Xref: utzoo comp.ai:3208 talk.philosophy.misc:1900 sci.lang:4027 Path: utzoo!utgpu!attcan!uunet!lll-winken!ames!mailrus!cornell!uw-beaver!ssc-vax!bcsaic!rwojcik From: rwojcik@bcsaic.UUCP (Rick Wojcik) Newsgroups: comp.ai,talk.philosophy.misc,sci.lang Subject: Re: Categorization Keywords: Crisp Sets and Fuzzy Sets Message-ID: <9750@bcsaic.UUCP> Date: 25 Jan 89 17:07:28 GMT References: <681@cogsci.ucsd.EDU> <2959@uhccux.uhcc.hawaii.edu> <2899@xyzzy.UUCP> <43780@linus.UUCP> Reply-To: rwojcik@bcsaic.UUCP (Rick Wojcik) Organization: Boeing Computer Services AI Center, Seattle Lines: 38 In article <43780@linus.UUCP> bwk@mbunix.mitre.org (Barry Kort) writes: >This discussion reminds me of the notion of Fuzzy Sets, as >introduced by Berkeley's Lofti Zadeh some twenty years ago. >By way of contrast, Stanford's Tom Cover coined the phrase >Crisp Sets to emphasize Stevan's concept of reliable all-or-none >categorization. The discussion ought to remind you of Zadeh. The discussion started as a reaction to Lakoff's work, which has very strong historical ties to Zadeh. (Read Lakoff's book. Stevan doesn't want to take the time, but it is worth the effort.) Linguists have long been aware of the problems with all-or-none categorization. What Stevan does is he simply defines the word 'categorization' to suit his all-or-none criterion, without any regard for the way in which humans actually assign categories. But consider the classic examples of 'semantic vagueness'. We have the mental illusion that mountains and waves are discrete objects. Questions like 'How many mountains are there in the Cascades?' or 'How many waves are there in the ocean?' are semantically well-formed, but impossible to answer from a conceptual point of view. There are no natural discrete boundaries to these categories, such that you can always tell where one mountain or wave leaves off and another begins. It is also relevant to the discussion to consider how we categorize objects in the earliest stages of language. The child's earliest uses involve complexive organization, overextensions, and underextensions (the last being very difficult to detect). 'Complexive' organization, a term coined by Melissa Bowerman, seems to involve some kind of shifting categorization. A child might use the word 'doggie' on different occasions to refer to four-legged things, furry things (e.g. a blanket), things that move, etc. It is quite easy to relate such gross 'miscategorizations' to the many legitimate examples of complex adult categoriztion cited in Lakoff's book. Such behavior is very reminiscent of what Lakoff calls 'radially structured' categories. Overextensions and underextensions seem to involve a fine-tuning of categorization that looks more like the so-called 'classical' type. -- Rick Wojcik csnet: rwojcik@atc.boeing.com uucp: uw-beaver!ssc-vax!bcsaic!rwojcik