One-Factor ANOVA Model Using Trapezoidal Fuzzy Numbers Through Alpha Cut Interval Method

Most of our traditional tools in descriptive and inferential statistics is based on crispness (preciseness) of data, measurements, random variable, hypotheses, and so on.  By crisp we mean dichotomous that is, yes-or-no type rather than more-or-less type.  But there are many situations in which the above assumptions are rather non-realistic such that we need some new tools to characterize and analyze the problem.  By introducing fuzzy set theory, different branches of mathematics are recently studied.  But probability and statistics attracted more attention in this regard because of their random nature.  Mathematical statistics does not have methods to analyze the problems in which random variables are vague (fuzzy). In this regard, a simple and new technique for testing the hypotheses under the fuzzy environments is proposed.  Here, the employed data are in terms of trapezoidal fuzzy numbers (TFN) which have been transformed into interval data using  interval method and on the grounds of the transformed fuzzy data, the one-factor ANOVA test is executed and decisions are concluded.  This concept has been illustrated by giving two numerical examples. Keywords: Fuzzy set, , Trapezoidal fuzzy number (TFN), Test of hypotheses, One-factor ANOVA model, Upper level data, Lower level data

A confidence set analysis for observed samples: a Fuzzy set approach

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parameter value. In this paper, we provide a confidence set analysis for an observed sample based on fuzzy set theory by using the concept of membership functions. We show that the traditional ad hoc thresholds (the confidence and significance levels) can be attained from a general membership function. The applicability of the newly proposed theory is demonstrated by using well-known examples from the statistical literature and an application in the context of contingency tables.Confidence sets are generally interpreted in terms of replications of an experiment. However, this interpretation is only valid before observing the sample. After observing the sample, any confidence sets have probability zero or one to contain the parame186FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOCNPQ - CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICOFundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)2012/19445-0; 2011/17400-6; 2014/25595-02011/305054-2; 200115/2015-4/PD

Fuzzy logika az agrár- és környezetkutatásokban

A bemutatott tanulmányok alátámasztják MCBRATNEY és ODEH (1997), valamint JETTER és KOK (2014) összegzését, akik a fuzzy modellezés jelenlegi helyzetének részletes értékelése során kifejtették, hogy a fuzzy rendszerek és modellek a jövő fontos kutatási eszközei lehetnek. A „lágy” számítási módszerek a talaj- az, agrár- és a környezettudományok területén egyre nagyobb teret hódítanak meg. Nagy előnyt jelent a bizonytalan, nem vagy nehezen számszerűsíthető adatok használatának és a határvonalak nem éles, kategóriánként eltérő kijelölésének lehetősége. Megfelelő matematikai és interdiszciplináris kutatói hátteret feltételezve egyszerű, gyors és olcsó módszer, amely a hagyományos eljárásoknál pontosabb, és a laikusok által is értelmezhető eredményeket szolgáltat. | The papers presented support the summaries of MCBRATNEY and ODEH (1997) and JETTER and KOK (2014), who stated during the detailed evaluation of the present state of fuzzy modelling, that fuzzy systems and models may be the important research methods of the future. “Soft” computing methods are gaining ever more ground in the field of soil, agricultural and environmental sciences. The possibility of setting boundaries that are not defined as categories with precisely set, distinctive definitions, and of working with data that are not easily quantifiable and insecure presents a great advantage. Provided a satisfactory mathematical and interdisciplinary research background is available, this is a comparatively simple, fast and cost-effective method, which is more exact than conventional ones, and which supplies results that can also be understood by laymen

The Effect of Sill Height on Decay in Air-Seasoning Crossties

The sustainable use of wood for rail ties requires chemical treatment to increase service life and maintain structural integrity. Treatment can only be applied after lengthy air-seasoning to reduce moisture content in wood, but seasoning leaves ties exposed to attack by decay fungi for up to a year. One factor affecting the rate of decay is proximity to soil contact. The height of sills used to raise untreated ties above ground contact while drying is mandated by national standards to be 12 inches, but there is little research examining the effects of deviating from this height on decay risk. This study examined the effects of varying sill height on colonization by decay fungi and flexural properties of black gum and red oak ties. The objective was to relate sill height with populations of decay fungi and to changes in wood strength during air-seasoning. Sampling of blackgum railroad ties from the Koppers plant in Guthrie, Kentucky at three time points during seasoning showed that the incidence of decay fungi increased at an even rate over time with little or no difference attributed to distance of stacks above the ground. Red oak ties sampled three times over 11 months showed that red oak yielded few decay fungi for 6 months followed by a rapid increase in fungal populations. Stacks of red oak and blackgum had completely different fungal populations and colonization rates despite being stored in close proximity. Changes in fungi colonizing ties and their effect on tie properties were not strongly related to height between 6 and 33 inches, and there was no relation to sill heights of 6, 8, or 12 inches. Isolates of decay fungi recovered from ties were evaluated for decay potential and produced a wide range of decay capabilities. Blackgum ties were colonized most by white rot fungi, while red oak ties were colonized by both white rot and brown rot fungi. Many cultures isolated from blackgum had weak decay capabilities. The results indicate that decreasing sill height from 12 to 6 inches had no significant effect on fungal colonization or timber properties of the two species evaluated.Key Words: Railroad ties, crossties, blackgum, red oak, fungal colonization, air-seasoning, decay, decay out of ground-contact

Statistische Tests bei Unschärfe

Statistische Tests beim Vorliegen unscharfer Daten (Fuzzy-Daten) und zum Testen unscharfer Hypothesen werden untersucht. Tests für den (unscharfen) Erwartungswert einer unscharfen Zufallsvariable (Fuzzy-Zufallsvariable) werden konstruiert. Die Gütefunktionen werden zum Vergleich der verschiedenen Tests bestimmt. Die angegebenen Tests sind dabei zum Teil optimal. Es wird aufgezeigt, wann bei Tests für scharfe Daten deren Verunschärfung nicht mit in die Testentscheidung einbezogen werden muss und wann die Einbeziehung zu einer Verbesserung der Testentscheidung führt. Weiter wird gezeigt, wie und wann die Erweiterung der Teststatistik, des P-Wertes und des zum Test gehörigen Konfidenzintervalles zur gleichen unscharfen Testfunktion führen. Beim Testen unscharfer Hypothesen werden klassische Begriffe wie maximale Wahrscheinlichkeit für den Fehler 1.Art zum einen scharf zum anderen unscharf verallgemeinert. Für beide Fälle ist, mit diesen verallgemeinerten Begriffen und unter gewissen Voraussetzungen, ein optimaler Test bestimmbar

Testing fuzzy hypotheses with crisp data

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, D-21400 Kiel W 1084 (8) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Fuzzy p-value in testing fuzzy hypotheses with crisp data

Testing hypotheses, Monotone likelihood ratio, Fuzzy hypothesis, Fuzzy p-value, Fuzzy significance level,