fuzzy operator

Collaboration diagram for fuzzy operator:

Functions
a_real	a_fuzzy_not (a_real x)
	complementary operator
a_real	a_fuzzy_cap (a_real a, a_real b)
	fuzzy intersection operator
a_real	a_fuzzy_cap_algebra (a_real a, a_real b)
	algebraic product operator
a_real	a_fuzzy_cap_bounded (a_real a, a_real b)
	bounded product operator
a_real	a_fuzzy_cup (a_real a, a_real b)
	fuzzy union operator
a_real	a_fuzzy_cup_algebra (a_real a, a_real b)
	algebraic sum operator
a_real	a_fuzzy_cup_bounded (a_real a, a_real b)
	bounded sum operator
a_real	a_fuzzy_equ (a_real a, a_real b)
	equilibrium operator
a_real	a_fuzzy_equ_ (a_real gamma, a_real a, a_real b)
	equilibrium operator

Detailed Description

Function Documentation

a_fuzzy_cap()

a_real a_fuzzy_cap	(	a_real	a,
		a_real	b )

fuzzy intersection operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( \min(a,b) \)

a_fuzzy_cap_algebra()

a_real a_fuzzy_cap_algebra	(	a_real	a,
		a_real	b )

algebraic product operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( ab \)

a_fuzzy_cap_bounded()

a_real a_fuzzy_cap_bounded	(	a_real	a,
		a_real	b )

bounded product operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( \max(a+b-1,0) \)

a_fuzzy_cup()

a_real a_fuzzy_cup	(	a_real	a,
		a_real	b )

fuzzy union operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( \max(a,b) \)

a_fuzzy_cup_algebra()

a_real a_fuzzy_cup_algebra	(	a_real	a,
		a_real	b )

algebraic sum operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( a+b-ab \)

a_fuzzy_cup_bounded()

a_real a_fuzzy_cup_bounded	(	a_real	a,
		a_real	b )

bounded sum operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( \min(a+b,1) \)

a_fuzzy_equ()

a_real a_fuzzy_equ	(	a_real	a,
		a_real	b )

equilibrium operator

Parameters

[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( \sqrt{ab}\sqrt{1-(1-a)(1-b)} \)

a_fuzzy_equ_()

a_real a_fuzzy_equ_	(	a_real	gamma,
		a_real	a,
		a_real	b )

equilibrium operator

Parameters

[in]	gamma	gamma operator
[in]	a	left-hand operand
[in]	b	right-hand operand

Returns

= \( (ab)^{1-\gamma}(1-(1-a)(1-b))^{\gamma} \)

a_fuzzy_not()

a_real a_fuzzy_not

(

a_real

x

)

complementary operator

Parameters

[in]

x

membership

Returns

= \( 1-x \)