Boolean, bibliometrics,
and beyond
Part 1
LIS 670
donna Bair-Mundy
Our roadmap
Boolean
Boolean exercises
Fuzzy sets
Bibliometrics
Boolean
Boolean algebra
• Developed by George Boole, an
English mathematician, circa
1850
• Set theory
• Boolean logic is binary
• Widely used in electronic design
• Widely used in information
retrieval systems
Two ways of defining a set
Enumeration (listing the
elements)
A = {1, 2, 3, 4, 5}
Specification of a distinguishing
property all elements of the set
have in common
B = {x | x is a prime number}
Set operators (1)
Given sets A = {1, 2, 3, 4, 5}
B = {1, 3, 5, 7}
C = {6, 7, 8}
Union - produces a set containing all
members of both operand
sets
A  C = {1, 2, 3, 4, 5, 6, 7, 8}
Set
Set
Resultant Set
Set operators (2)
Given sets A = {1, 2, 3, 4, 5}
B = {1, 3, 5, 7}
C = {6, 7, 8}
Intersection - produces a set
containing members in
the first set that also
occur in the second set
A  B = {1, 3, 5}
Set operators (3)
Given set A = {1, 2, 3, 4, 5}
Complement - produces a set containing
all members of the
universal set that are not a
member of the operand set
If D is the universal set of all positive
integers, then:
A = {6, 7, 8, …}
Boolean operators
Words and symbols to denote set operators.
Boolean
Set
Theory
OR
Union

+
AND
Intersection

*
-
-
NOT
Complement
Algebraic
Symbol symbol
Algebraic operations on sets
Given sets
A = {1, 2, 3, 4, 5}
B = {1, 3, 5, 7}
C = {6, 7, 8}
A * (B + C) = A * B + A * C
A AND (B OR C) = (A AND B) OR (A AND C)
{1,2,3,4,5} AND {1,3,5,6,7,8}
1, 3, 5
= {1,3,5} OR {null}
= 1, 3, 5
Venn diagrams
John Venn
Charles
Dodgson
Set 1
Set 3
Set 2
Venn diagram - OR
Poodles Retrievers
Poodles OR Retrievers
yields all documents about either
poodles or retrievers
Venn diagram - AND
Poodles Retrievers
Poodles AND Retrievers
yields all documents that deal with both
poodles and retrievers
Venn diagram - NOT
Poodles Retrievers
Poodles NOT Retrievers
yields documents about poodles but not
about retrievers
Venn diagram - Exclusive OR
Poodles Retrievers
Poodles XOR Retrievers
yields all documents that deal with either
poodles or retrievers but not both
Rules of precedence
Complementation
(NOT)
Intersection
(AND)
Cats
Dogs
Union
(OR)
dogs OR cats AND fleas
will be read as
dogs OR (cats AND fleas)
Fleas
Specifying order of
performance
(dogs OR cats) AND fleas
Dogs
Cats
Fleas
Boolean searching:
advantages
Ideally suited for inverted file
Cats and
1,3,7,9,13
indexes - each index entry
Dogs
2,5,6,15
set of pointers constitutes
Fleas a 6,7,9,17
Gnus
19,27
set
Guppies 4,14,18
Hamsters 22,25,31
Allows user to broaden (using
OR) or narrow (using AND,
NOT) searches
Boolean Exercises
The Scenario – part I
You are the librarian at the
Happy Tastebuds Vegetarian
School of Culinary Arts.
Chef Kweezee is planning
the menus for this week’s
demonstrations. He comes to
the reference desk and asks
you to search the recipe
database for him.
The Scenario – part II
The search command for
this database is FIND followed
by key words. The system
accommodates Boolean
operators and allows
parentheses. It does not
accommodate phrase searching.
The Scenario – part III
To impress the chef, who
stays to watch you search, you
formulate a single search
statement for each menu.
Sample Boolean exercise
Sample record
Cuisine:
Title:
Ingredients:
Mexican
Enchilada
Corn tortillas, tomato sauce,
chili peppers, beans, onions,
garlic, cilantro…
Menu
Mexican Cuisine
Enchilada
Refried beans
Search statement
FIND mexican AND (enchilada OR (refried and beans))
FIND mexican AND (enchilada OR (refried AND beans))
refried
enchiladamexican
beans
Exercise 1
Menu
Mexican Cuisine
Mexican casserole
Tostada
FIND ( Casserole OR Tostada ) AND Mexican
Exercise 1 Venn Diagram
Menu
Mexican Cuisine
Mexican casserole
Tostada
FIND ( Casserole OR Tostada ) AND Mexican
Casserole
Mexican
Tostada
Exercise 2
Menu
Italian Cuisine
Pasta with grilled artichoke hearts
Baked garlic
FIND
Exercise 3
Menu
Greek Cuisine
Vegetarian moussaka
Greek salad featuring kalamata
olives
FIND
Exercise 4
Menu
Chinese Cuisine
Hot and sour soup
Fried eggplant
Tofu and broccoli dish
FIND
Exercise 5
Menu
Indian Cuisine
Eggplant curry
Samosa
Raita
Tamarind sauce
FIND
Boolean searching:
disadvantages (1)
• Counterintuitive
– AND retrieves fewer items
• Two-valued logic - items
meet criteria or they do not
– Good for computers
– Does not reflect user relevancy
determinations
Boolean searching:
disadvantages (2)
Research topic: Digital music libraries
Documents
Current research on digital music
libraries
Introduction to digital libraries
Information architecture in the digital
environment
Libraries of ancient Babylonia
Fuzzy sets
Binary versus fuzzy sets
Ri = any record
Q = user query
Test each record
against query
Yes or no:
retrieved
or not
Binary set S(Ri x Q)  0,1
Retrieval set for query Q is all records Ri such
that S(Ri x Q) = 1
Brackets
Fuzzy set S(Ri x Q)  [0,1]
indicate
range
S expresses not whether or not R is in the set
but the degree of strength of the association
of R with the set.
Fuzzy set
highly
relevant
1
nonrelevant
0
FIND Agni Vedic fire ritual
highly
relevant
1
Analysis of the
Agni Vedic fire
ritual
(1)
Structural
analysis of a
Vedic fire ritual
(0.75)
nonrelevant
0
Characteristics
of Agni
(0.25
Analysis of a fire
ritual of India
(0.5)
Implementing fuzzy sets (1)
User enters list of words
FIRE, RITUAL, SACRIFICE
Retrieval system examines each record
or document in the database
Computes score by number of query
words that appear in the document
System presents ordered list of
documents, along with their scores
Implementing fuzzy sets (2)
FIRE, RITUAL, SACRIFICE
Rank
100%
66%
33%
Title
The fire sacrifice ritual of early
Vedic period India
Fire and sacrifice in proto-IndoEuropean society
How to build a fire the Girl
Scout way
Implementing fuzzy sets (3)
User enters list of words
FIRE, RITUAL, SACRIFICE
Retrieval system examines each
document or record in the database,
computing score for that item by adding
1 for each time any of the words on the
user's list appears in the document or
record
System presents ordered list of
documents, along with their scores
Implementing fuzzy sets (4)
FIRE, RITUAL, SACRIFICE
Rank



Document
The fire sacrifice ritual of early
Vedic period India. The fire
sacrifice ritual is one of many
sacrifice rituals observed as being
performed…
Fire and sacrifice in proto-IndoEuropean society. Discussion of
the role of fire…
How to build a fire the Girl Scout
way. Demonstrates fire building…
Fuzzy sets in Voyager (1)
Agni, vedic
Fuzzy sets in Voyager (2)
Agni, vedic
Fuzzy sets in Voyager (3)
Agni, vedic
Fuzzy sets in Voyager (4)
Agni, vedic
Fuzzy sets in Voyager (5)
Agni, vedic
Field-weighting terms
Terms weighted by fields in which they occur
5
5
Title:
Descriptors:
Euphoria; Tiddlywinks
Abstract:
The authors studied the brain
waves of 175 tiddlywinks
winners and found euphoria
induced by winning lasted an
average of 3 hours.
Text:
Researchers have long held
that tiddlywinks, unlike other
sports, do not induce a
significant affective…
2
1
Winning-induced euphoria in
tiddlywinks players
User-weighting terms
Terms weighted at time of search by user
*
Weighted
term