# Extension Of Inagaki General Weighted Operators And A New Fusion Rule Class Of Proportional Redistribution Of Intersection Masses

Florentin Smarandache Chair of Math & Sciences Depart. 

University of New Mexico, Gallup, USA 
Abstract. In this paper we extend Inagaki Weighted Operators fusion rule (WO) [see 1, 2] in information fusion by doing redistribution of not only the conflicting mass, but also of masses of non-empty intersections, that we call Double Weighted Operators (DWO). Then we propose a new fusion rule Class of Proportional Redistribution of Intersection Masses (CPRIM), which generates many interesting particular fusion rules in information fusion. Both formulas are presented for 2 and for n ≥ 3 sources. An application and comparison with other fusion rules are given in the last section. Keywords: Inagaki Weighted Operator Rule, fusion rules, proportional redistribution rules, DSm classic rule, DSm cardinal, Smarandache codification, conflicting mass 

## Acm Classification: I.4.8. 1 1. Introduction.

Let θ = {θθ θ 1 2 , ,..., n} , for n ≥ 2 , be the frame of discernment, and S ( ) ,,, θ = ∪∩ θ τ its super-power set, where τ(x) means complement of x with respect to the total ignorance. 

Let total ignorance t I = = θ1c θ2c…cθn, and Φ be the empty set. 

S 2 θ = ^θrefined = 2^(2^θ) = Dθcθc, when refinement is possible, where θc = {τ(θ1), τ(θ2), 
…, τ(θn)}. 

 We consider the general case when the domain is Sθ , but Sθ can be replaced by Dθ= 
(θ,c,1) or by 2θ = (θ,c) in all formulas from below. 

 Let 1 2 m m ( ) and ( ) ⋅ ⋅ be two normalized masses defined from Sθ to [0,1]. 

 We use the conjunction rule to first combine 1 m ( )⋅ with 2 m ( )⋅ and then we redistribute the mass of *mX Y* ( ) I ≠ 0 , when X Y I = Φ . 