[racket] fuzzy set representation in Racket

Why don't you simply use a hash-table?  (mutable or immutable
according to your need).



On Fri, Aug 23, 2013 at 9:49 PM, Rian Shams <rian.shams at gmail.com> wrote:
> Hello All,
>
> My name is Rian and I am a new Racket user and a novice programmer (Racket
> is my first language). First let me say that I am very grateful for the
> resources available online and the books, HTDP and Realm of Racket. I find
> your teaching methods very clear and as a result I am picking up Racket
> faster than I originally thought.
>
> I am a System Science graduate student whose primary research focus is on
> Fuzzy Set Theory. A fuzzy set is a collection of distinct elements where
> each element has a degree of membership associated with it.
>
> The representation I am currently using for a fuzzy set is the following:
> First I create a struct called fuzzy-element which consists of 2 fields; the
> first is the name of the element and the second is the elements degree of
> membership to the set which ranges from 0 to 1.
>
> ;; Data Definition
>
> #lang racket
>
> (struct fuzzy-element (member degree-of-membership)
>   #:transparent
>   #:guard (lambda (member degree-of-membership type-name)
>             (cond
>               [(not (and (number? degree-of-membership)
>                          (<= 0 degree-of-membership 1)
> degree-of-membership))
>                (error type-name
>                       "~e is not a number between 0 and 1"
>                       degree-of-membership)]
>               [else (values member degree-of-membership)])))
>
> ;; fuzzy-element is (fuzzy-element Symbol Number[0, 1])
> ;; interp. a fuzzy-element as a struct in which:
> ;;         -the first field is the member's name
> ;;         -the second field is the respective members degree of membership
>
> Then I combine them with a list so what I have now is a list of fuzzy
> elements.
>
> ;; ListOfFuzzyElement is one of:
> ;; - empty
> ;; - (cons fuzzy-element ListOfFuzzyElement)
>
> The problem with this data definition is that it allows for duplicate
> structs with the same field-1 elements.
>
> What I am looking to create is
>
> ;; A Fuzzy-Set is one of:
> ;; - empty list
> ;; - (cons distinct fuzzy-element ListOfFuzzyElement)
>
>
>
> Ideally the type of representation I would like to use should look like:
>
> (fuzzy-set (fuzzy-element 'a .1)
>                (fuzzy-element 'b .2)
>                (fuzzy-element 'c .3)
>                (fuzzy-element 'a .3))
>
> -> (fuzzy-set (fuzzy-element 'a .1)
>                    (fuzzy-element 'b .2)
>                    (fuzzy-element 'c .3))
>
> Upon evaluation, the last element, (fuzzy-element 'a .3) is deleted because
> there already exists a member named 'a (fuzzy-element 'a .1). It should work
> exactly like the built in "set" data type, except in this case it is a set
> of structures that checks the first fields of all structures and eliminates
> latter duplicates.
>
> Any guidance on how to create fuzzy-set representation this way or if you
> can suggest more concise and elegant methods I would be greatly
> appreciative.
>
> Thanks,
> --
> Rian Shams
>
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