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.

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

Estimating facilities maintenance cost using post-occupancy evaluation and fuzzy set theory

2018 ◽  
Vol 24 (4) ◽  
pp. 449-467 ◽  
Author(s):  
Adel Alshibani ◽  
Mohammad A. Hassanain
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Maintenance Cost ◽  
New Approach ◽  
Content Type ◽  
Post Occupancy Evaluation ◽  
Complex Simulation ◽  
Alternative Approach ◽  
Facility Maintenance

Purpose The purpose of this paper is to introduce a new general approach for estimating the maintenance cost of constructed facilities. The proposed approach consists of four components, including: facility work breakdown structure; historical maintenance cost and cost contingency data of actual completed projects; feedback obtained from the post-occupancy evaluation (POE); and fuzzy set theory (FST) to define the uncertainty associated with the maintenance cost and cost contingency as an alternative approach to simulation. Design/methodology/approach Literature review of the existing methods used for estimating maintenance cost of constructed facilities was conducted to highlight the limitations of the existing methods and models. The paper then introduced a new approach in which the results obtained from POE are integrated with the estimator’s judgment in estimating maintenance cost of constructed facility. As a proof of concept, the developed approach is tested on a private school facility in the city of Khobar, Saudi Arabia. The application of the proposed approach in this case project demonstrates its applicability and features in comparison with the existing practice. Findings The application of the developed approach on a school case project demonstrated that the developed approach can provide a reliable facility maintenance cost estimate, narrow the uncertainties and vagueness associated with the estimated cost, and provide the estimator with the necessary information to conduct risk analysis with less effort, less computations and less complexity comparing with that provided by complex simulation. The results also showed that integrating POE in the estimating process can provide more accurate cost estimate with high level of confidence. Originality/value The paper presents a new approach for estimating facility maintenance cost. The developed approach introduced a new concept that assists maintenance contractors in preparing facility maintenance estimate with improved accuracy while satisfying the facility user’s needs. The proposed approach integrates the estimator’s judgment with POE to model the uncertainties associated with cost using FST as an alternative approach for complex simulation.

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 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.

Generalized Fuzzy Relations

2018 ◽  
Vol 14 (02) ◽  
pp. 187-202 ◽  
Author(s):  
John N. Mordeson ◽  
Sunil Mathew ◽  
Davender S. Malik
Keyword(s):  
Fuzzy Logic ◽  
Graph Theory ◽  
Human Trafficking ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Illegal Immigration ◽  
Fuzzy Relations ◽  
Fuzzy Graph ◽  
Arbitrary Norm

Fuzzy relations are fundamental in applications of fuzzy set theory and fuzzy logic. The entire literature on fuzzy relations as applied to fuzzy graph theory are based on Rosenfeld’s relations. Rosenfeld used minimum and maximum as the norm and conorm in his study of compositions of fuzzy relations. In this paper, we generalize fuzzy relations using arbitrary [Formula: see text]-norms and [Formula: see text]-conorms. Many of the results do not hold when minimum and maximum are replaced by an arbitrary norm and an arbitrary conorm. Reflexive, symmetric and transitive generalized fuzzy relations are also discussed and an application to human trafficking and illegal immigration is presented.

Some results on fuzzy relations

2021 ◽  
pp. 1-17
Author(s):  
Yini Wang ◽  
Sichun Wang
Keyword(s):  
Set Theory ◽  
Fuzzy Set Theory ◽  
Attribute Reduction ◽  
Heterogeneous Data ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Main Research ◽  
Effectiveness Analysis ◽  
Uncertainty Measurement ◽  
Partial Dependence

Fuzzy relation is one of the main research contents of fuzzy set theory. This paper obtains some results on fuzzy relations by studying relationships between fuzzy relations and their uncertainty measurement. The concepts of equality, dependence, partial dependence and independence between fuzzy relations are first introduced. Then, uncertainty measurement for a fuzzy relation is investigated by using dependence between fuzzy relations. Moreover, the basic properties of uncertainty measurement are obtained. Next, effectiveness analysis is carried out. Finally, an application of the proposed measures in attribute reduction for heterogeneous data is given. These results will be helpful for understanding the essence of a fuzzy relation.

DOMINATION OF AGGREGATION OPERATORS AND PRESERVATION OF TRANSITIVITY

2002 ◽  
Vol 10 (supp01) ◽  
pp. 11-35 ◽  
Author(s):  
SUSANNE SAMINGER ◽  
RADKO MESIAR ◽  
ULRICH BODENHOFER
Keyword(s):  
Aggregation Operator ◽  
Aggregation Operators ◽  
Equivalence Relations ◽  
Fuzzy Relations ◽  
Basic Properties ◽  
Vital Interest ◽  
Aggregation Processes ◽  
Fuzzy Orderings

Aggregation processes are fundamental in any discipline where the fusion of information is of vital interest. For aggregating binary fuzzy relations such as equivalence relations or fuzzy orderings, the question arises which aggregation operators preserve specific properties of the underlying relations, e.g. T-transitivity. It will be shown that preservation of T-transitivity is closely related to the domination of the applied aggregation operator over the corresponding t-norm T. Furthermore, basic properties for dominating aggregation operators, not only in the case of dominating some t-norm T, but dominating some arbitrary aggregation operator, will be presented. Domination of isomorphic t-norms and ordinal sums of t-norms will be treated. Special attention is paid to the four basic t-norms (minimum t-norm, product t-norm, Łukasiewicz t-norm, and the drastic product).

scholarly journals Roughness of soft sets and fuzzy sets in semigroups based on set-valued picture hesitant fuzzy relations

2022 ◽  
Vol 7 (2) ◽  
pp. 2891-2928
Author(s):  
Rukchart Prasertpong ◽  
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Equivalence Relations ◽  
Prime Ideals ◽  
Fuzzy Relations ◽  
Binary Relations ◽  
Soft Sets ◽  
Rough Fuzzy Set

<abstract><p>In the philosophy of rough set theory, the methodologies of rough soft sets and rough fuzzy sets have been being examined to be efficient mathematical tools to deal with unpredictability. The basic of approximations in rough set theory is based on equivalence relations. In the aftermath, such theory is extended by arbitrary binary relations and fuzzy relations for more wide approximation spaces. In recent years, the notion of picture hesitant fuzzy relations by Mathew et al. can be considered as a novel extension of fuzzy relations. Then this paper proposes extended approximations into rough soft sets and rough fuzzy sets from the viewpoint of its. We give corresponding examples to illustrate the correctness of such approximations. The relationships between the set-valued picture hesitant fuzzy relations with the upper (resp., lower) rough approximations of soft sets and fuzzy sets are investigated. Especially, it is shown that every non-rough soft set and non-rough fuzzy set can be induced by set-valued picture hesitant fuzzy reflexive relations and set-valued picture hesitant fuzzy antisymmetric relations. By processing the approximations and advantages in the new existing tools, some terms and products have been applied to semigroups. Then, we provide attractive results of upper (resp., lower) rough approximations of prime idealistic soft semigroups over semigroups and fuzzy prime ideals of semigroups induced by set-valued picture hesitant fuzzy relations on semigroups.</p></abstract>

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