The definition of a D-number is given by Y. Deng in his paper, " D-numbers: Theory and Applications" published in the Journal of Information & Computational Science 9: 9 (2012), pp. 2421-2428 is perhaps not correct.
Let us look at the definition:
Let Omega be a finite nonempty set, D number is a mapping D from Omega to [0, 1] such that
Sum of (D(B): B is a subset of Omega} is Less than or equal to 1.
By its definition D has the domain Omega. So, D is applicable to elements of Omega. How it is applied to subsets of Omega?
Should we replace the definition as D is a mapping from P(Omega) to [0, 1]?
The way I understand the above sentences is that D is a mapping from the power set P(Omega) to R_0, the nonnegative real numbers (not just [0,1]; the mapping D(Omega):[0,1] induces the derived mapping D(P(Omega):R_0).
The condition D(B)
Dear Prof.Sykora,
Thanks for your reply. I also, feel that it should be from P(Omega). Then only its similarity with mass function in Dempster- Shafer theory can be established.
But, the other part like the range can be R_0, i have a doubt. Because for the mass function in DS theory, it is taken as [0, 1] only. Can you please go through the paper of Y. Deng, which i have mentioned in my query!!
Bets regards,
B. K. Tripathy
Dear Dr.Tripathy,
The definition of D numbers has been proposed in the literature in two ways:
1) For omega as the article you mentioned
2) For the power set of omega similar to Dempster-Shafer like these articles:
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Article D numbers theory based game-theoretic framework in adversari...
In the first definition the elements should be in the form of singletons not subsets.
The interesting and main point is when SUM OF D
Thanks Dr. Seiti. But, i could not get any of the two papers you have referred as the full texts are not available in RG.
I have put a request to the authors and hope to get copies of the papers soon to verify your suggestions.
regards,
B. K. Tripathy
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