Rough Sets and Knowledge Technology: 9th International by Duoqian Miao, Witold Pedrycz, Dominik Ślȩzak, Georg Peters,

By Duoqian Miao, Witold Pedrycz, Dominik Ślȩzak, Georg Peters, Qinghua Hu, Ruizhi Wang

This booklet constitutes the completely refereed convention court cases of the ninth overseas convention on tough units and data know-how, RSKT 2014, held in Shanghai, China, in October 2014. The 70 papers awarded have been conscientiously reviewed and chosen from 162 submissions. The papers during this quantity conceal issues similar to foundations and generalizations of tough units, characteristic relief and have choice, purposes of tough units, clever structures and functions, wisdom expertise, domain-oriented data-driven information mining, uncertainty in granular computing, advances in granular computing, giant info to clever judgements, tough set conception, and three-way judgements, uncertainty, and granular computing.

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Additional resources for Rough Sets and Knowledge Technology: 9th International Conference, RSKT 2014, Shanghai, China, October 24-26, 2014, Proceedings

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8 X. Zhang and D. Chen Table 2. 6, we get all the dominating classes [x]R (x ∈ U ) C and dominated classes [x]R (x ∈ U ) with respect to condition attribute set C C as Table 2. 2, for any xi ∈ U (i = 1, 2, · · · , 10), C(xi ) = ⊕5k=1 f (xi , ck ) denotes the comprehensive evaluation value of xi with respect to all condition attributes ck , k = 1, 2, 3, 4, 5, where f (xi , ck ) = ck (xi ) = (μck (xi ), νck (xi )). 000). 99892. Then, we rank all the objects xi by using s(C(xi ))(i = 1, 2, · · · , 10): x9 = x10 x5 x8 x7 x1 x6 x3 x2 x4 .

1 and suppose to have a further base set B4 = {P13 , P14 , P15 }. So, we have that nl (S) = ∅, n(S) = {P14 , P15 } and np (S) = B4 . Moreover, we can define a new upper approximation as un (S) = ∪{B ∈ B|B ∩ S = ∅} \ np (S) (12) and a new boundary: bn (S) = un (S) \ l(S) (13) and we have un (S) ⊆ u(S) and bn (S) ⊆ b(S) and both un , bn are monotonic. Now, by means of the lower approximation and the two upper approximations we can define four different notions of exact sets: – – – – E1 E2 E3 E4 = {S = {S = {S = {S : l(S) = u(S)} : l(S) = S = u(S)} : l(S) = un (S)} : l(S) = S = un (S)} We have that both E1 and E2 conditions imply that bn (S) = b(S) = bp (S) = ∅.

B ⊆ DB ⊆ P(U ) and ∅ ∈ DB (the definable sets) We will denote the union of all the definable sets as D = ∪D∈DB D. 3. EB ⊆ P(U ) and ∅ ∈ EB (the exact sets) 4. l, b, u, n : P(U ) → DB are, respectively, the lower, boundary, upper and negative mappings. 1. The substructure (U, B, DB , l, u) with corresponding properties is a Generalized Approximation Space as defined in [8]. The substructure (P(U ), l, u) is a Boolean Approximation Algebra as defined in [3]. As a trivial consequence of the above definition, we have that l(∅) = ∅.

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