Module Tofn

module Tofn: sig .. end

Typed ordered fuzzy numbers (OFNs) and associated operations, following "Rings of Typed Ordered Fuzzy Numbers."

exception OFN_type_mismatch

Incompatible OFN type families.

exception Improper_OFN

An OFN is improper when it has no membership function.

type family =

`\|`	`Trapezoidal`
`\|`	`Gaussian`
`\|`	`Exponential`

Supported families are trapezoidal, Gaussian, and exponential.

type tofn = {

	`ofn_type : family;`
	`au : float;`
	`bu : float;`
	`ad : float;`
	`bd : float;`

}

OFN with type family and essential tuple (a_u, b_u, a_d, b_d). Components of the tuple are represented as individual fields (as opposed to an element of float * float * float * float) for ease-of-access.

val sametype : tofn -> tofn -> bool

Determine if two given OFNs are of the same type.

val tuplemap : (float -> float -> float) -> tofn -> tofn -> tofn

Apply a binary operator to the essential tuples of two OFNs.

val tuplemap_safe : (float -> float -> float) -> tofn -> tofn -> tofn

Apply a binary operator to the essential tuples of two OFNs only when the types match. Raises OFN_type_mistmatch if arguments are not of the same type.

val base_function : family -> float -> float

Base functions for each family.

val inv : family -> float -> float

Inverses of base functions

val (|+|) : tofn -> tofn -> tofn

OFN addition.

val (|-|) : tofn -> tofn -> tofn

OFN subtraction.

val (|*|) : tofn -> tofn -> tofn

OFN multiplication.

val (|/|) : tofn -> tofn -> tofn

OFN division

val is_increasing : tofn -> bool

Determine if an OFN is increasing.

val is_decreasing : tofn -> bool

Determine if an OFN is decreasing.

val is_proper : tofn -> bool

Detect if an OFN has a type I or type II pathology (see Section 1.4 of the paper. Type III pathologies are automatically fixed by membership. *

val membership : tofn -> float -> float

The membership function associated to an OFN. Raises Improper_OFN if the OFN is improper. Automatically fixes type III pathologies.