**5. QBN-Multi-Criteria Decision Making Method**

**Definition 18.** *Let U* = (*u*1, *u*2, ..., *um*) *be a set of alternatives, A* = (*a*1, *a*2, ..., *an*) *be the set of attributes, w* = (*w*1, *w*2, ..., *wn*) *T be the weight vector assigned to a<sup>j</sup>* (*j* = 1, 2, ...*n*) *such that w<sup>k</sup>* ≥ 0 *and n* ∑ *k*=1 *w<sup>k</sup>* = 1*. Let* [*bij*]*m*×*<sup>n</sup>* = h*T P ij* , *C P ij*, *U P ij*, *F P ij* , *T N ij* , *C N ij* , *U N ij* , *F N ij* i *represents the rating values of the alternatives in term of QSVBNS. a*<sup>1</sup> *a*<sup>2</sup> · · · *a<sup>n</sup> u*<sup>1</sup> *b*1,1 *b*1,2 · · · *b*1,*<sup>n</sup>* 

*Then, u*<sup>2</sup> *b*2,1 *b*2,2 · · · *b*2,*<sup>n</sup> . . . . . . . . . . . . . . . u<sup>m</sup> bm*,1 *bm*,2 · · · *bm*,*<sup>n</sup> is called the QBN-multi-attribute decision making matrix.*

The positive ideal QBN solution of the decision matrix [*bij*]*m*×*<sup>n</sup>* is defined as: ¯*<sup>b</sup>* ∗ *<sup>j</sup>* = hmax *i* {*T P ij*}, max *i* {*C P ij*}, min *i* {*U P ij*}, min *i* {*F P ij* }, min *i* {*T N ij* }, min *i* {*C N ij* }, max *i* {*U N ij* }, max *i* {*F N ij* },i. The negative ideal QBN solution of the decision matrix [*bij*]*m*×*<sup>n</sup>* is defined as:

$$\underline{b}\_{j}^{\*} = \langle \underset{\stackrel{\circ}{\text{i}}}{\text{min}} \{ \prescript{P}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{max}} \{ \prescript{P}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{max}} \{ \prescript{P}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{max}} \{ \prescript{N}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{max}} \{ \prescript{N}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{min}} \{ \prescript{N}{}{l\_{\text{ij}}} \}, \underset{\stackrel{\circ}{\text{i}}}{\text{min}} \{ \prescript{N}{}{l\_{\text{ij}}} \}.$$

We now propose an algorithm based on the quadripartitioned weighted similarity measure to select the best alternative for multi-attribute decision making problem in quadripartitioned bipolar neutrosophic enviornment which is given in Algorithm 1 :
