
$$m(X)=m i n\Big\{m_{1}\big(X_{i}\big),m_{2}\big(X_{j}\big)\Big\}$$
operator:  $m(X)=m_{1}(X_{i})m_{2}(X_{j})$  operator:  $m_{1}(X_{i})m_{2}(X_{j})$
$$\mathbf{\Pi}(T)$$

 ( ) = { 1 ( i) 2 (*Xm,XmminXm* j)} (6) 
Algebraic product operator:  $\left(\begin{array}{c}\\ \end{array}\right)$
$$m(X)=\operatorname*{max}\left\{0,\left[m_{1}(X_{i})+m_{2}(X_{j})-1\right]\right\}$$
 ( ) ( ) ( ) = 1 i 2 *Xm.XmXm* j (7) 
 Xm = { [ 1 i + 2 *XmXm* j −1)()(,0max)( ]} (8) 
Bounded product operator:  $m(X)=$ ma
$$({\boldsymbol{8}})$$
$$\widetilde{m}_{12}\left(X\right)=T_{n o r m}\left\{m_{1}\left(\theta_{i}\right),m_{2}\left(\theta_{j}\right)\right\}$$
 ( ) norm { ( i) *m,mTXm* ( j)} ~12 = 1 θ 2 θ (9) 
) ~ ~ () () ( ( )) + ∪ + ∪ = ( ) ( ( ) ( )) + ∪ + ∪ = m,mT m,mT m,mTm θθθ θ θ θ m,mT m,mT m,mTm θθθ θ θ θ 1 2 1 2 12 1 2 ( ) ( ) ( ) norm ji i norm i ji i norm i j 1 2 1 2 12 1 2 ( ) ( )( norm ji j norm j ji j norm j i ( ) ( ) ( ( ) () ( )    (10)  ) θθθ θθθ ( ) ( ( ) ( )) m ji norm ji m,mT ji ~ 12 θ ∪θ = 1 θ ∪θ 2 θ ∪θ

$$(9)$$

## Step 2: Distribution Of The Mass, Assigned To The Conflict.

$${\boldsymbol{m}}$$

The way of association between the focal elements of the given two sources of information, (.m ) 1 and ( ).m , is defined as 2 X θ ∩= θ ji and the degree of association is as follows: 
where ( ) Xm~12 represents the basic belief assignments (bba) after the fusion, associated with the given proposition X by using particular t-norm based conjunctive rule. 

In some degree it follows the distribution of conflicting mass in the most sophisticated DSmT based Proportional Conflict Redistribution rule number 5, but the procedure here relies on fuzzy operators. The total conflicting mass is distributed to all non-empty sets proportionally with respect to the Maximum (Sum) between the elements of corresponding mass matrix's columns, associated with the given element of the power set. It means the bigger mass is redistributed towards the element, involved in the conflict and contributing to the conflict with the maximum specified probability mass. The general procedure for fuzzy based conflict redistribution is as follows: 
X
- Calculate all partial conflict masses separately; 
- If θ ∩θ ji ∅= , then θi and θ j are involved in the conflict; redistribute the corresponding masses 12 θ ∩θ ji )(m > 0 , involved in the particular partial conflicts to the non-empty sets θi and θ j with respect to max{ (m θ i m), 2 θ j )( } and with respect to 1 { 1 θ j 2 θ i *)(m),(mmax* }; 
- Finally, for the given above two sources, the *Tnorm* conjunctive consensus yields: 
Step 3: The basic belief assignment, obtained as a result of the applied TCN rule becomes: 