Basic concepts for a theory of evaluation: Hierarchical aggregation via autodistributive connectives in fuzzy set theory

1985 ◽  
Vol 20 (2) ◽  
pp. 221-233 ◽  
Author(s):  
Harald Dyckhoff
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hierarchical Aggregation ◽  
Basic Concepts

The Basic Concepts of the Fuzzy Set Theory

2011 ◽  
pp. 1-41 ◽  
Author(s):  
Olga Poleshchuk ◽  
Evgeniy Komarov
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Basic Concepts

scholarly journals Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 432 ◽  
Author(s):  
Vilém Novák
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Type Theory ◽  
Rough Set Theory ◽  
Basic Concepts ◽  
Alternative Set

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.

scholarly journals Fuzzy Insurance

1990 ◽  
Vol 20 (1) ◽  
pp. 33-55 ◽  
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.

scholarly journals Evaluating the Effectiveness of an Intrusion Detection System Based on Matrix Games and Fuzzy Sets

2021 ◽  
Vol 2096 (1) ◽  
pp. 012007
Author(s):  
V B Vilkov ◽  
A I Dergachev ◽  
A K Chernykh ◽  
M S Abu-Khasan
Keyword(s):  
Intrusion Detection ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intrusion Detection System ◽  
Detection System ◽  
Matrix Game ◽  
Practical Application ◽  
Matrix Games ◽  
Basic Concepts

Abstract We consider a problem formulated as a matrix game in which the gain of officials using a specific intrusion detection system (criminal actions) of intruders (player 1) is the probability of timely detection of these criminal actions (player 2). As a rule, it is not possible to unambiguously set the probability of timely detection of criminal actions, so it is proposed to use the apparatus of fuzzy set theory to evaluate it. Reviewed and discussed the basic concepts of fuzzy set theory, and an example of practical application of this theory to assess the efficiency of the detection system of criminal damage. Application of fuzzy set theory in assessing the possible actions of an attacker can detect existing vulnerabilities in information security of automated systems continue to spend improving the detection of criminal acts (hackers) to prevent the possibility of applying economic and other damage to the company.

BASIC CONCEPTS OF FUZZY SET THEORY

1988 ◽  
pp. 14-65
Author(s):  
YEE LEUNG
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Basic Concepts

Basic concepts and history of fuzzy set theory and fuzzy logic

2004 ◽  
Author(s):  
George Klir ◽  
Bo Yuan
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
History Of ◽  
Basic Concepts
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