Application of Ordered Fuzzy Numbers in a New OFNAnt Algorithm Based on Ant Colony Optimization

Paprzycki

2017

Self Cite

The chapter includes a hybrid concept combining bee colony optimization with the application of Ordered Fuzzy Numbers. This is another research, after the OFNAnt method, prepared in AIRlab -Artificial Intelligence and Robotics Laboratory at Kazimierz Wielki University in Bydgoszcz, in which authors enriched metaheuristics by implementing the arithmetics of Ordered Fuzzy Numbers (OFNs). Applied fuzzy observation enabled very faithful modeling of the navigation mechanism used by bees when orienting with reference to the position of the sun. Experiments aimed at verification of the developed concept have been carried out on a set of several commonly known benchmarks. The preliminary results of experiments allow us to nurture grounded hope that further modifications of the metaheuristics using OFN arithmetics shall enable smooth control of the optimization criteria of the tested phenomena.

Section: Selected Ofn Issuesmentioning

confidence: 99%

A New OFNBee Method as an Example of Fuzzy Observance Applied for ABC Optimization

Ewald

Paprzycki

2017

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“…Then visualizations T and W demonstrate declines from the local peak. As the chart above may not be unambiguous in terms of the trend interpretation the authors introduce the logic of Ordered Fuzzy Numbers [14,24,30] in order to interpret the quotations. Table 11.2 shows the OFN characteristic points with the Nasdaq Composite quotation parameters as listed in Table 11.2.…”

Section: Application Of Ofn Notation For the Fuzzy Observation Of Nasmentioning

confidence: 99%

“…In comparison to existing methods, more accurate forecasting methods can be obtained using a rule-based forecasting (RBF), a technique combining data extrapolation [7,13,14,25,26,[43][44][45], time series [28,29,44,45], and elements of expert systems [5-7, 22, 23, 34, 37, 46]. The four most important methods of extrapolation were used: linear regression, random walk, and Brown's exponential smoothing, as well as Holt's exponential smoothing.…”

Section: Introductionmentioning

confidence: 99%

Detecting Nasdaq Composite Index Trends with OFNs

Zarzycki

Dobrosielski

2017

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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.

“…Through years of development of fuzzy logic, many researchers have been developing methods of comparing sets and fuzzy numbers. Among them, it is impossible not to recall that several fuzzy number comparison methods and indices have been researched since 1977 by Zadeh [12], Yager [10,11], Kaufman [14,15], Chang [5], and Amado [1]. Bortolan and Degani [5] and Dadgostar [1] reviewed some of the methods for ranking fuzzy sets, including Yager's first, second, and third indexes, Chang's algorithm, Adamo's method, Baas and Kwakernaak's method [2], Baldwin and Guild's method [3], Kerre's method [9], Jain's method [7,8], and Dubois and Prade's four grades [6] of dominance (PD, PSD, ND, NSD).…”

Section: Introductionmentioning

confidence: 99%

Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes

Dobrosielski

Filipowicz

2017

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This chapter concerns an issue of comparing fuzzy numbers. The relationship of similarity is probably the most widely used and most difficult to determine the measure of compliance precisely. Analysis of the similarity between two objects is an essential tool in biology, taxonomy, and psychology, and is the basis for reasoning by analogy. This chapter describes methods for determining the similarity used in fuzzy logic. Many of them were dedicated only to triangular or trapezoidal fuzzy numbers. This was a computing inconvenience and raised the question about the axiological basis for such comparisons. The authors have proposed two new approaches to comparing fuzzy numbers using one of the known fuzzy number extensions that are Ordered Fuzzy Numbers (OFNs). This has allowed us to simplify operations and eliminate said dualism. Two order-sensitive defuzzification methods are presented in the chapter. For OFN numbers with positive order (compliant with the direction of the OX axis increase) the results of defuzzifications are results for numbers of different notations, for example, L-R, whereas for numbers with negative orders, the defuzzification result changes. An important part of the chapter is a catalogue of the shapes of numbers in OFN notation. This is probably the first summary of basic shapes of those numbers with the results of defuzzifications using several methods.