scholarly journals Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1351
Author(s):  
Qingsong Mao ◽  
Huan Huang
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
Fuzzy Set ◽  
Point Of View ◽  
Arithmetic Operations ◽  
Finite Arithmetic ◽  
Important Characterization ◽  
The Relationship

Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithmetic operations of fuzzy sets. The interval range is an important characterization of a fuzzy set. The interval range is also useful for analyses and applications of arithmetic. In this paper, we present general conclusions on crucial problems related to interval ranges of fuzzy sets induced by this arithmetic. These conclusions indicate that the corresponding conclusions in previous works should be modified: firstly, we give properties of the arithmetic and the composites of finite arithmetic. Then, we discuss the relationship between the domain of a gradual set and the range of its induced fuzzy set, and the relationship between the domain of a gradual set and the interval range of its induced fuzzy set. Based on the above results, we present the relationship between the intersection of the interval ranges of a group of fuzzy sets and the interval ranges of their resulting fuzzy sets obtained by compositions of finite arithmetic. Furthermore, we construct examples to show that even under conditions stronger than in previous work, there are still various possibilities in the relationship between the intersection of interval ranges of a group of fuzzy sets and the ranges of their resulted fuzzy sets, and there are still various possibilities in the relationship between the intersection of the interval ranges of a group of fuzzy sets and the interval ranges of their resulting fuzzy sets.

scholarly journals A p-Ideal in BCI-Algebras Based on Multipolar Intuitionistic Fuzzy Sets

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 993
Author(s):  
Jeong-Gon Lee ◽  
Mohammad Fozouni ◽  
Kul Hur ◽  
Young Bae Jun
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Sets ◽  
Finite Degree ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Ideal ◽  
The Relationship

In 2020, Kang, Song and Jun introduced the notion of multipolar intuitionistic fuzzy set with finite degree, which is a generalization of intuitionistic fuzzy set, and they applied it to BCK/BCI-algebras. In this paper, we used this notion to study p-ideals of BCI-algebras. The notion of k-polar intuitionistic fuzzy p-ideals in BCI-algebras is introduced, and several properties were investigated. An example to illustrate the k-polar intuitionistic fuzzy p-ideal is given. The relationship between k-polar intuitionistic fuzzy ideal and k-polar intuitionistic fuzzy p-ideal is displayed. A k-polar intuitionistic fuzzy p-ideal is found to be k-polar intuitionistic fuzzy ideal, and an example to show that the converse is not true is provided. The notions of p-ideals and k-polar ( ∈ , ∈ ) -fuzzy p-ideal in BCI-algebras are used to study the characterization of k-polar intuitionistic p-ideal. The concept of normal k-polar intuitionistic fuzzy p-ideal is introduced, and its characterization is discussed. The process of eliciting normal k-polar intuitionistic fuzzy p-ideal using k-polar intuitionistic fuzzy p-ideal is provided.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

Characterizing ventricular mechanics and energetics following repeated coronary microembolization

1997 ◽  
Vol 272 (1) ◽  
pp. H186-H194 ◽  
Author(s):  
K. Todaka ◽  
D. Leibowitz ◽  
S. Homma ◽  
P. E. Fisher ◽  
C. Derosa ◽  
...  
Keyword(s):  
Diastolic Pressure ◽  
Systolic Pressure ◽  
Control Group ◽  
Myocardial Mechanics ◽  
Ventricular Mechanics ◽  
Volume Relation ◽  
The Right ◽  
Important Characterization ◽  
The Relationship

Myocardial mechanics and energetics were investigated in an animal model of moderate chronic heart failure (CHF) created by repeated coronary microembolizations in six dogs. The final fractional area change was 34 +/- 4%. Hearts of these animals were isolated and cross-perfused, and balloons were placed in the left ventricle (LV). Chamber contractile state was markedly depressed in embolized hearts as assessed by the slope (Ees 2.74 +/- 0.49 vs. 4.00 +/- 1.18 mmHg/ml, P < 0.01) and volume axis intercept (V: 8.7 +/- 5.9 vs. 1.0 +/- 3.2 ml, P < 0.01) of end-systolic pressure-volume relation compared with a group of six normal dogs. The end-diastolic pressure-volume relation of embolized hearts was shifted to the right, indicating a dilation of the LV. However, systolic and diastolic stress strain relationships were similar in the two groups, suggesting that the average myocardial properties of the embolized hearts are similar to those of normal hearts. The relationship between oxygen consumption and pressure-volume area in embolized hearts had smaller intercept (2.98 +/- 0.44 vs 3.92 +/- 0.39 x 10(-2) ml O2.beat-1.100 g LV-1, P < 0.01) compared with the control group, with no change in the slope. These results contrast with previous findings in pacing CHF and serve as an important characterization of ventricular properties in this model of CHF from different etiology.

scholarly journals Plurality of Points of Views and knowing of a Plural Reality

2018 ◽  
Vol Épistémologies du pluriel (Articles) ◽  
Author(s):  
Claude Compagnone
Keyword(s):  
Knowledge Production ◽  
Point Of View ◽  
Social Nature ◽  
The Social ◽  
International Audience ◽  
Points Of View ◽  
The Relationship ◽  
Interactional Features ◽  
The Way

International audience El objetivo de éste artículo es dar cuenta de la manera por la cual las concepciones plurales de la realidad son inherentes al proceso de conocimiento. Asimismo, el artículo apunta a mostrar de qué manera los distintos puntos de vista de los actores sobre ésta realidad son social y materialmente situados. Apoyándose en el enfoque de J.-P. Darré , el neo-pragmatismo de H. Putnam, así como en los aportes de lingüistas y psicólogos, el presente trabajo ilumina la manera en la cual la relación entre realidad y conocimiento puede establecerse. El artículo destaca que la verdad depende de la adecuación del conocimiento a la realidad y pone en relieve las propiedades interactivas de las cosas. Finalmente, permite revelar la naturaleza social de las concepciones y discute, a partir de la noción de punto de vista de A. Schütz, la caracterización social de estos puntos de vista. The purpose of this article is to report the way in which the plural understandings of reality are inherent to the process of knowledge production. It alsoaims to show what it means that actors’ point of view are socially and materially situated. Relying on J.-P. Darré’s approach, Putnam’s pragmatism, as well as on linguists’ and psychologists’ works, it highlights how the relationship between reality and knowledge may be understood. It underlines that truth depends on the adequacy of knowledge to reality and emphasizes the interactional features of things. Then, it focuses on the social nature of understanding and discusses the social characterization of points of view, drawing on A. Schütz’s works. Le but de cet article est de rendre compte de la façon dont desconceptions plurielles de la réalité sont inhérentes au processus de connaissance.Il vise aussi à montrer comment on peut entendre que les points de vue des acteurs sur cette réalité sont socialement et objectivement situés. S’appuyant sur l’approche de J.-P. Darré, sur le néopragmatisme de H. Putnam, ainsi que sur les travaux de linguistes et de psychologues, il éclaircit la façon dont on peut entendre le rapport qui peut être établi entre réalité et connaissance. Il souligne que la vérité dépend de l’adéquation de la connaissance à la réalité et met en valeur les propriétés interactionnelles des choses. Il fait ensuite apparaître la nature sociale des conceptions et discute, à partir de la notion de point de vue de A. Schütz, de la caractérisation sociale de ces points de vue.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
Vol 41 (2) ◽  
pp. 3173-3181
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

scholarly journals Students’ Admission Process based on a Novel Fermatean Fuzzy Distance Measure Algorithm

2021 ◽  
Author(s):  
Augustine Ejegwa ◽  
Idoko Charles Onyeke
Keyword(s):  
Fuzzy Sets ◽  
Soft Computing ◽  
Programming Language ◽  
Fuzzy Set ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Admission Process ◽  
Algorithmic Approach ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy

Abstract Fermatean fuzzy set is a competent tool in curbing indeterminacy embedded in soft computing. Fermatean fuzzy set generalizes both intuitionistic fuzzy sets and Pythagorean fuzzy sets in an effective way to handle imprecision by expanding the spatial scope of Pythagorean/intuitionistic fuzzy sets. Distance measure has become an integral aspect of utilizing generalized fuzzy sets in soft computing. In this paper, a novel distance measure between Fermatean fuzzy sets is introduced with a better and reliable output. Some properties of the proposed distance measure are characterized. It is demonstrated that the new distance measure between Fermatean fuzzy sets is more reliable than the existing Fermatean fuzzy distance measure. In addition, it is shown that Fermatean fuzzy set is more equipped to curb imprecision than Pythagorean/intuitionistic fuzzy sets. In terms of application, the new Fermatean fuzzy distance measure is utilized in executing students’ admission process using an algorithmic approach implemented by a programming language to enhance accuracy and ease of computations.

scholarly journals Future and immortality in the religious philosophy of F.M. Dostoyevsky (from the novel «Crime And Punishment»)

2020 ◽  
pp. 137-149
Author(s):  
Li Tianyun
Keyword(s):  
Religious Faith ◽  
Point Of View ◽  
The Novel ◽  
Main Character ◽  
Religious Philosophy ◽  
Crime And Punishment ◽  
Fundamental Point ◽  
Unusual Combination ◽  
The Relationship

This article attempts to establish the relationship between the concept of immortality and the future of mankind and the religious faith of the characters of F.M. Dostoevsky's works. This problem is considered with reference to the example of a detailed analysis of the views of the main character of Dostoevsky’s novel «Crime and Punishment» (Rodion Raskolnikov). The characterization of the hero is given in terms of his religiosity. The features of Raskolnikov's worldview are noted; they consist in a combination of faith in God and lack of faith in immortality. It is suggested that the source of such an unusual combination of religious ideas is the historical concept of I.G. Fichte. On the basis of the comparison of the views of other heroes of the novel, the article concludes that the most fundamental point is their idea of immortality as a continuation of the existence of a person in earthly reality. It demonstrates that this point of view corresponds to the religious faith of Dostoevsky himself.

On 2-absorbing bipolar fuzzy ideals over LA -semigroups

2021 ◽  
pp. 1-9
Author(s):  
Pairote Yiarayong
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Bipolar Fuzzy Sets ◽  
The Relationship

The aim of this manuscript is to apply bipolar fuzzy sets for dealing with several kinds of theories in LA -semigroups. To begin with, we introduce the concept of 2-absorbing (quasi-2-absorbing) bipolar fuzzy ideals and strongly 2-absorbing (quasi-strongly 2-absorbing) bipolar fuzzy ideals in LA -semigroups, and investigate several related properties. In particular, we show that a bipolar fuzzy set A = ( μ A P , μ A N ) over an LA -semigroup S is weakly 2-absorbing if and only if [ B ⊙ C ] ⊙ D ⪯ A implies B ⊙ C ⪯ A or C ⊙ D ⪯ A or B ⊙ D ⪯ A for any bipolar fuzzy sets B = ( μ B P , μ B N ) , C = ( μ C P , μ C N ) and D = ( μ D P , μ D N ) . Also, we give some characterizations of quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S by bipolar fuzzy points. In conclusion of this paper we prove that the relationship between quasi-strongly 2-absorbing bipolar fuzzy ideals over an LA -semigroup S and quasi-2-absorbing bipolar fuzzy ideals over S.

Granular Computing

2011 ◽  
pp. 774-780
Author(s):  
Georg Peters
Keyword(s):  
Probability Theory ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Sets ◽  
Granular Computing ◽  
Information Granularity ◽  
Relationship Of ◽  
The Relationship

It is well accepted that in many real life situations information is not certain and precise but rather uncertain or imprecise. To describe uncertainty probability theory emerged in the 17th and 18th century. Bernoulli, Laplace and Pascal are considered to be the fathers of probability theory. Today probability can still be considered as the prevalent theory to describe uncertainty. However, in the year 1965 Zadeh seemed to have challenged probability theory by introducing fuzzy sets as a theory dealing with uncertainty (Zadeh, 1965). Since then it has been discussed whether probability and fuzzy set theory are complementary or rather competitive (Zadeh, 1995). Sometimes fuzzy sets theory is even considered as a subset of probability theory and therefore dispensable. Although the discussion on the relationship of probability and fuzziness seems to have lost the intensity of its early years it is still continuing today. However, fuzzy set theory has established itself as a central approach to tackle uncertainty. For a discussion on the relationship of probability and fuzziness the reader is referred to e.g. Dubois, Prade (1993), Ross et al. (2002) or Zadeh (1995). In the meantime further ideas how to deal with uncertainty have been suggested. For example, Pawlak introduced rough sets in the beginning of the eighties of the last century (Pawlak, 1982), a theory that has risen increasing attentions in the last years. For a comparison of probability, fuzzy sets and rough sets the reader is referred to Lin (2002). Presently research is conducted to develop a Generalized Theory of Uncertainty (GTU) as a framework for any kind of uncertainty whether it is based on probability, fuzziness besides others (Zadeh, 2005). Cornerstones in this theory are the concepts of information granularity (Zadeh, 1979) and generalized constraints (Zadeh, 1986). In this context the term Granular Computing was first suggested by Lin (1998a, 1998b), however it still lacks of a unique and well accepted definition. So, for example, Zadeh (2006a) colorfully calls granular computing “ballpark computing” or more precisely “a mode of computation in which the objects of computation are generalized constraints”.

scholarly journals The basic arithmetic operations on fuzzy numbers and new approaches to the theory of fuzzy numbers under the classification of space images

2020 ◽  
Vol 3 ◽  
pp. 49-59
Author(s):  
S.I. Alpert ◽  
Keyword(s):  
Remote Sensing ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Fuzzy Numbers ◽  
Mathematical Tool ◽  
Classification Problems ◽  
Arithmetic Operations

Classification in remote sensing is a very difficult procedure, because it involves a lot of steps and data preprocessing. Fuzzy Set Theory plays a very important role in classification problems, because the fuzzy approach can capture the structure of the image. Most concepts are fuzzy in nature. Fuzzy sets allow to deal with uncertain and imprecise data. Many classification problems are formalized by using fuzzy concepts, because crisp classes represent an oversimplification of reality, leading to wrong results of classification. Fuzzy Set Theory is an important mathematical tool to process complex and fuzzy da-ta. This theory is suitable for high resolution remote sensing image classification. Fuzzy sets and fuzzy numbers are used to determine basic probability assignment. Fuzzy numbers are used for detection of the optimal number of clusters in Fuzzy Clustering Methods. Image is modeled as a fuzzy graph, when we represent the dissimilitude between pixels in some classification tasks. Fuzzy sets are also applied in different tasks of processing digital optical images. It was noted, that fuzzy sets play an important role in analysis of results of classification, when different agreement measures between the reference data and final classification are considered. In this work arithmetic operations of fuzzy numbers using alpha-cut method were considered. Addition, subtraction, multiplication, division of fuzzy numbers and square root of fuzzy number were described in this paper. Moreover, it was illustrated examples with different arithmetic operations of fuzzy numbers. Fuzzy Set Theory and fuzzy numbers can be applied for analysis and classification of hyperspectral satellite images, solving ecological tasks, vegetation clas-sification, in remote searching for minerals.

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