Fuzzy Reals with Algebraic Operations: Algorithmic approach

Kosiński, Witold; Prokopowicz, Piotr; Ślęzak, Dominik

doi:10.1007/978-3-7908-1777-5_33

Cited by 53 publications

(46 citation statements)

References 3 publications

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“…Many of them are unattractive due to their complicated structure. An interesting alternative to describing the phenomenon of the trend is the application of fuzzy numbers and fuzzy logic [4,10,11,31,32]. The chapter presents Ordered Fuzzy Numbers, which use five specific index parameters as well as index analysis methods to identify the occurrence of a trend.…”

Section: Discussionmentioning

confidence: 99%

Detecting Nasdaq Composite Index Trends with OFNs

Zarzycki

Czerniak

Dobrosielski

2017

Theory and Applications of Ordered Fuzzy Numbers

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The chapter presents a novel way of describing changes in the stock index and the identification of potential trends. The authors already used a similar approach to describe the stock exchange index [16]; this chapter is a continuation and another application of work on this issue. The method for detecting patterns in a trend by means of linguistic variables is described. The use of computational operations on numbers in the Ordered Fuzzy Number (OFN) notation [40][41][42] enables us to set the values of linguistic variables and thus conduct fuzzification of the input. By using one OFN number it is possible to store five parameters of index quotations (open, high, low, and close values as well as a change direction). The OFN numbers are conveyed into a linguistic form. In order to find trend sequence similarity the following applies: sequence identity with the input frame expressed as a percentage, frame size, the level of threshold conformity with the frame (threshold), and how often the pattern is present (frequency). A dedicated computer program to detect patterns is implemented. The program used data from the index Nasdaq Composite from the years 2006-2016. The results represent a further step to develop effective methods of rule-based forecasting.

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Section: Discussionmentioning

confidence: 99%

Detecting Nasdaq Composite Index Trends with OFNs

Zarzycki

Czerniak

Dobrosielski

2017

Theory and Applications of Ordered Fuzzy Numbers

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“…Definition 1. By an Ordered Fuzzy Number we understand a pair of functions ( , ) defined on the unit interval [0,1], which are continuous functions (or of bounded variations) [Kosiński et al, 2002;Kosiński et al, 2003, Kosiński, 2006. On OFN, denoted by ℛ (or ℛ ), four algebraic operations have been proposed between fuzzy numbers and crisp (real) numbers, in which component wise operations are present.…”

Section: Discussionmentioning

confidence: 99%

“…Proposed recently by Kosiński and his two co-workers Prokopowicz and Ślęzak [Kosiński et al, 2002, Kosiński et al, 2003, Kosiński, 2006 an extended model of Convex…”

Section: Appendixmentioning

confidence: 99%

Optimizing of a Company’s Cost under Fuzzy Data and Optimal Orders Under Dynamic Conditions

Sobol

Kacprzak

Kosiński³

2014

Optimum

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SummaryThe purpose of this article is to suggest tools of inventory management which would determine economically optimal order quantities. One of them is based on the so-called fixed order quantity model which takes into account several elements of inventory cost, such as ordering cost, transportation and storing cost, frozen capital cost, as well as extra discounts. The tool is based on fuzzy concepts represented by Ordered Fuzzy Numbers. The second tool takes into account the dynamics and works on the basis of replenishment system. This tool can be treated as a kind of controller. Examples of using this tools are presented.

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“…Pojęcie skierowanych liczb rozmytych (w skrócie OFN) zostało wprowadzone przez Kosińskiego i współautorów w serii artykułów [Kosiński, Prokopowicz, Ślęzak, 2002a;2002b;2003;Kosiński, 2006] jako rozszerzenie pojęcia FN. Stąd dowolna OFN powinna być określona jako taki podzbiór rozmyty przestrzeni liczb rzeczywistych ℝ, którego funkcja przynależności spełnia warunki definicji 1. lub definicji 2.…”

Section: Istota I Określenie Skierowanych Liczb Rozmytychunclassified

O pewnych modyfikacjach teorii skierowanych liczb rozmytych

Piasecki

2017

Optimum

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StreszczenieSkierowane liczby rozmyte zostały zdefiniowane w doskonały i intuicyjny sposób przez Witolda Kosińskiego. Z tej przyczyny skierowane liczby rozmyte coraz częściej określa się mianem liczb Kosińskie-go. W pierwszej części tej pracy zaproponowano w pełni sformalizowaną definicję liczby Kosińskiego. Definicję tę następnie uogólniono do przypadku skierowanej liczby rozmytej z nieciągłą funkcją przynależności. Istotną wadą arytmetyki zaproponowanej przez Kosińskiego był brak zamknięcia przestrzeni skierowanych liczb rozmytych ze względu na podstawowe działania arytmetyczne, takie jak: dodawanie, odejmowanie, mnożenie i dzielenie. Głównym celem prezentowanej pracy jest taka modyfikacja działań arytmetycznych, aby przestrzeń liczb Kosińskiego była zamknięta z racji zmodyfikowanych działań arytmetycznych. Słowa kluczowe: skierowane liczby rozmyte, arytmetyka ON CERTAIN MODIFICATIONS OF ORDERED FUZZY NUMBERS THEORY SummaryOrdered fuzzy numbers have been defined in an excellent, intuitive way by Witold Kosiński. For this reason, they are increasingly referred to as Kosiński's numbers. A fully formalized definition of a Kosiński's number is proposed in the first part of this work. This definition is generalized so as to fit an ordered fuzzy number with an upper semi-continuous membership function. A significant drawback of Kosiński's arithmetic is that the space of ordered fuzzy numbers is not closed under addition, subtraction, multiplication, or division. The main aim of this paper is to modify the arithmetic in such a way that the space of ordered fuzzy numbers is closed under the modified arithmetic operations.

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Fuzzy Reals with Algebraic Operations: Algorithmic approach

Cited by 53 publications

References 3 publications

Detecting Nasdaq Composite Index Trends with OFNs

Detecting Nasdaq Composite Index Trends with OFNs

Optimizing of a Company’s Cost under Fuzzy Data and Optimal Orders Under Dynamic Conditions

O pewnych modyfikacjach teorii skierowanych liczb rozmytych

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