By Zeshui Xu
"Linguistic choice Making: idea and strategies" is the 1st monograph which commonly bargains with the interdisciplinary topic of computing with phrases, info fusion and selection research. It presents an intensive and systematic advent to the linguistic aggregation operators, linguistic choice family members, and numerous versions for and methods to multi-attribute choice making with linguistic details. It additionally deals a variety of useful examples with tables and figures to demonstrate the idea and techniques mentioned. Researchers and pros engaged within the correct fields will locate it an invaluable reference booklet.
Professor Zeshui Xu, senior member of the IEEE, works on the PLA college of technological know-how and Techology, China.
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Additional info for Linguistic Decision Making: Theory and Methods
To solve this issue, Xu (2006a) introduced a linguistic hybrid aggregation operator. 55) where sβj is the jth largest of the linguistic weighted arguments s¯αi (i = 1, 2, · · · , n) (¯ sαi = nwi sαi , i = 1, 2, · · · , n), w = (w1 , w2 , · · · , wn )T is the weight vector of n the linguistic arguments sαi (i = 1, 2, · · · , n), wi 0 (i = 1, 2, · · · , n), wi = 1, i=1 and n is the balancing coeﬃcient, which plays a role of balance (in such a case, if the vector (w1 , w2 , · · · , wn )T approaches (1/n, 1/n, · · · , 1/n)T , then the vector (nw1 sα1 , nw2 sα2 , · · · , nwn sαn )T approaches (sα1 , sα2 , · · · , sαn )).
79) where w = (w1 , w2 , · · · , wn )T is the weighting vector of s˜i (i = 1, 2, · · · , n), with n wi 0 (i = 1, 2, · · · , n) and wi = 1, then the function ULWA is called an uncertain i=1 linguistic weighted averaging (ULWA) operator. In particular, If w = (1/n, 1/n, · · · , 1/n)T , then the ULWA operator reduces to the ULA operator. 2)T be their weight vector. 25 (Xu, 2004a) Let ULOWA : S˜2n → S˜2 . 80) then the function ULOWA is called an uncertain linguistic ordered weighted averaging (ULOWA) operator, where s˜σj is the jth largest of the uncertain linguistic arguments s˜i (i = 1, 2, · · · , n), ω = (ω1 , ω2 , · · · , ωn )T is the weighting vector associated with the n ULOWA operator, ωi 0 (i = 1, 2, · · · , n) and ωi = 1.
Thus, 2 sα ⊕ sαj sα ⊕ sαj we get ui , i and uj , i . Similarly, if k items are tied, then we 2 2 replace these by k replica’s of their average. 15)T. We ﬁrst utilize the values of ui (i = 1, 2, 3, 4, 5) to rank the OWA pairs ui , sαi (i = 1, 2, 3, 4, 5). 20, s−3 respectively, then u1 = μ3 = μ5 . , (s2 ⊕ s4 ⊕ s−3 )/3 = s1 . 45 =s1 The IOWA operator, which essentially aggregates objects that are pairs, provides a very general family of aggregation operators. Particularly noteworthy is its ability to provide for aggregations in environments that mix linguistic and numeric variables.