurement, distance measurement, entropy measurement, definition of cross entropy [13,14], aggregation operator [15][16][17][18], and decision method [19,20]. INS adopts the form of the interval number to represent the truth information, indeterminacy information, and falsity information, which can effectively catch and express more information in case of uncertainty [21].…”

A multiperiod hybrid decision support model for medical diagnosis and treatment based on similarities and three‐way decision theory

“…An SVNS A in a space of points X can be denoted by A = {⟨ x , T A ( x ), I A ( x ), F A ( x )⟩| x ∈ X }. Many scholars have studied certain measurements for SVNS; the measurements include similarities (Karaaslan, ; Ye & Fu, ; Ye & Zhang, ) and entropies (Aydoğdu, ; Biswas, Pramanik, & Giri, ). In addition, some studies have applied SVNS to multiple criteria decision making (M. Radwan, Senousy, & M. Riad, ; Sun, Hu, & Chen, ; Yang, Hu, Sun, & Chen, ; Ye, ).…”