### Introduction to Soft Computing University of Tsukuba

#### Course Overview

ソフトコンピューティングの諸技法は、人間の関与する場面の多い状況、特にリスク解析においてその威力を発揮する。また、ソフトコンピューティングの理論修得を通じて、従来のハードコンピューティングの諸技法に対する認識を深めることもできる。そこで、本講義では、ソフトコンピューティングのうちで特に重要と思われる、不確実性理論、様相論理、ファジィ理論、ベイズ推定、期待効用理論、プロスペクト理論、ファジィ理論を中心に論じる。抽象的な理論のみならず、現実問題への応用などにも言及する。

#### Learning Achievement

Soft computing techniques are very powerful in situations where humans are involved, especially in risk analysis. In addition, through the acquisition of soft computing theory, students can deepen their awareness of conventional hard computing techniques. Therefore, this lecture will focus on uncertainty theory, modal logic, fuzzy theory, Bayesian estimation, expected utility theory, and prospect theory, which are considered to be particularly important in soft computing. It refers not only to abstract theories, but also to their application to real-world problems.

1) Ability to understand the basic terms and their usage in propositional logic, modal logic, Bayesian inference, and expected utility hypothesis.

2) Ability to compute simple examples of the semantics of modal logic.

3) Understanding the basics of rough sets

4) Ability to explain the difference between objective and subjective probability with examples.

5) Ability to provide examples of the expected utility hypothesis and prospect theory in practice.

#### Competence

The lecture is related to "1. Ability to use knowledge" in Generic Competences, "1. Fundamentals of engineering", "2. Knowledge of basic theories and related skills", "1. Research ability" and "2. Specialized knowledge" in Specific Competences, and "3. Knowledge of issues in the real world", "4. Broad perspective overlooking circumstance" in Specific Competences in Risk & Resilience Engineering Master's/Doctoral Program, and ,Specific Competences.

#### Course prerequisites

None in particular.

#### Grading Philosophy

In the case of face-to-face classes, 25% of the total points must be earned from the exercises and 75% from the final exam, for a total of 60% of the credits.

In the case of online classes, a comprehensive report will be given in place of the final exam because it is difficult to conduct the final exam fairly. The total score of 25% for the exercise assignment and 75% for the comprehensive report, for a total of 60%, is a requirement for earning credits. The total score of the exercises may be used in place of the comprehensive report.

#### Course schedule

All classes should be face-to-face or all classes should be online.

In the first half of the classes, we will discuss aspect logic. Modal logic is the most fundamental theoretical system for dealing with uncertainty, and it is rich in descriptive power. In these classes, we will see how to bridge the gap between the logic of uncertainty and its applications by describing the theory of aspectual logic and rough sets suitable for its applications.

In the latter half of the classes, we will discuss Bayesian estimation, expected utility theory, and prospect theory. By reviewing various theories including Bayesian estimation rooted in subjective probability, we will deepen our understanding of the difference between Laplace's method and objective probability and the more flexible description of human indeterminacy.

Prof. Endo will be in charge of the first and seventh to tenth lectures, and Prof. Miyamoto will be in charge of the second to sixth lectures.

Uncertainty and Risk

Introduction to Logic of Uncertainty

Propositional Logic and Modal Logic

Semantics of Modal Logic and S5 System

Kripke Model

Rough Sets and Modal Logic

Basis of Probability

Bayesian Estimation

Expected Utility Theory

Prospect Theory

#### Course type

Lectures and Class Exercises

#### Online Course Requirement

#### Instructor

Miyamoto Sadaaki,Endo Yasunori

#### Other information

Other(Behavioral expectations and points to note for students during coursework)

No prior knowledge is required.

Same as 01CF120.

Online (on-demand) depending on the situation.

Cannot be taken in combination with "Fundamentals of Soft Computing I" and/or "Fundamentals of Soft Computing II".

#### Site for Inquiry

Link to the syllabus provided by the university