REVISITING Xor-IMPLICATIONS: CLASSES OF FUZZY (CO)IMPLICATIONS BASED ON f-Xor (f-XNor) CONNECTIVES

Author(s):  
BENJAMÍN BEDREGAL ◽  
RENATA HAX SANDER REISER ◽  
GRAÇALIZ PEREIRA DIMURO

The main contribution of this paper is the introduction of an intrinsic definition of the connective “fuzzy exclusive or” E (f-Xor E), based only on the properties of boundary conditions, commutativity and partial isotonicity-antitonicity on the the end-points of the unit interval U = [0,1], in a way that the classical definition of the boolean Xor is preserved. We show three classes of the f-Xor E that can be also obtained from the composition of fuzzy connectives, namely, triangular norms, triangular conorms and fuzzy negations. A discussion about extra properties satisfied by the f-Xor E is presented. Additionally, the paper introduces a class of fuzzy equivalences that generalizes the Fodor and Roubens's fuzzy equivalence, and four classes of fuzzy implications induced by the f-Xor E, discussing their main properties. The relationships between those classes of fuzzy implications and automorphisms are explored. The action of automorphisms on f-Xor E is analyzed.

2020 ◽  
Vol 28 (1) ◽  
pp. 121-128
Author(s):  
Adam Grabowski

SummaryWe continue in the Mizar system [2] the formalization of fuzzy implications according to the book of Baczyński and Jayaram “Fuzzy Implications” [1]. In this article we define fuzzy negations and show their connections with previously defined fuzzy implications [4] and [5] and triangular norms and conorms [6]. This can be seen as a step towards building a formal framework of fuzzy connectives [10]. We introduce formally Sugeno negation, boundary negations and show how these operators are pointwise ordered. This work is a continuation of the development of fuzzy sets [12], [3] in Mizar [7] started in [11] and partially described in [8]. This submission can be treated also as a part of a formal comparison of fuzzy and rough approaches to incomplete or uncertain information within the Mizar Mathematical Library [9].


2005 ◽  
Vol 01 (03) ◽  
pp. 329-358 ◽  
Author(s):  
ANA PRADERA ◽  
ENRIC TRILLAS ◽  
ELOY RENEDO

This paper analyzes the main issues involved in the construction of Fuzzy Set Theories. It reviews both standard solutions (based on the well-known triangular norms and conorms) as well as less the conventional proposals that provide alternative views on, for example, the definition of fuzzy connectives or the study of their properties.


2020 ◽  
Vol 79 (Suppl 1) ◽  
pp. 1633.2-1634
Author(s):  
F. Cosan ◽  
O. M. Gedar

Background:Reactive arthritis (ReA) is defined by 1999 ACR criteria as arthritis preceding a bacterial genitourinary (GUS) or gastrointestinal (GIS) infection in 3 days-6 weeks and evidence of triggering infection. Recently, ReA is classified as SpA and patients who do not fulfill SpA criteria are classified as undifferentiated spondyloarthritis (USpA) according to ASAS/EULAR SpA classification criteria.Objectives:In several case reports which are associated with other infective agents are reported and the definition is extended for some clinicians so that SpA which is occurred after any infection is called as ReA. On the other hand, some researchers still accept the classical definition of ReA. The problem with the heterogeneity of opinions and unstandardized definition of ReA hinders studies about pathogenesis and standardization of treatments. In this study, we aimed to determine the spectrum of the use of the definition of reactive arthritis in publications in PubMed between 2009-2019.Methods:The ReA keyword is searched in PubMed for the years between 2009-2019. 248 different publications have been identified and included in this research. 89 articles, 47 reviews, 108 case reports, 2 guidelines, and 2 editorials reviewed for the definition of ReA.Results:Only 42.7% (106 patients) of these publications meet the classical definition which suggests ReA after only GIS and GUS infections. In 4 (1.6%) of the publications ReA was defined after GIS, GUS and oropharyngeal infections; in 3 (1,2%) of the publications after any bacterial infection; in 9 (3.6%) of the publications after any infection. In 8 (3.2%) of the publications, ReA and USPA was used correspondingly. In 39 (15,7%) of the publications the term agent related, ReA was used without making a general definition for ReA. 79 publications (31,9%) have not defined ReA.According to causative agent and ReA relationship, in 64 (24,6%) general infective agents, in 75 (30,2%) classical agents, in 22 (8,9%) other bacterial agents, in 23 (9,3%) streptococcus, in 10(4%) intravesical BCG, in 6 (2.4%) HIV, in 6 (2.4%) tuberculosis, in 12 (4,8%) clostrudium difficle, in 2 (0.8%) parasites were reported. In 31 (12,5%) of the publications the causative agent for the ReA was unknown, the diagnosis was made clinically.Conclusion:In this study, it is aimed to draw attention terminology intricacy and the need for the standardization of the definition of ReA and USpA. It is clear that to standardize the definition of Rea and USpA is necessary. Between 2009-2019 there are reported cases diagnosed as ReA associated with bacterial infections (especially with Clostridium difficile, streptococcus and tuberculosis infections), and viral infections (by a majority with HIV), and parasitic infections. It is not clear if we need to define them classically or define them as USPA. Another important consideration is the necessity of extended laboratory investigations to find out the real causative agent even if the patient is clinically diagnosed with ReA. The requirement of the differentiation between ReA and USpA must be revealed for therapeutic researches.References:[1]A proposal for the classification of patients for clinical and experimental studies on reactive arthritis. Pacheco-Tena C, Burgos-Vargas R, Vázquez-Mellado J, Cazarín J, Pérez-Díaz JA. J Rheumatol. 1999 Jun;26(6):1338-46.[2]The Assessment of SpondyloArthritis International Society classification criteria for peripheral spondyloarthritis and for spondyloarthritis in general. Rudwaleit M, van der Heijde D, Landewé R, Akkoc N, Brandt J, Chou CT, Dougados M, Huang F, Gu J, Kirazli Y, et al. Ann Rheum Dis. 2011;70:25–31.Disclosure of Interests:None declared


Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1388
Author(s):  
Daniele Oboe ◽  
Luca Colombo ◽  
Claudio Sbarufatti ◽  
Marco Giglio

The inverse Finite Element Method (iFEM) is receiving more attention for shape sensing due to its independence from the material properties and the external load. However, a proper definition of the model geometry with its boundary conditions is required, together with the acquisition of the structure’s strain field with optimized sensor networks. The iFEM model definition is not trivial in the case of complex structures, in particular, if sensors are not applied on the whole structure allowing just a partial definition of the input strain field. To overcome this issue, this research proposes a simplified iFEM model in which the geometrical complexity is reduced and boundary conditions are tuned with the superimposition of the effects to behave as the real structure. The procedure is assessed for a complex aeronautical structure, where the reference displacement field is first computed in a numerical framework with input strains coming from a direct finite element analysis, confirming the effectiveness of the iFEM based on a simplified geometry. Finally, the model is fed with experimentally acquired strain measurements and the performance of the method is assessed in presence of a high level of uncertainty.


2018 ◽  
Vol 10 (2) ◽  
pp. 306-323
Author(s):  
Salvatore Tufano

Abstract The present paper suggests that the recurring appeal to kinship diplomacy undermines a fixed idea of ‘nation’ in Archaic Greece, especially in the first two decades of the fifth century BC. It aims to present a series of test cases in Herodotus that explain why contemporary patterns and theories on ancient ethnicity can hardly explain the totality of the historical spectrum. Blood ties could sometimes fortify ethnic relationships, as in the case of Aristagoras’ mission to Sparta (Hdt. 5.49.3), since the common Greekness could elicit the Spartan to help to the Ionians. In other times, the same blood ties were applied to divine genealogies, and they could also be used to show the feeble devotion of cities like Argos to the Greek cause (7.150.2: Xerxes expects the Argives to join the Persian cause, since they descend from Perses). Habits and traditions, often taken as indicia of national feeling, could be thought of as clues of ancient migrations (so the Trojans became Maxyes in Lybia: 4.191). Even language might not help in justifying ethnic relationships: for instance, the Greeks living in the Scythian Gelonus spoke a mixed language (4.108). These few case studies may shed a different light on the classical definition of Greekness (to hellenikon) in terms of blood, language, cults, and habits, all given by Herodotus (8.144). Far from being a valid label for all the Greeks of the fifth century, this statement owes much to a specific variety of the language of kinship diplomacy. The final section argues for the opportunity to avoid the later and misleading idea of nation when studying Herodotus and the age of the Persian Wars, which are instead characterized by various and contrasting strategies. Greek groups and ethne can be better described as networks of lightly defined communities.


2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
M. Conijn ◽  
G. J. Krings

With the help of computational fluid dynamics (CFD), hemodynamics of the pulmonary arteries (PA’s) can be studied in detail and varying physiological circumstances and treatment options can be simulated. This offers the opportunity to improve the diagnostics and treatment of PA stenosis in biventricular congenital heart disease (CHD). The aim of this review was to evaluate the methods of computational studies for PA’s in biventricular CHD and the level of validation of the numerical outcomes. A total of 34 original research papers were selected. The literature showed a great variety in the used methods for (re) construction of the geometry as well as definition of the boundary conditions and numerical setup. There were 10 different methods identified to define inlet boundary conditions and 17 for outlet boundary conditions. A total of nine papers verified their CFD outcomes by comparing results to clinical data or by an experimental mock loop. The diversity in used methods and the low level of validation of the outcomes result in uncertainties regarding the reliability of numerical studies. This limits the current clinical utility of CFD for the study of PA flow in CHD. Standardization and validation of the methods are therefore recommended.


2021 ◽  
Vol 2 ◽  
pp. 20-42
Author(s):  
A.R. Ivanova ◽  
◽  
E.N. Skriptunova ◽  
N.I. Komasko ◽  
A.A. Zavialova ◽  
...  

Dust storm episodes at the aerodromes in the Asian part of Russia / Ivanova A.R., Skriptunova E.N., Komasko N.I., Zavialova A.A.// Hydrometeorological Research and Forecasting, 2021, no. 2 (380), pp. 20-42. According to 2001-2020 METAR data, episodes of dust storms at 26 international aerodromes in the Asian Russia causing poor visibility are studied. The conditions for issuing reports on dust storms, their correspondence to the definition of a dust storm are discussed. It was found that out of 337 reports describing dust transport by strong wind, only 7 episodes registered at the aerodromes of Irkutsk, Abakan, Omsk, and Blagoveshchensk corresponded to the classical definition. The others detected at 15 of 26 aerodromes may be defined as “dust events” – the episodes of dust transfer causing the nonessential visibility reduction. The seasonal variation in such episodes and its connection with changes in visibility are studied. The characteristics of dusty air masses and the direction of their advection are given. Keywords: dust storm, dust events, aerodromes of Asian Russia, seasonal variation, trajectory analysis


2020 ◽  
Vol 57 (2) ◽  
pp. 79-95
Author(s):  
Elena G. Dragalina-Chernaya ◽  

According to Alfred Tarski’s classical definition, logical consequence is necessary and formal. This paper focuses on the question: In what sense (if any) is material consequence a logical relation? For Tarski, material consequence has no modal force. Treating all terms (of a language with a fixed domain) as logical, he reduces logical consequence to material consequence. Thus, Tarskian material consequence seems to be a logical oxymoron designed to emphasize the importance of the distinction between logical and extra-logical terms for the definition of logical consequence. Historically, however, there have been different approaches to material consequences. This paper attempts to provide an investigation into the parallels between Tarski’s dichotomy of formal and material consequence and the modern


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