Engineering optimization 2014 by Aurelio Araujo PDF

By Aurelio Araujo

ISBN-10: 1138027251

ISBN-13: 9781138027251

ISBN-10: 1315732106

ISBN-13: 9781315732107

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We define the similarity measure the similarity measure between A and B as follows: l xi Definition 3: Let φhAB (i) = 2l1x s=1 |hAσ(s) (i) − hBσ(s) (i)| and φgAB (i) = 2k1x i Then we define kxi s=1 i |gAσ(s) (i) − gBσ(s) (i)|. 4 In this section first we formulate the mathematical model of dual hesitant fuzzy assignment problem with restrictions (DHFAPR) than we give the procedure to find the optimal solution of DHFAPR. Here, 0 < p < ∞, lxi = max{l(hA ), l(hB )}, kxi = max {k(hA ), k(hB )} for each xi ∈ X , where l(hA ) and l(hB ) represents the number of values in hA (xi ) and hB (xi ), respectively, and, k(hA ) and k(hB ) represents the number of values in gA (xi ) and gB (xi ), respectively.

This is due to non-dominated solutions, found by the MODPSO algorithms, which are still significantly far from the reference Pareto front. Figures 2, 3, and 4 show the relative variance of GD, IGD and GMF, retained by each of the MODPSO parameters (coefficient set, swarm size, initialization), for Pp Pg , AOFp Pg and VEPSO respectively. All parameters affect significantly the algorithms’ performance, and therefore deserve a careful investigation. The best performance overall is given by Pp Pg with the coefficient set from Clerc (2006), a swarm size equal to 32Ndv Nof and initialization of particles over the whole domain with null velocity.

In 2012, Zhu et al. proposed a dual hesitant fuzzy sets (DHFSs) as a extension of HFSs, which encompass fuzzy sets, intuitionistic fuzzy sets, hesitant fuzzy sets, and fuzzy multisets (Yager 1987) as special cases, and investigated the basic operations and properties of DHFSs. DHFSs consist of two parts, one is the membership hesitancy function and other is the nonmembership hesitancy function. The existing sets, including fuzzy sets, intuitionistic fuzzy set, HFSs, and fuzzy multi sets, can be regarded as special cases of DHFSs.

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Engineering optimization 2014 by Aurelio Araujo

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