Our work on regression and classification provides a new contribution to the analysis of time series used in many areas for years. Owing to the fact that convergence could not obtained with the methods used in autocorrelation fixing process faced with time series regression application, success is not met or fall into obligation of changing the models' degree. Changing the models' degree may not be desirable in every situation. In our study, recommended for these situations, time series data was fuzzified by using the simple membership function and fuzzy rule generation technique (SMRGT) and to estimate future an equation has created by applying fuzzy least square regression (FLSR) method which is a simple linear regression method to this data. Although SMRGT has success in determining the flow discharge in open channels and can be used confidently for flow discharge modeling in open canals, as well as in pipe flow with some modifications, there is no clue about that this technique is successful in fuzzy linear regression modeling. Therefore, in order to address the luck of such a modeling, a new hybrid model has been described within this study.In conclusion, to demonstrate our methods' efficiency, classical linear regression for time series data and linear regression for fuzzy time series data were applied to two different data sets, and these two approaches performances were compared by using different measures. SMGRT Yöntemi İle Bulanıklaştırılmış Zaman Serileri İçin Bulanık Doğrusal RegresyonAnahtar Kelimeler Zaman serileri, Doğrusal regresyon, Bulanık doğrusal regresyon, Bulanık en küçük kareler yöntemi, SMRGT yöntemi Özet: Regresyon ve sınıflandırma üzerine yaptığımız bu çalışma, yıllardır birçok alanda kullanılan zaman serileri analizine yeni bir katkı sağlamaktadır. Zaman serileri için regresyon uygulamasında karşılaşılan otokorelasyonun kaldırılması aşamasında çoğu kez ya uyum sağlanamadığından başarıya ulaşılamamakta ya da modelin derecesinin değiştirilmesi zorunluluğuyla karşı karşıya kalınmaktadır. Modelin derecesinin değiştirilmesi ise her zaman istenilen bir durum olmayabilir. Böyle durumlarda kullanılmak üzere önerilen çalışmamızda, zamana bağlı veriler basit üyelik fonksiyonu ve bulanıklık kuralı üretim tekniği (SMRGT) ile bulanıklaştırılmış ve elde edilen değişkenler için bulanık en küçük kareler (Bulanık EKK) modeli ile basit doğrusal regresyon yöntemi uygulanarak geleceğe yönelik tahmine ilişkin bir denklem oluşturulmuştur. SMRGT açık kanallarda debi akışını belirlemede başarılı olmasına ve açık kanallarda debi akışını modellemede güvenle kullanılabilmesine rağmen bu tekniğin bulanık doğrusal regresyon modellemesinde de başarılı olacağı hakkında hiçbir ip ucu yoktur. Bu nedenle bu tür bir modellemenin eksikliği adres gösterilerek yeni bir hibrit model bu çalışma kapsamında tarif edilmiştir. Sonuç olarak yöntemin geçerliliğinin ölçülebilmesi bakımından zaman serileri için doğrusal regresyon ve bulanık zaman serileri için doğrusal regresyon iki ayrı veri setine uygulanmış ve bu iki ya...
In this paper, we introduce an alternative method to calculate the topological entropy of each member of an infinite family of pseudo-Anosov braids on the finitely punctured disk making use of -train tracks The method is based on Thurston's theory of surface homeomorphisms and presents positive matrices alternative to Dynnikov matrices which compute the topological entropy of a given pseudo-Anosov braid.
This study includes free union of a disjoint non-empty collection of topological spaces and research on the disjoint union topology (topological summed). Definitions, theorems and some results for topological summed have been obtained by using the known definitions and theorems for the topological spaces.
<abstract><p>In this work, sums of fuzzy soft topological spaces are defined with free union of a pairwise disjoint non-empty family of fuzzy soft topological spaces. Firstly, we give general information of fuzzy soft topological spaces. Then, we define free union of fuzzy soft topological spaces and disjoint union topology of fuzzy soft topological spaces. We call the free union of a pairwise disjoint non-empty family of fuzzy soft topological spaces the sum of fuzzy soft topological spaces. We show what are the interchangeable properties between fuzzy soft topological spaces and the sum of fuzzy soft topological spaces. For example, there are fuzzy soft interior, fuzzy soft closure, fuzzy soft limit points. Also, we provide some properties showing the relationships between fuzzy soft topological spaces and their sums. Some of these are fuzzy soft base, fuzzy soft sequences, fuzzy soft connected-disconnected, fuzzy soft compact spaces. Also, part of the research for this article is work on fuzzy soft convergence on fuzzy soft topological sum. With this paper, some results, theorems and definitions for fuzzy soft topological sum have been acquired with the help of results, theorems and definitions given in previous studies about fuzzy soft topological spaces.</p></abstract>
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