Basic Trope: Character A does not consider character B to belong to group C, because of his/her actions or attributes.
Straight: Alice tells Bob, "All true Goths wear clunky combat boots. Everyone knows that." When Bob points out that their friend Ravenna prefers sleek stiletto boots, Alice says, "In that case, I guess she's not a real Goth."
Alice ends up defining "real" Goths so narrowly that the majority of Goths do not fit her definition.
Alice defines Ravenna as not being a Goth by something pointlessly silly, like wearing a very specific nail polish which is hard to get.
Alice's exclusion isn't inherently part of the definition (if it was, it wouldn't be the fallacy at all) but is still something most people really wouldn't associate with the group, e.g. "Goths don't wear pink lipstick."
Alice randomly flips between defining Ravenna as being a Goth, and as not being one.
Justified: Alice believes that Ravenna isn't a true Goth because of her boots.
Alice tells Bob, "No woman other than a Goth would dye her hair black. " When Bob points out that Susan dyes her hair black, Alice replies, "Well, then I guess she's a Goth too, even if she doesn't think so."
Alice considers Ravenna to be a Goth because she follows many of the habits of Goths, even though she never claims to be one.
Subverted: Alice says that Ravenna is not a true Goth, but only because of a list of clearly-defined attributes, which the others agree she doesn't meet.
Double Subverted: Many of Alice's attributes are constantly changed and made narrower and narrower as time goes on.
Zig Zagged: ???
Averted: No one makes a generalization about any group of people.
Enforced: "For this gag, we need Alice not to consider Ravenna a Goth. Let's have her go by a pre-determined definition."
Lampshaded: "Alice's definition of 'Goth' is all wrong. For one thing, it excludes Ravenna."
Invoked: Alice does not consider Ravenna a Goth, so she arbitrarily redefines the term. She then tells Bob her definition, knowing that he will list Ravenna as a counterexample.
Exploited: Carol acts like a Goth, but for some reason, she does not want Alice to consider her one. Knowing Alice's definition of Goths, she starts wearing stiletto boots.
Defied: "Well, okay, Ravenna's a Goth too, but most Goths aren't like that."
Discussed: "Is Ravenna a true Goth?" "What do you mean? She certainly looks and acts like one." "Yes, but does wearing stiletto boots disqualify her from being a Goth?" "No. Why would you think that?"
Conversed: "What the hell, Alice? Ravenna is so a Goth!"
Played For Laughs: Alice's made-up definitions are a Running Gag.