scholarly journals Aggregation of Indistinguishability Fuzzy Relations Revisited

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1441
Author(s):  
Juan-De-Dios González-Hedström ◽  
Juan-José Miñana ◽  
Oscar Valero
Keyword(s):  
Equivalence Relation ◽  
Fuzzy Relations ◽  
Measure Of Similarity ◽  
Dual Notion ◽  
The Relationship

Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

scholarly journals Bipolar Fuzzy Relations

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1044 ◽  
Author(s):  
Jeong-Gon Lee ◽  
Kul Hur
Keyword(s):  
Equivalence Class ◽  
Level Set ◽  
Equivalence Relation ◽  
Level Sets ◽  
Equivalence Classes ◽  
Fuzzy Relation ◽  
Fuzzy Relations ◽  
Transitive Relation ◽  
Fuzzy Partition

We introduce the concepts of a bipolar fuzzy reflexive, symmetric, and transitive relation. We study bipolar fuzzy analogues of many results concerning relationships between ordinary reflexive, symmetric, and transitive relations. Next, we define the concepts of a bipolar fuzzy equivalence class and a bipolar fuzzy partition, and we prove that the set of all bipolar fuzzy equivalence classes is a bipolar fuzzy partition and that the bipolar fuzzy equivalence relation is induced by a bipolar fuzzy partition. Finally, we define an ( a , b ) -level set of a bipolar fuzzy relation and investigate some relationships between bipolar fuzzy relations and their ( a , b ) -level sets.

Toward a Generalization of Rough Sets Based on Active and Passive Relations

2006 ◽  
Vol 10 (6) ◽  
pp. 939-945
Author(s):  
Masashi Emoto ◽  
◽  
Rolly Intan ◽  
Masao Mukaidono ◽  
Keyword(s):  
Conditional Probability ◽  
Equivalence Relation ◽  
Rough Sets ◽  
Probability Relation ◽  
Data Elements ◽  
The Relationship

In the generalization of rough sets, many concepts use a relation weaker than the equivalence relation usually used in classical rough sets, e.g., induced by a conditional probability relation. The conditional probability relation is binary and assumes that the relationship between two data (elements or objects) resembles a relationship between two events in conditional probability. We use the asymmetric property of the conditional probability relation to propose active and passive relations, then discuss a generalization and properties of rough sets based on active and passive relations.

scholarly journals Types of Complex Fuzzy Relations with Applications in Future Commission Market

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Madad Khan ◽  
Muhammad Zeeshan ◽  
Seok-Zun Song ◽  
Sohail Iqbal
Keyword(s):  
Fuzzy Sets ◽  
Equivalence Relation ◽  
Order Relation ◽  
Fuzzy Relations ◽  
Inverse Relation ◽  
Transitive Relation ◽  
Temporal Dependence ◽  
Symmetric Relation ◽  
Asymmetric Relation ◽  
Fuzzy Order

In this paper, we introduce types of relations on complex fuzzy sets such as the complex fuzzy (CF) inverse relation, complex fuzzy reflexive relation, complex fuzzy symmetric relation, complex fuzzy antisymmetric relation, complex fuzzy transitive relation, complex fuzzy irreflexive relation, complex fuzzy asymmetric relation, complex fuzzy equivalence relation, and complex fuzzy-order relation. We study some basic results and particular examples of these relations. Moreover, we discuss the applications of complex fuzzy relations in Future Commission Market (FCM). We show that the introduction of CF relations to applications of FCMs can give a significant method for describing the temporal dependence between parameters of a Future Commission Market.

Lyric, Nation, and Dialogism

Poetics Today ◽  
2020 ◽  
Vol 41 (4) ◽  
pp. 595-617
Author(s):  
Morani Kornberg
Keyword(s):  
Political Activism ◽  
Nationalist Discourse ◽  
Right Of Return ◽  
Close Analysis ◽  
Ethical Role ◽  
Dual Notion ◽  
Law Of Return ◽  
First Time ◽  
The Relationship

This article introduces, for the first time, the marginalized writings of Israeli-statehood-generation poet Maxim Ghilan (1931–2005), who lived in self-exile in Paris as a result of his political activism. By investigating the relationship between lyric poetry and nationalism, the article introduces Ghilan’s early poetry, followed by a close analysis of his groundbreaking and understudied poem “In Enemy Land,” written upon his return to Israel. Ghilan’s poetry overturns nationalist discourse by revisiting the events of 1948 and evoking the dual notion of return, namely, the Israeli Law of Return and the Palestinian Right of Return. In an effort to contribute to New Lyric Studies, the article offers a new form of lyric reading, the “trans-national lyric,” a hyphenated form of transnationalism used to emphasize crossing over and moving beyond the nation. The trans-national lyric dismantles the lyric speaker’s sovereign position and consequently uncovers the silent — and silenced — dialogic voices that are an inseparable part of the genre. The article concludes with an analysis of lyric address and the ethical role of reading, whereby readers are implicated in the process of forced remembering and historical revision.

scholarly journals The weak and the strong equivalence relation and the asymptotic inversion

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 29-36
Author(s):  
Dragan Djurcic ◽  
Ivan Mitrovic ◽  
Mladen Janjic
Keyword(s):  
Equivalence Relation ◽  
Functional Class ◽  
Asymptotic Equivalence ◽  
Measurable Functions ◽  
Functional Classes ◽  
Half Axis ◽  
The Relationship ◽  
Rapidly Varying Functions

In this paper we discuss the relationship between the weak and the strong asymptotic equivalence relation and the asymptotic inversion, for positive and measurable functions defined on a half-axis [a,+?) (a > 0). As the main results, we prove a certain characterizations of the functional class of all rapidly varying functions, as well as some other functional classes.

scholarly journals On Fuzzy Corsini's Hyperoperations

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Yuming Feng ◽  
P. Corsini
Keyword(s):  
Fuzzy Relations ◽  
Basic Properties ◽  
The Relationship

We generalize the concept of C-hyperoperation and introduce the concept of F-C-hyperoperation. We list some basic properties of F-C-hyperoperation and the relationship between the concept of C-hyperoperation and the concept of F-C-hyperoperation. We also research F-C-hyperoperations associated with special fuzzy relations.

scholarly journals Energy and Entropy Measures of Fuzzy Relations for Data Analysis

2018 ◽  
Author(s):  
Ferdinando Di Martino ◽  
Salvatore Sessa
Keyword(s):  
Fuzzy Set ◽  
Fuzzy Rule ◽  
Threshold Value ◽  
Fuzzy Relation ◽  
Fuzzy Rules ◽  
Fuzzy Relations ◽  
Input Output ◽  
Input And Output ◽  
Entropy Measures ◽  
The Relationship

We present a new method for assessing the strength of fuzzy rules with respect to a dataset, based on the measures of the greatest energy and smallest entropy of a fuzzy relation. Considering a fuzzy automaton (relation) in which A is the input fuzzy set and B the output fuzzy set, the fuzzy relation R1 with greatest energy provides information about the greatest strength of the input-output and the fuzzy relation R2 with the smallest entropy provides information about uncertainty of the relationship input-output. We consider a new index of the fuzziness of the input-output based over R1 and R2. In our method this index is calculated for each pair of input and output fuzzy sets in a fuzzy rule. A threshold value is set for choosing the most relevant fuzzy rules with respect to the data.

Formal Methods for Assessing Patient Satisfaction in a Patient-Doctor Relationship

2018 ◽  
pp. 201-219
Author(s):  
Aleksandra Mreła ◽  
Oleksandr Sokołov
Keyword(s):  
Fuzzy Logic ◽  
Patient Satisfaction ◽  
Fuzzy Sets ◽  
Formal Methods ◽  
Classical Logic ◽  
Fuzzy Relations ◽  
The Relationship

When patients visit a doctor, they not only expect to be cured, but also to feel that they are taken care of. The patients like to be treated like guests, sit in a nice place during waiting for a doctor and feel that they are taken care of seriously at the reception desk. All these factors are important for the patients but the relationship with doctors seems to be the most valid. When the patients can choose a clinic where they want to make an appointment with a doctor, the owners and managers of the clinics try to persuade people to choose their clinic. Hence more and more often managers of the clinics try to find out the opinion of the patients, so scientists carried out the research on this phenomenon and called it Patient Satisfaction. This chapter presents the application of fuzzy sets and fuzzy relations to gather and analyze the information from patients and compute their contentment. Using classical logic is less appropriate because the patients can only choose two values: they are satisfied or dissatisfied. Fuzzy logic let the patients choose more phrases for their opinions.

scholarly journals T-Equivalences: The Metric Behavior Revisited

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 495 ◽  
Author(s):  
Pilar Fuster-Parra ◽  
Javier Martín ◽  
Jordi Recasens ◽  
Óscar Valero
Keyword(s):  
Artificial Intelligence ◽  
Computer Science ◽  
Equivalence Relation ◽  
Special Interest ◽  
Fuzzy Relations ◽  
New Approach ◽  
New Type

Since the notion of T-equivalence, where T is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations. Concretely, a few techniques to induce metrics from T-equivalences, and vice versa, have been developed. In several fields of computer science and artificial intelligence, a generalization of pseudo-metric, known as partial pseudo-metrics, have shown to be useful. Recently, Bukatin, Kopperman and Matthews have stated that the notion of partial pseudo-metric and a type of generalized T-equivalence are linked. Inspired by the preceding fact, in this paper, we state a concrete relationship between partial pseudo-metrics and the aforesaid generalized T-equivalences. Specifically, a method for constructing partial pseudo-metrics from the new type of T-equivalences and, reciprocally, for constructing the generalized T-equivalences from partial pseudo-metrics are provided. However, important differences between the new approach and the classical one are established. Special interest is paid to the case in which the minimum, drastic, and Łukasiewicz t-norms are under consideration.

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

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