Reliability and Importance Discounting of Neutrosophic Masses

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Advances and Applications of DSmT for Information Fusion. Collected Works. Volume 4

Reliability and Importance Discounting of Neutrosophic Masses Florentin Smarandache Originally published in Smarandache, F. - Neutrosophic Theory and its Applications, Collected Papers, Vol. I. 2014. <hal-01092887v2>, and reprinted with permission.

„•–”ƒ…–Ǥ In this paper, we introduce for the first time the discounting of a neutrosophic mass in terms of reliability and respectively the importance of the source. We show that reliability and importance discounts commute when dealing with classical masses. ͳǤ Â?–”‘†—…–‹‘Â?Ǥ Let ÎŚ = {ÎŚ1 , ÎŚ2 , ‌ , ÎŚn } be the frame of discernment, where đ?‘› ≼ 2, and the set of ˆ‘…ƒŽ elemeÂ?–•: đ??š = {đ??´1 , đ??´2 , ‌ , đ??´đ?‘š }, for đ?‘š ≼ 1, đ??š ⊂ đ??ş đ?›ˇ . (1) Let đ??ş đ?›ˇ = (đ?›ˇ,âˆŞ,∊, đ?’ž) be the ˆ—•‹‘n •’ƒ…‡. A Â?‡—–”‘•‘’Š‹… Â?ƒ•• is defined as follows: đ?‘šđ?‘› : đ??ş → [0, 1]3 for any đ?‘Ľ ∈ đ??ş, đ?‘šđ?‘› (đ?‘Ľ) = (đ?‘Ą(đ?‘Ľ), đ?‘–(đ?‘Ľ), đ?‘“(đ?‘Ľ)), (2) where

đ?‘Ą(đ?‘Ľ) = believe that đ?‘Ľ will occur (truth); đ?‘–(đ?‘Ľ) = indeterminacy about occurence; and đ?‘“(đ?‘Ľ) = believe that đ?‘Ľ will not occur (falsity).

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