On a Linguistic Description of Dependencies in Data

Perception-Based Functions in Qualitative Forecasting

“…in [2,3]. In these methods it was supposed that additionally to the rules Here we propose a new method of reconstruction of PBF when the initial value is given by a crisp number (T 0 , Y 0 ) and fuzzification of PBF is produced after concatenation of all crisp shape patterns given in consequents of the rules.…”

“…In this chapter we propose the methods of modeling of expert knowledge and judgments about shapes of functions and time series by fuzzy perception-based function (PBF) [2,3,15,16]. PBF is a fuzzy function obtained as a result of reconstruction of human judgments given by a sequence of rules R k : If T is T k then S is S k , where T k are perceptionbased intervals defined on the domain of independent variable T, and S k are perception-based shape patterns of variable S on interval T k .…”

“…Such reconstruction is based mainly on scaling and granulation of human knowledge. The methods of reconstruction of PBF were developed in the framework of Computational Theory of Perceptions (CTP) and Computing with Words and Perceptions (CWP) [2][3][4][5][15][16][17] dependence based on such rules is considered as a solution of granular initial value problem [3]. Generally boundary conditions or additional information can be defined [4].…”

An approach to the linguistic summarization of time series using a fuzzy quantifier driven aggregation

“…For an example of a language for the representation and extraction of temporal patterns, based on the changes of the first and second derivative, and the analysis of the increasing/decreasing, and convex/concave functions, see, e.g., Stockman, Kanal, Kyle, Yager and Zadrożny, 28 Cheung and Stephanopoulos 29 or Konstantinov and Yoshida. 30 Boyd 31 and Batyrshin and Wagenknecht 25 propose a system-generating linguistic descriptions of time series as IF-THEN rules, with fuzzy intervals as values in the case of the latter work. A rule-based description of times series via linguistic (fuzzy) summaries by using the so-called moving approximation transform is given by Batyrshin et al 26,27 Baldwin et al 32 propose a model time series by using linguistic shape descriptors represented by parametrized functions and use the FRIL system based on evidential reasoning for prediction.…”

Computing with words with the use of inverse RDM models of membership functions

“…The idea of CwW created by Lotfi Zadeh has been presented in scientific journals after 1990 (Zadeh, 1996a;1996b;2004;2006a;2006b;2009, Zadeh and. From the very beginning, CwW has been connected with fuzzy and interval arithmetic (Hansen, 1975;Kaufmann and Gupta, 1991;Piegat, 2001;Hanss, 2005;Tomaszewska, 2014), with granular computing (Batyrshin, 2002;Pedrycz and Gomide, 2007;Aliev et al, 2012;Piegat and Landowski, 2013a), with human-centric computing (Pedrycz and Gomide, 2007), with data mining, database querying and data analysis (Kacprzyk and Zadrożny, 1999;2010;Zadeh and Kacprzyk, 1999;Grzegorzewski and Hryniewicz, 2002;Batyrshin and Wageknecht, 2002), and with plant control (Zhou,676 A. Piegat and M. Pluciński the creator of the CwW idea, formulated many challenge problems.…”