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On Some Properties and Comparative Analysis for Different OWA Monoids
Author(s) -
Jin LeSheng,
Kalina Martin,
Mesiar Radko,
Qian Gang
Publication year - 2017
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.21885
Subject(s) - monoid , multiplication (music) , lattice (music) , monotonic function , mathematics , syntactic monoid , free monoid , algebra over a field , arithmetic , computer science , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , physics , acoustics
We study the properties of OWA multiplication monoid. By introducing and‐accumulation vectors of OWA operators, we consider the set of all n ‐dimensional OWA operators as a lattice. Then, we analyze some monotonicity properties of OWA operators based on an ordering induced by and‐accumulation vectors. We also show that the lattice‐theoretical operations are a kind of counterpart of the OWA multiplication monoid (and its dual, additive monoid). An example of using the OWA multiplication monoid and the lattice‐theoretical structure in decision making problem is provided.