TAXES BASED ON INCOME (Details 4) - USD ($) $ in Millions	12 Months Ended
	Jan. 02, 2016	Jan. 03, 2015	Dec. 28, 2013
Taxes Based on Income
Effective tax rate (as a percent)	32.90%	31.50%	34.00%
Discrete tax benefits impacting the effective tax rate related to retroactive reinstatement of the federal research and development tax credit			$ 11.0
Tax expense (benefit) on changes in certain tax reserves and valuation allowances			24.9
Tax expense (benefit) on changes in certain tax reserves, including interest and penalties, resulting from settlements of audits	$ (5.8)	$ (10.2)
Tax expense (benefit) on changes in certain tax reserves, including interest and penalties, resulting from lapses and statute expirations	(8.2)	(18.1)
Tax benefit from the extension of the federal research and development credit	2.6
Tax expense associated with the tax cost to repatriate non-permanently reinvested 2015 earnings of certain foreign subsidiaries	20.0
Repatriation tax benefit related to certain foreign losses		(9.8)
Tax expense from the taxable inclusion of a net foreign currency gain related to revaluation of certain intercompany loans		9.1
Tax expense related to change in estimate of the potential outcome of uncertain tax issues in China and Germany		10.6
State tax expense primarily related to gains arising as a result of certain foreign reorganizations		$ 2.5
Expense for accrual of U.S. taxes on certain foreign earnings expected to be repatriated during 2013			12.1
Undistributed earnings of foreign subsidiaries considered indefinitely reinvested in foreign operations	$ 1,900.0
Benefits from favorable tax rates associated with certain earnings from the entity's operations in lower-tax jurisdictions throughout the world			$ 11.2