On Algebraic Operations on Fuzzy Numbers

Kosiński, Witold; Prokopowicz, Piotr; Ślęzak, Dominik

doi:10.1007/978-3-540-36562-4_37

Cited by 55 publications

(30 citation statements)

References 6 publications

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“…Ordered Fuzzy Candlesticks are Ordered Fuzzy Numbers, hence, thanks to their welldefined arithmetic [1,4,13] can be used to construct a fuzzy version of technical analysis indicators such as the simple moving average.…”

Section: Ordered Fuzzy Technical Analysis Indicatorsmentioning

confidence: 99%

Ordered Fuzzy Candlesticks

Marszałek

Burczyński

2017

Theory and Applications of Ordered Fuzzy Numbers

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The purpose of this chapter is to present how Ordered Fuzzy Numbers (OFNs) can be used with financial high-frequency time series. Considering this approach the financial data are modeled using OFNs called further ordered fuzzy candlesticks. Their use allows modeling uncertainty associated with financial data and maintaining more information about price movement at an assumed time interval than compared to commonly used price charts (e.g., Japanese Candlestick chart). Furthermore, in a simple way, it is possible to include the information about volume and the bid-ask spread. Thanks to the well-defined arithmetic of OFNs, one can be used in technical analysis or to construct models of fuzzy time series in the form of classical equations. Examples of an ordered fuzzy moving average indicator and ordered fuzzy autoregressive process are presented. IntroductionHigh-frequency financial data are observations on financial variables such as quotations of shares, futures, or currency pairs, quoted daily or at a finer timescale. Data containing the most complete knowledge about quotations of the financial instrument are prices corresponding to each single transaction made on this instrument.

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Section: Ordered Fuzzy Technical Analysis Indicatorsmentioning

confidence: 99%

Ordered Fuzzy Candlesticks

Marszałek

Burczyński

2017

Theory and Applications of Ordered Fuzzy Numbers

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“…Main concepts of the idea of Kosinski's Fuzzy Numbers were introduced and developed in the series of papers [15], [4], [5], [6], [13], [16], [14]. As it is an unusual model of imprecise information, before introducing a formal definition, it will be useful to clarify a background of concept.…”

Section: Kosinski's Fuzzy Number (Kfn)mentioning

confidence: 99%

“…An alternative solution is the Kosinski's Fuzzy Numbers mathematical model [4], [5]. This model takes into account the order of the characteristic parts of a fuzzy number giving the fuzzy number an additional feature -direction.…”

Section: Introductionmentioning

confidence: 99%

Analysis of the Changes in Processes Using the Kosinski's Fuzzy Numbers

Prokopowicz¹

2016

Annals of Computer Science and Information Systems

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Abstract-This paper presents the analysis of potential of the Kosinski's Fuzzy Number (KFN) idea in the modeling trends of the processes which are described imprecisely. KFNs conception is an alternative for the classical fuzzy numbers ideas as model to represent of the imprecise quantitative data. They introduces new feature into vagueness of the information -a direction. It is base for good arithmetical properties of calculations. Furthermore, a direction also extends a potential in the modeling of information by the additional interpretation, what is a subject of this article. This new potential is presented and explained basing on the example of modeling of quantity of liquid in a reservoir. The environment is changing dynamically what is described as the changes in inflow and outflow. Proposed example explains how to interpret the direction of KFN and how to understand the results of calculations and its influence.

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“…Several operations performed on given L-R numbers can result in numbers that are too broad and as a result they can become less useful. Solving equations using conventional operations on fuzzy numbers [7] is usually impossible either. An A + X = C equation can always be solved using conventional operations on fuzzy numbers only when A is a real number.…”

Section: Introductionmentioning

confidence: 99%

“…First attempts to redefine new operations on fuzzy numbers were undertaken at the beginning of the 1990-ties by Witold Kosiński and his PhD student -P. SŞysz [8]. Further studies of W. Kosiński published in cooperation with P. Prokopowicz and D.Ślęzak [9], [7], [10] led to introduction of the ordered fuzzy numbers model -OFN. We call f and g the up and down-parts of the fuzzy number A, respectively.…”

Section: Introductionmentioning

confidence: 99%

Representation of a trend in OFN during fuzzy observance of the water level from the crisis control center

Czerniak¹,

Dobrosielski²,

Apiecionek³

et al. 2015

Annals of Computer Science and Information Systems

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Abstract-This paper presents the issue of fuzzy arithmetic calculations in two different notations. The well-known L-R notation proposed by Dubois-Prade, which enjoys a well-earned recognition of the researchers dealing with fuzzy logic was presented on one hand. On the other hand, a OFN notation introduced by Kosiński was discussed. Comparative calculations were performed using the data of the benchmark "Dam and Crisis control center paradox". That benchmark is available in two versions, where the opposite trend is visible at the dam and at the CCC (Crisis control center). In one of the versions, the water level at the observed area decreases and increases at the dam, while in the other version the situation is opposite. The trend difference detection can aid the short-term forecast of the situation change at the monitored area. Results of the applied calculations in OFN notation show that this arithmetic is sensitive to trend differences related to the order characteristic for those numbers. Relationship between the fuzzy logic and the trend of the observed phenomena is an added value to the generalization of OFN and it is also a good signal for the future development of applications of such fuzzy calculations, being their unique feature at the same time.

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On Algebraic Operations on Fuzzy Numbers

Cited by 55 publications

References 6 publications

Ordered Fuzzy Candlesticks

Ordered Fuzzy Candlesticks

Analysis of the Changes in Processes Using the Kosinski's Fuzzy Numbers

Representation of a trend in OFN during fuzzy observance of the water level from the crisis control center

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