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where Î§ is the universe, Âµ A ( x ) represents the membership function and Âµ: Î§ â [ 0,1] . For example, one could define a membership function for the set of numbers much less than 100 as follows: Âµ <<100 ( x ) = 1 x2 1+ 100 Typically, the following definitions of fundamental logical operations (intersection, union and complement) on sets are used: Âµ Aâ© B Âµ ( x ) = min( Âµ ( x ), Âµ ( x )) A B (2) ( x ) = max( Âµ ( x ), Âµ ( x )) A B (3) Âµ ( x) = 1 â Âµ (x) A A (4) Aâª B The above operators satisfy certain desired properties. For example, if set containment is defined as A â B if âx â X Âµ A ( x ) â¤ Âµ B ( x ), then the following always holds A â A âª B and A â© B â A . Depending on the application, other operators from within the triangular norm and co-norm classes may be more appropriate than the above minimum and maximum functions [16]. For example, the framework of Dombi [17] is used in this work. Specifically: Âµ Aâ© B 1 ( x) = 1 1 + (( with Î» â¥ 1. (5) 1 1 â 1) Î» + ( â 1)Î» ) Î» Âµ (x) Âµ ( x) A B Increasing the parameter Î» will increase the emphasis on the smaller membership value. One can define the union operation by allowing Î» â¤ -1. Notice as Î» â â , (5) approaches either (2) or (3) and in practice, values of Î» larger than two or three renders this form essentially equivalent to minimum and maximum 8