Mysql – Does it make sense to define a new “Data type”? Is there a way to do so

Why must the employees working on a project strictly belong to the same division that owns the project? That sounds more like a business rule that you can leave up to your application to enforce rather than something that requires DRI.

But let's say you need to enforce this using DRI. You said you have a many-to-many table associating employees with projects. Assuming you are using SQL Server, you could expand this table as follows:

CREATE TABLE dbo.Employee_Project (
     ProjectID            INT
   , ProjectDivisionID    INT

   , EmployeeID           INT
   , EmployeeDivisionID   INT

   , Hours                INT

   , CONSTRAINT FK_Project FOREIGN KEY (ProjectID, ProjectDivisionID) 
        REFRENCES dbo.Project(ProjectID, DivisionID)

   , CONSTRAINT FK_Employee FOREIGN KEY (EmployeeID, EmployeeDivisionID) 
        REFERENCES dbo.Employee(EmployeeID, DivisionID)

   , CONSTRAINT CK_EmployeeProjectSameDivision CHECK (ProjectDivisionID = EmployeeDivisionID)
);

This is what's going on here:

• We have two composite foreign keys here, one for Employee and one for Project, so we can have the DivisionID for both entities in the same table and guaranteed by DRI to be correct.
• These composite foreign keys require a UNIQUE index on the referenced tables. So in addition to your primary keys on EmployeeID and ProjectID in those tables, you'll need unique keys on (EmployeeID, DivisionID) and (ProjectID, DivisionID).
• The CHECK constraint guarantees that an employee can only be assigned to a project owned by the same division.

If you want to see another example of this design pattern, here's the answer I gave to a design problem that had similar requirements.

I personally would use a model similar to the following:

The product table would be pretty basic, your main product details:

create table product
(
  part_number int, (PK)
  name varchar(10),
  price int
);
insert into product values
(1, 'product1', 50),
(2, 'product2', 95.99);

Second the attribute table to store the each of the different attributes.

create table attribute
(
  attributeid int, (PK)
  attribute_name varchar(10),
  attribute_value varchar(50)
);
insert into attribute values
(1, 'color', 'red'),
(2, 'color', 'blue'),
(3, 'material', 'chrome'),
(4, 'material', 'plastic'),
(5, 'color', 'yellow'),
(6, 'size', 'x-large');

Finally create the product_attribute table as the JOIN table between each product and its attributes associated with it.

create table product_attribute
(
  part_number int, (FK)
  attributeid int  (FK) 
);
insert into product_attribute values
(1,  1),
(1,  3),
(2,  6),
(2,  2),
(2,  6);

Depending on how you want to use the data you are looking at two joins:

select *
from product p
left join product_attribute t
  on p.part_number = t.part_number
left join attribute a
  on t.attributeid = a.attributeid;

See SQL Fiddle with Demo. This returns data in the format:

PART_NUMBER | NAME       | PRICE | ATTRIBUTEID | ATTRIBUTE_NAME | ATTRIBUTE_VALUE
___________________________________________________________________________
1           | product1   | 50    | 1           | color          | red
1           | product1   | 50    | 3           | material       | chrome
2           | product2   | 96    | 6           | size           | x-large
2           | product2   | 96    | 2           | color          | blue
2           | product2   | 96    | 6           | size           | x-large

But if you want to return the data in a PIVOT format where you have one row with all of the attributes as columns, you can use CASE statements with an aggregate:

SELECT p.part_number,
  p.name,
  p.price,
  MAX(IF(a.ATTRIBUTE_NAME = 'color', a.ATTRIBUTE_VALUE, null)) as color,
  MAX(IF(a.ATTRIBUTE_NAME = 'material', a.ATTRIBUTE_VALUE, null)) as material,
  MAX(IF(a.ATTRIBUTE_NAME = 'size', a.ATTRIBUTE_VALUE, null)) as size
from product p
left join product_attribute t
  on p.part_number = t.part_number
left join attribute a
  on t.attributeid = a.attributeid
group by p.part_number, p.name, p.price;

See SQL Fiddle with Demo. Data is returned in the format:

PART_NUMBER | NAME       | PRICE | COLOR | MATERIAL | SIZE
_________________________________________________________________
1           | product1   | 50    | red   | chrome   | null
2           | product2   | 96    | blue  | null     | x-large

As you case see the data might be in a better format for you, but if you have an unknown number of attributes, it will easily become untenable due to hard-coding attribute names, so in MySQL you can use prepared statements to create dynamic pivots. Your code would be as follows (See SQL Fiddle With Demo):

SET @sql = NULL;
SELECT
  GROUP_CONCAT(DISTINCT
    CONCAT(
      'MAX(IF(a.attribute_name = ''',
      attribute_name,
      ''', a.attribute_value, NULL)) AS ',
      attribute_name
    )
  ) INTO @sql
FROM attribute;

SET @sql = CONCAT('SELECT p.part_number
                    , p.name
                    , ', @sql, ' 
                   from product p
                   left join product_attribute t
                     on p.part_number = t.part_number
                   left join attribute a
                     on t.attributeid = a.attributeid
                   GROUP BY p.part_number
                    , p.name');

PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

This generates the same result as the second version with no need to hard-code anything. While there are many ways to model this I think this database design is the most flexible.