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Author: Admin | 2025-04-27
) E ( L 2 ( p ) ) , then L 1 ( p ) ≺ L 2 ( p ) ;(3) If E ( L 1 ( p ) ) = E ( L 2 ( p ) ) , while σ ( L 1 ( p ) ) σ ( L 2 ( p ) ) , then L 1 ( p ) ≻ L 2 ( p ) ; while σ ( L 1 ( p ) ) > σ ( L 2 ( p ) ) , then L 1 ( p ) ≺ L 2 ( p ) ; while σ ( L 1 ( p ) ) = σ ( L 2 ( p ) ) , then L 1 ( p ) ≈ L 2 ( p ) . 2.2. Distance Measures between PLTSsPLTSs can more accurately represent qualitative information of DMs in complex linguistic environments. However, existing distance measures may distort the original information and lead to unreasonable results. For this reason, a new generalized hybrid distance based on the classical distance is proposed.Definition 6.Let L 1 ( p ) = L 1 ( k ) ( p 1 ( k ) ) L 1 ( k ) ∈ S , p 1 ( k ) ≥ 0 , k = 1 , 2 , ⋯ , # L 1 ( p ) , ∑ k = 1 # L 1 ( p ) p 1 ( k ) = 1 and L 2 ( p ) = L 2 ( k ) ( p 2 ( k ) ) L 2 ( k ) ∈ S , p 2 ( k ) ≥ 0 , k = 1 , 2 , ⋯ , # L 2 ( p ) , ∑ k = 1 # L 2 ( p ) p 2 ( k ) = 1 be two PLTSs, # L 1 ( p ) = # L 2 ( p ) , L 1 ( k ) and L 2 ( k ) are the k t h linguistic terms of L 1 ( p ) and L 2 ( p ) respectively, p 1 ( k ) and p 2 ( k ) are the probabilities of the k t h linguistic terms of L 1 ( p ) and L 2 ( p ) respectively, α
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