scholarly journals Functional Partial Fuzzy Relations

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2191
Author(s):  
Martina Daňková
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Membership Functions ◽  
Fuzzy Relations ◽  
Partial Functions ◽  
Special Operations ◽  
Suitable Combination ◽  
Basic Characteristics ◽  
Definition Of ◽  
Meaningful Definition

We study fuzzy relations that satisfy the functionality property and that their membership functions can be partial functions. Such fuzzy relations are called partial fuzzy relations, and the variable-domain fuzzy set theory is a framework that provides powerful tools for handling these objects. There, the special operations based on connectives and quantifiers of a partial fuzzy logic are in use. The undefined degrees of membership are carried via those special operations. Furthermore, we show that a suitable combination of these operations leads to a meaningful definition of the functionality property, and we investigate its basic characteristics.

Evaluation of Quantified Statements Using Gradual Numbers

2011 ◽  
pp. 246-269 ◽  
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.

A SIMILARITY-BASED GENERALIZATION OF FUZZY ORDERINGS PRESERVING THE CLASSICAL AXIOMS

2000 ◽  
Vol 08 (05) ◽  
pp. 593-610 ◽  
Author(s):  
ULRICH BODENHOFER
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Main Part ◽  
Equivalence Relations ◽  
Fuzzy Relations ◽  
Strong Connection ◽  
Alternative Approach ◽  
Key Concepts ◽  
Fuzzy Partitions ◽  
Fuzzy Orderings

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of fuzzy orderings is still lagging far behind, although there are a lot of possible applications, for instance, in fuzzy preference modeling and fuzzy control. The present paper is devoted to this missing link. After a brief motivation, we will critically analyze the existing approach to fuzzy orderings. In the main part, an alternative approach to fuzzy orderings, which also takes the strong connection to gradual similarity into account, is proposed and studied in detail, including several constructions and representation results.

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.

Generating Fuzzy Sets and Fuzzy Relations Based on Information

2021 ◽  
Vol 20 ◽  
pp. 178-185
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced

AN ORDINAL INFORMATION RETRIEVAL MODEL

2001 ◽  
Vol 09 (supp01) ◽  
pp. 63-75 ◽  
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.

scholarly journals Fuzzy machines in a category

1975 ◽  
Vol 13 (2) ◽  
pp. 169-210 ◽  
Author(s):  
Michael A. Arbib ◽  
Ernest G. Manes
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fuzzy Systems ◽  
Fuzzy Theory ◽  
Minimal Realization ◽  
Realization Theory ◽  
Realization Problem ◽  
Sequential Machines ◽  
Finite Lattices ◽  
Definition Of

“Fuzzy theories” and “distributive laws” are used to define “fuzzy systems” in an arbitrary category. The resulting minimal realization theory provides new insights even in classical cases (so that, for non-deterministic sequential machines, the minimal realization problem is reformulated in terms of the structure of join-irreducibles in finite lattices). The definition of “fuzzy theory” is of independent interest and meshes well with philosophical aspects of fuzzy set theory.

scholarly journals Uncertain Analysis of a Stationary Solar Compound Parabolic Concentrator PV Collector System Using Fuzzy Set Theory

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Hoe-Gil Lee ◽  
Singiresu S. Rao
Keyword(s):  
Solar Energy ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Uncertain Parameters ◽  
Membership Functions ◽  
Solar Pv ◽  
Compound Parabolic Concentrator ◽  
Collector System ◽  
Analysis Methodology

The uncertain analysis of fixed solar compound parabolic concentrator (CPC) collector system is investigated for use in combination with solar PV cells. Within solar CPC PV collector systems, any radiation within the collector acceptance angle enters through the aperture and finds its way to the absorber surface by multiple internal reflections. It is essential that the design of any solar collector aims to maximize PV performance since this will elicit a higher collection of solar radiation. In order to analyze uncertainty of the solar CPC collector system in the optimization problem formulation, three objectives are outlined. Seasonal demands are considered for maximizing two of these objectives, the annual average incident solar energy and the lowest month incident solar energy during winter; the lowest cost of the CPC collector system is approached as a third objective. This study investigates uncertain analysis of a solar CPC PV collector system using fuzzy set theory. The fuzzy analysis methodology is suitable for ambiguous problems to predict variations. Uncertain parameters are treated as random variables or uncertain inputs to predict performance. The fuzzy membership functions are used for modeling uncertain or imprecise design parameters of a solar PV collector system. Triangular membership functions are used to represent the uncertain parameters as fuzzy quantities. A fuzzy set analysis methodology is used for analyzing the three objective constrained optimization problems.

scholarly journals Implementation of Equilibrium Optimizer Algorithm for MPPT in a wind turbine with PMSG

2021 ◽  
Vol 16 ◽  
Author(s):  
Radwan Abu- Gdairi ◽  
Ibrahim Noaman
Keyword(s):  
Wind Turbine ◽  
Fuzzy Sets ◽  
Knowledge Discovery ◽  
Set Theory ◽  
Membership Function ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Relation ◽  
Knowledge Discovery In Databases ◽  
Fuzzy Relations

Fuzzy set theory and fuzzy relation are important techniques in knowledge discovery in databases. In this work, we presented fuzzy sets and fuzzy relations according to some giving Information by using rough membership function as a new way to get fuzzy set and fuzzy relation to help the decision in any topic . Some properties have been studied. And application of my life on the fuzzy set was introduced.

scholarly journals The Method of Logic Cyber Attack Detection of Abuse Functionality Type on Nginx Http-Server and Apache on the Basis of Fuzzy Logic

2020 ◽  
Vol 9 (8) ◽  
pp. 702-705
Keyword(s):  
Fuzzy Logic ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fuzzy Inference ◽  
Attack Detection ◽  
The Internet ◽  
Cyber Attack ◽  
Membership Functions ◽  
Mathematical Apparatus ◽  
Client Behavior

The article presents a method of abuse detection functionality of the most common open source http-servers Nginx and Apache, which currently implement a full web stack and serve more than 60% of traffic on the Internet. The proposed method is based on the application of the mathematical apparatus of fuzzy set theory and fuzzy inference to the selected analysis parameters corresponding to the properties of a logical cyber attack that realizes the vulnerability of web server data. To obtain the most accurate results of fuzzy inference the direction of adaptation of membership functions to the conditions of server operation (changes on the server and analysis of client behavior) based on the application of the mathematical apparatus of genetic algorithms is determined

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