Vagueness in the Exact Sciences 1st Edition by Apostolos Syropoulos, Basil K Papadopoulos ISBN 3110704188 9783110704181

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ISBN 10: 3110704188
ISBN 13: 9783110704181
Author: Apostolos Syropoulos, Basil K Papadopoulos

Vagueness in the Exact Sciences 1st Edition Table of contents:

Ken Akiba 1 Vagueness from the philosophical point of view

1.1 Wherein lies vagueness?

1.1.1 Introduction

1.1.2 Representations

1.1.3 Objects in the world

1.1.4 Fuzzy set theory and fuzzy logic

1.1.5 Disquotational truth

1.1.6 Conclusion

1.2 Why do philosophers dismiss fuzzy theory?

1.2.1 Introduction

1.2.2 Nihilism about vagueness and the sorites paradox

1.2.3 Where does degree 1 (or 0) end?

1.2.4 Penumbral connections and logical truths

1.3 Philosophical literature on vagueness

Apostolos Syropoulos, Eleni Tatsiou 2 Vague mathematics

2.1 Introduction

Plan of the chapter

2.2 Fuzzy mathematics

2.3 Rough sets

2.4 Supervaluational mathematics

2.5 Context and mathematics

2.6 Vagueness and the law of excluded middle

2.7 Conclusions

Apostolos Syropoulos 3 Vague theory of computation

3.1 Introduction

Plan of the chapter

3.2 Fuzzy computation

3.3 Rough set computation

3.4 Paraconsistent logics and computation

3.5 Context-aware computing

3.6 Supervaluation and computing

3.7 Conclusions

Nikos Mylonas, Basil Papadopoulos 4 Fuzzy hypotheses tests with crisp data using nonasymptotic fuzzy estimators

4.1 Introduction

4.2 Fuzzy estimators

4.2.1 Estimation of the mean of a normal variable with known variance

4.2.2 Estimation of the mean of a random variable from a large sample

4.2.3 Estimation of the mean of a normal variable with unknown variance

4.2.4 Estimation of the difference μ1−μ2 of the means of two normal variables with known variances

4.2.5 Estimation of the difference μ1−μ2 of the means of two normal variables with unknown variances from two large samples

4.2.6 Estimation of the difference μ1−μ2 of the means of two normal variables with unknown variances

4.2.7 Estimation of the probability of success p of a binomial distribution

4.2.8 Estimation of the difference p1−p2 of the probabilities of success of two binomial distributions

4.2.9 Estimation of the variance of a normal variable

4.2.10 Estimation of σ12/σ22 for the variances of two normal distributions

4.3 Ordering fuzzy numbers

4.4 Hypotheses testing using fuzzy test statistics and fuzzy critical values or fuzzy p-value

4.4.1 Using fuzzy critical values

4.4.2 Using fuzzy p-value

4.5 Tests on the mean of a normal distribution with known variance

4.5.1 Using fuzzy critical values

4.5.2 Using fuzzy p-value

4.6 Tests on the mean of a random variable with any distribution from a large sample

4.7 Tests on the means of two normal distributions with known variances

4.7.1 Using fuzzy critical values

4.7.2 Using fuzzy p-value

4.8 Tests on the mean of a normal variable with unknown variance

4.8.1 Using fuzzy critical values

4.8.2 Using fuzzy p-value

4.9 Tests on the variance of a normal distribution

4.9.1 Using fuzzy critical values

4.9.2 Using fuzzy p-value

4.10 Tests on the variances of two normal distributions

4.10.1 Using fuzzy critical values

4.10.2 Using fuzzy p-value

4.11 Conclusions

Jarosław Pykacz 5 Fuzzy sets in quantum mechanics

5.1 Introduction

5.2 Fuzzy set representation of Birkhof–von Neumann “quantum logic”

5.3 Interpretation of Łukasiewicz operations

5.4 Other attempts to apply fuzzy set ideas in quantum mechanics

Pier Luigi Gentili, Apostolos Syropoulos 6 Vagueness in chemistry

6.1 Introduction

Plan of the chapter

6.2 Molecules as fuzzy sets

6.3 Vagueness in biochemical life

6.4 Discussion

Bjørn Hofmann 7 Vagueness in medicine: on indistinct phenomena, vague concepts, and uncertain knowledge

7.1 Medicine as a vague discipline

7.2 Ont(olog)ical vagueness: continuity

7.3 Conceptual vagueness

7.3.1 Different concepts of malady

7.3.2 Polyvalent concepts in medicine

7.3.3 Expanding the borders of medicine: expansion of the concept of disease

7.4 Epistemic vagueness: uncertainty

7.5 Vagueness due to fact-value interactions

7.6 Vagueness in diagnosis

7.7 Conclusion

Fabio Krykhtine 8 Vagueness in technology

Acknowledgement

8.1 Introduction

8.2 Uncertainty from theory to practice

8.3 Thinking from simple to complex

8.3.1 Case 1 – classifying apples

8.3.2 Case 2 – rockets and toys

8.3.3 Case 3 – Location studies and economic issues

8.4 The uncertainty is part of the future

Ioannis Kanellos, Elena Ciobanu 9 The semiotic topos of vagueness

9.1 Vagueness, where are you? — A vague and skeptical exploration of vagueness

9.2 A vague typology of vagueness: the heritage of the semiotic locus

9.2.1 Vagueness as imprecision

9.2.2 Vagueness as instability

9.2.3 Vagueness as indetermination

9.2.4 Vagueness as indecision

9.3 Discussion and conclusion

9.3.1 Vagueness and meaning-making

9.3.2 Vagueness and doubt

9.3.3 Vagueness and sciences

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Tags: Apostolos Syropoulos, Basil K Papadopoulos, Vagueness, Sciences