Table 2 Symbols and its meanings.

From: Novel concept of linguistic fractional fuzzy information for effective water filtration decision-making problem based on WASPAS method

Symbols

Meaning

Symbols

Meaning

\(\mathcal{U}\)

Fixed set/Universal set

\(\kappa\)

\(\upkappa \in \mathcal{U}\)

\({\varvec{\mu}}\left({\varvec{\kappa}}\right)/{\varvec{\nu}}\left({\varvec{\kappa}}\right)\)

TG/FG

\(A\)

FS

\({\varvec{\pi}}\)

Grade of indeterminacy

\(I/F\)

IFS/FFS

\(\cup ,\boldsymbol{ }\cap\)

Union/Intersection

\(f\)

Fractional value

\({\mathcal{L}}_{{{\varvec{F}}}_{1}}^{{\varvec{C}}}\)

Complement of LFFV

\(\mathcal{S}/{\mathcal{L}}_{F}\)

LTS/LFFS

\({\varvec{S}}{\varvec{c}}/{\varvec{A}}{\varvec{c}}{\varvec{c}}\)

Rating function/Accuracy function

\({\mathcal{L}}_{{F}_{i}}\)

LFFVs

\({\mathcal{d}}_{\mathcal{H}\mathcal{d}}\)

Standardized Hamming distance

\(\aleph\)

Any scaler greater than 0

\({{\varvec{\omega}}}_{{\varvec{j}}}/{\boldsymbol{\Phi }}_{{\varvec{j}}}\)

Criteria weight/Expert weight

\(M\)

Collection of LFFVs

\(\mathfrak{Q}\)

LFFAM

\({\mathcal{L}}_{{F}_{\sigma \left(i\right)}}\)

Largest LFFV

\(\oplus ,\boldsymbol{ }\otimes\)

Addition, multiplication

\({\mathcal{A}}_{i}/{\mathcal{B}}_{j}\)

Alternative/Criteria

\({\mathcal{S}}_{{\varvec{i}}}^{\left({\varvec{a}}\right)}/\boldsymbol{ }{\mathcal{S}}_{{\varvec{i}}}^{\left({\varvec{b}}\right)}\)

Weighted sum/weighted product

l

Number of experts

\(\calligra{t}\)

Sensitivity combined factor

\({\mathcal{S}}_{i}\)

Combined measure