Application of Γ-fuzzy soft relation in decision-making
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This study explores the extension of $I = [0, 1]$-fuzzy soft relations to $\Gamma$-fuzzy soft relations using the $\Gamma = [0, 1]^{|E|}$-lattice. When the parameter set $E$ contains only one parameter, $\Gamma = I = [0, 1]$, resulting in applications similar to those found in conventional fuzzy scenarios. However, when $E$ contains at least two parameters, the applications resemble typical fuzzy soft situations where $I = [0, 1]$ fuzzifies the soft set. It is posited that the concept of an "$I = [0, 1]$"-fuzzy soft relation naturally extends to a "$\Gamma = [0, 1]^{|E|}$"-fuzzy soft relation. This extension is significant because it considers the individual impact of each parameter element in the subset $A$ of the parameter set $E$, rather than simultaneously assessing the effects of all parameters. This generalization is illustrated, and its relevance to decision-making-related problems is demonstrated through an application example.
Abstract
This study explores the extension of $I = [0, 1]$-fuzzy soft relations to $\Gamma$-fuzzy soft relations using the $\Gamma = [0, 1]^{|E|}$-lattice. When the parameter set $E$ contains only one parameter, $\Gamma = I = [0, 1]$, resulting in applications similar to those found in conventional fuzzy scenarios. However, when $E$ contains at least two parameters, the applications resemble typical fuzzy soft situations where $I = [0, 1]$ fuzzifies the soft set. It is posited that the concept of an "$I = [0, 1]$"-fuzzy soft relation naturally extends to a "$\Gamma = [0, 1]^{|E|}$"-fuzzy soft relation. This extension is significant because it considers the individual impact of each parameter element in the subset $A$ of the parameter set $E$, rather than simultaneously assessing the effects of all parameters. This generalization is illustrated, and its relevance to decision-making-related problems is demonstrated through an application example.