Fuzziness: From Epistemic Considerations to Terminological Clarification

Using some semantical considerations and results from basic philosophy and some basic mathematical concepts we try to fix suitable explanations for some fundamental notions of fuzzy set theory on a semiformal level. This will – to the author's knowledge for the first time at all – lead us to a proposal for a definition of what is to be understood by the term 'fuzziness', simultaneously clarifying its epistemic rôle.

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The definition of the niche by fuzzy set theory

Ecological Modelling ◽

10.1016/0304-3800(93)e0071-a ◽

1995 ◽

Vol 77 (1) ◽

pp. 65-71 ◽

Cited By ~ 14

Author(s):

Guangxia Cao

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Definition Of

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Evaluation of Quantified Statements Using Gradual Numbers

Handbook of Research on Fuzzy Information Processing in Databases ◽

10.4018/978-1-59904-853-6.ch010 ◽

2011 ◽

pp. 246-269 ◽

Cited By ~ 7

Author(s):

Ludovic Liétard ◽

Daniel Rocacher

Keyword(s):

Decision Making ◽

Expert Systems ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Relational Databases ◽

Fuzzy Numbers ◽

Theoretical Background ◽

Definition Of ◽

Flexible Querying

This chapter is devoted to the evaluation of quantified statements which can be found in many applications as decision making, expert systems, or flexible querying of relational databases using fuzzy set theory. Its contribution is to introduce the main techniques to evaluate such statements and to propose a new theoretical background for the evaluation of quantified statements of type “Q X are A” and “Q B X are A.” In this context, quantified statements are interpreted using an arithmetic on gradual numbers from Nf, Zf, and Qf. It is shown that the context of fuzzy numbers provides a framework to unify previous approaches and can be the base for the definition of new approaches.

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Fuzzy Insurance

Astin Bulletin ◽

10.2143/ast.20.1.2005482 ◽

1990 ◽

Vol 20 (1) ◽

pp. 33-55 ◽

Cited By ~ 67

Author(s):

Jean Lemaire

Keyword(s):

Decision Making ◽

Set Theory ◽

Fuzzy Set ◽

Life Insurance ◽

Fuzzy Set Theory ◽

Fuzzy Numbers ◽

Fuzzy Decision Making ◽

Fuzzy Decision ◽

Basic Concepts ◽

Definition Of

AbstractFuzzy set theory is a recently developed field of mathematics, that introduces sets of objects whose boundaries are not sharply defined. Whereas in ordinary Boolean algebra an element is either contained or not contained in a given set, in fuzzy set theory the transition between membership and non-membership is gradual. The theory aims at modelizing situations described in vague or imprecise terms, or situations that are too complex or ill-defined to be analysed by conventional methods. This paper aims at presenting the basic concepts of the theory in an insurance framework. First the basic definitions of fuzzy logic are presented, and applied to provide a flexible definition of a “preferred policyholder” in life insurance. Next, fuzzy decision-making procedures are illustrated by a reinsurance application, and the theory of fuzzy numbers is extended to define fuzzy insurance premiums.

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AN ORDINAL INFORMATION RETRIEVAL MODEL

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488501000995 ◽

2001 ◽

Vol 09 (supp01) ◽

pp. 63-75 ◽

Cited By ~ 21

Author(s):

GLORIA BORDOGNA ◽

GABRIELLA PASI

Keyword(s):

Information Retrieval ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Query Evaluation ◽

Retrieval Model ◽

Ordinal Information ◽

Index Terms ◽

Evaluation Mechanism ◽

Definition Of

In this paper an ordinal Information Retrieval model is proposed, which is formalised within fuzzy set theory and is based on the notion of linguistic granules of information. Linguistic expressions are defined to represent and manage the importance of both the index terms as descriptors of the information items and the query terms (content selectors) as descriptors of users' needs. The advantage of this approach with respect to the (numeric) fuzzy IR models is that the query evaluation mechanism and the definition of the importance semantics are simplified.

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Certain fuzzy hyperstructures from a fuzzy set

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-191054 ◽

2020 ◽

Vol 39 (3) ◽

pp. 2775-2782

Author(s):

B.O. Onasanya ◽

T.S. Atamewoue ◽

S. Hoskova-Mayerova

Keyword(s):

Fuzzy Sets ◽

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Real Life ◽

Mathematical Concepts

Fuzzy set theory and also the hypergroups in the sense of Marty are both generalizations of some existing mathematical concepts which are used for modeling many real life situations. The main purpose of this paper is the study of the link between fuzzy sets and fuzzy hypergroups and fuzzy semihypergroups. As a matter of fact, some commutative fuzzy hypergroups and fuzzy semihypergroups have been constructed from fuzzy set and some of their properties were investigated.

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(L,M)-Fuzzyσ-Algebras

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/2010/356581 ◽

2010 ◽

Vol 2010 ◽

pp. 1-11 ◽

Cited By ~ 2

Author(s):

Fu-Gui Shi

Keyword(s):

Set Theory ◽

Fuzzy Set ◽

Fuzzy Set Theory ◽

Fuzzy Subset ◽

Measurable Set ◽

Definition Of

The notion of (L,M)-fuzzyσ-algebras is introduced in the lattice value fuzzy set theory. It is a generalization of Klement's fuzzyσ-algebras. In our definition of (L,M)-fuzzyσ-algebras, eachL-fuzzy subset can be regarded as anL-measurable set to some degree.

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