Abstract
The basic ideas of rough sets and intuitionistic fuzzy sets (IFSs) are precise statistical instruments that can handle vague knowledge easily. The EDAS (evaluation based on distance from average solution) approach plays an important role in decision‐making issues, particularly when multicriteria group decision‐making (MCGDM) issues have more competing criteria. The purpose of this paper is to introduce the intuitionistic fuzzy rough Frank EDAS (IFRF‐EDAS) methodology based on IF rough averaging and geometric aggregation operators. We proposed various aggregation operators such as IF rough Frank weighted averaging (IFRFWA), IF rough Frank ordered weighted averaging (IFRFOWA), IF rough Frank hybrid averaging (IFRFHA), IF rough Frank weighted geometric (IFRFWG), IF rough Frank ordered weighted geometric (IFRFOWG), and IF rough Frank hybrid geometric (IFRFHG) on the basis of Frank t‐norm and Frank t‐conorm. Information is given for the basic favorable features of the analyzed operator. For the suggested operators, a new score and precision functions are described. Then, using the suggested method, the IFRF‐EDAS method for MCGDM and its stepwise methodology are shown. After this, a numerical example is given for the established model, and a comparative analysis is generally articulated for the investigated models with some previous techniques, showing that the investigated models are much more efficient and useful than the previous techniques.
Highlights
E basic ideas of rough sets and intuitionistic fuzzy sets (IFSs) are precise statistical instruments that can handle vague knowledge . e EDAS approach plays an important role in decision-making issues, when multicriteria group decision-making (MCGDM) issues have more competing criteria. e purpose of this paper is to introduce the intuitionistic fuzzy rough Frank EDAS (IFRF-EDAS) methodology based on IF rough averaging and geometric aggregation operators
We proposed various aggregation operators such as IF rough Frank weighted averaging (IFRFWA), IF rough Frank ordered weighted averaging (IFRFOWA), IF rough Frank hybrid averaging (IFRFHA), IF rough Frank weighted geometric (IFRFWG), IF rough Frank ordered weighted geometric (IFRFOWG), and IF rough Frank hybrid geometric (IFRFHG) on the basis of Frank t-norm and Frank t-conorm
Study of the rough set has made considerable strides in both real applications and the theory on its own in past years. e idea of rough set theory has been expanded by several researchers in different ways. e definition of the fuzzy rough set was generated by Dubois and Prade [22] by introducing the fuzzy connection rather than the crisp discrete connection. e hybrid definition of IFS and rough set plays a key role in studying such various concepts, and the combined IF rough set analysis was created by Cornelis et al [23]
Summary
Some fundamental notions about the FS and IFS operators are given, which are used in our study. Let us have a fixed set X and for any subsets I ∈ IFS(X × X). ℘(I) 〈x, μ℘(I)(x), η℘(I)(x)〉|x ∈ X, where (℘(I), ℘(I)) is known as the rough set and ℘(I), ℘(I): P(N) ⟶ P(N) are the upper and lower approximation operators. Let us have a fixed set X and subset I ∈ IFS(X × X); an IF relation is defined as follows:. Consider X to be the universal set, and for any subset I ∈ IFS(X × X), we can define an IF relation. On the basis of pair (α, β), we can define the upper and lower approximation which is denoted by ℘(I) and ℘(I). E pair (℘(I), ℘(I)) is known to be the IFR set, where ℘(I) and ℘(I) are said to be the IFR upper and lower approximation, respectively. (2) If Sc(℘(I1)) Sc(℘(I2)), the accuracy function is compared as (a) If A⌣c(℘(I1)) < A⌣c(℘(I2)), ℘(I1) < ℘I2
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