Direct Sum of Intuitionistic Fuzzy Submodules of G-module
Keywords:
Intuitionistic fuzzy submodules, G-modules, direct sumAbstract
In this paper, we introduce the notion of direct sum ofintuitionistic fuzzy submodules of G-module M and discuss some relatedproperties. If B and C are intuitionistic fuzzy submodules of G-module Mand G-module N respectively, then we extend the denition of intuitionisticfuzzy submodules B and C to formulate intuitionistic fuzzy submodules ofthe direct sum M N: It is proved that the support of the direct sumof intuitionistic fuzzy submodules B and C is equal to the direct sumof supports of intuitionistic fuzzy submodules B and C: Also we analyzethe direct sum of arbitrary family of intuitionistic fuzzy submodules andobtained some results. We also introduce the notion of decomposability andindecomposility of intuitionistic fuzzy G-modules and prove some results.References
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