Fuzzy logic from the point of machine intelligence
National Taiwan University of Science and Technology
Advisor: Dr. Hahn-Ming ,Lee
Student: YI-WEN,LIEN
Number: M9409115
e-mail: M9409115@mail.ntust.edu.tw
Abstract
This paper presents the opinions on fuzzy logic from the viewpoint of
machine intelligence. First, it analyzes characteristics of fuzzy logic that are
adapted to the study of machine intelligence. Second, it presents its
opinions on machine intelligence. Final, it introduces its work on uncertain
and automated reasoning in the framework and discusses some future goals.
1. Introduction
Since Zadeh proposed the concept of "fuzzy set" in 1965, a great
number of papers and approaches on fuzzy set theory and fuzzy logic have
been published during the past 40 years. The theories and approaches based
on fuzzy sets and fuzzy logic are developed in different research fields and
approval, opposition, suspicion research in fuzzy sets and fuzzy logic are
reported. Finally, the big debate in 1994 clarified some disagreement among
research and developed the applications in fuzzy sets and fuzzy logic. As a
result, this discussion make the researchers more understand the essence of
fuzzy sets and fuzzy logic and prompt the research on them. This
paper presents the opinion on fuzzy logic from the viewpoint of machine
intelligence.
The reminder of the paper is organized as follows. In section 2, this
paper analyzes the characteristics of fuzzy logic that are suitable for
machine intelligence. In section 3, this paper presents its opinion on
machine intelligence. In section 4, this paper introduces the work of authors
on machine intelligence and suggests future work.
2. Fuzzy logic and machine intelligence
Logic is the laws of the thought that decides the operation of our mind
and all kinds of logic are created by people to model the actions and
interactions among objects in the real world. Among them, fuzzy logic has a
degree of truth ranging from 0 to 1 which provide an appropriate way to
describe the real world.
Because human thinking is filled with uncertainty, human thinking is
supplemented and modified. In order to model human thinking, artificial
intelligence is proposed. Artificial intelligence is the study of giving machines
ability to think in human way and act as people and the goal of machine
intelligence is to give machines the ability to learn knowledge, to resolve
complex knowledge, and so on. To achieve this aim, we should realize that
learning and applying knowledge is a characteristics of human intelligence.
Hence, the intelligent machine should have the ability to extract, classify,
understand, and represent all kinds of knowledge. For instance, we say "a
table is 1.2 m long". The fact can be represented in fuzzy logic is in degree
0.95. While in classical logic, the fact is described as "a table is exactly 1.2
m." Compare classical logic with fuzzy logic, fuzzy logic is closer to
human experience.
People can quickly adapt to a new environment, because he can select suitable
knowledge and modify inference to fit the current situation. But for machine
intelligence, it is not easy to do. Due to the fact that human knowledge is
incomplete and imprecise, fuzzy logic is better way to represent knowledge and
rules.
3. Our opinion on machine intelligence
This section describe the opinions of authors on machine intelligence. Authors
think that machine intelligence should focus on uncertainty and find ways to
deal with uncertainty.
3.1 Study of machine intelligence needs to deal with
incomparability
Besides the familiar fuzziness, we should think about "incomparability."
For instance, a company wants to choose one candidate from three
candidates to a position according to three factors, i.e., leadership,
professional ability, and social communicational ability. Suppose that
candidate A has long experience in managing, candidate B is familiar with
professional ability, and candidate C is a good mixer. It is obvious that there
is no criterion for leadership, professional ability, and social
communicational ability. So it is impossible to compare A, B, and C. As a
result, the more complicated an object is, the more factors it involves in.
3.2 Study of machine intelligence requires uncertain
reasoning with evaluating linguistic expressions
There exists various kinds of uncertainty in the real world and people have to
deal with a lot of uncertainty frequently. Therefore, we can find that uncertainty
is associated with two remarkable features:1. using natural language to describe
uncertainty, and 2. employing uncertain reasoning to form judgment and to make
decision. So, machine intelligence should shift its target to simulate human
intelligence by uncertain reasoning with words.
3.3 Study of uncertain reasoning in the framework of logic is
one of scientific methodologies
Inference from certain information has high confidence due to the strictness
and completeness of class logic and implementation of certain reasoning in
computers require precise models, algorithms, and deduction present in class
logic. Also, uncertain information require uncertain reasoning which is based on
non-classical logical. Of course, implementation of uncertain reasoning in
computers require precise models, algorithms, and deduction present in
non-class logic.
3.4 Study of machine intelligence also demands investigation
of automated reasoning with words
The course of human resolution can be treat as proofs of "soft-theorems", for
instance, conclusion with uncertainty. So research of machine intelligence
should study theories and approaches of automated reasoning to present
uncertainty.
4. Our works and goals on machine intelligence
In this section, this paper give a brief introduction of our work and future
goals. To illustrate the incomparability, this paper establish LIA to illustrate.
The definition of ILA is given in Definition 1.
Definition 1 (Lattice implication algebra (Xu [37])). Let (L,∨,∧,
,O, I) be
a bounded lattice with universal boundaries O(the least element) and I (the
greatest element) respectively, and “ ” an order-reversing involution. If
a mapping →: L × L −→ L satisfies for any x, y, z ∈ L,
(I1) x → (y → z) = y → (x → z),
(I2) x → x = I,
(I3) x → y = y
→ x,
(I4) if x → y = y → x = I , then x = y,
(I5) (x → y) → y = (y → x) → x,
(I6) (x ∨ y) → z = (x → z) ∧ (y → z),
(I7) (x ∧ y) → z = (x → z) ∨ (y → z),
then (L,∨,∧, ,→,O, I) is called a LIA.
In order to deal with uncertainty reasoning, this paper has proposed the
lattice-valued propositional logic LP(X) and its corresponding first-order
logic LF(X), and the gradational lattice-valued propositional logic Lvpl and
its corresponding first-order logic Lvfl. These are based on LIA, and studied
especially in correspondence with the topic of uncertain reasoning and
automated reasoning.
In the lattice-value logic, the syntactical system represents support for
interpretation and illustration of reasoning, and the semantic system
describes the transfer of degrees of truth of statements. Moreover, by
embedding widely used linguistic terms to the elements of LIA, we have
constructed a linguistic LIA and applied the lattice-valued logic to real
evaluating problems.
In the future, we want further to develop a concrete system of uncertain
and automated reasoning with words. The concrete goals include:
(1) To establish LIA with words (L-LIA).
(2) To select valuations from the lattice-valued propositional logic Lvpl
which are consistent with the implication in L-LIA and establish approaches
of uncertain and automated reasoning with words so that they preserve the
hierarchy reliability and completeness of Lvpl.
(3) To select interpretations of the lattice-valued first-order logic Lvfl that
are consistent with the implication in L-LIA, and to establish approaches of
uncertain and automated reasoning with words so that they preserve the
hierarchy reliability and completeness of Lvfl.
5. Conclusion
In this paper, the authors have analyzed characteristics of fuzzy logic from the
viewpoint of artificial intelligence and introduced its opinion on it. Also, the
authors introduced their work on machine intelligence and discuss future goal.
The authors think that artificial intelligence needs multidisciplinary studies
because there is not only one theory suitable for all problems.
In my opinion, this paper introduces the relation between fuzzy logic and
artificial intelligence and their work about uncertain reasoning. The authors
focus on uncertain reasoning and developed a model for uncertain reasoning. In
the future, they will add more functions on this model.