Insight into Fuzzy Modeling

Detection of Structural Breaks in Time Series Using Fuzzy Techniques

“…Their values over the areas characterized by the respective http://doi.org/10.5391/IJFIS.2018.18.1.1 fuzzy sets A k (from the fuzzy partition (1)) are evaluated by a specific evaluative expressions. The procedure, that is based on the theories of F-transform and FNL, is outlined below and in detail described in [6,9]. Note that a similar problem has been discussed also by Kacprzyk et al [35].…”

“…In this paper we suggest to use special "fuzzy" techniques for detection of structural breaks in time series, namely the fuzzy (F)-transform and one method of fuzzy natural logic (FNL). Application of these techniques to the analysis and forecasting of time series was described in several papers and also in the book [6]. The first application of the F-transform to detection of changes in a signal was described in [7] where the problem was to recognize network attacks.…”

Fuzzy Strategic Decision –Making Models Based on Formalized Strategy Maps

“…It must be noted that the equality in formula (6) should be regarded as a fuzzy equality in this case. In this regard, the method of calculating the degree of fuzzy equality may differ: the formulas of Lukasiewicz, Zadeh and others can be used to calculate the fuzzy inclusion measure [24]. The norm of vector W and value dW will be fuzzy.…”

“…In this regard, the fuzzy methods that can be used to formalize the strategy map were considered [21]. It was shown that the fuzzy analytic hierarchy process [22,23] and fuzzy inference method [24] could be used to rank the strategy map elements and simplify the finding of functional dependencies among the strategy map elements using previously proposed methods based on constructing the multicriteria utility functions satisfying certain requirements. A method was also proposed for finding the functional dependencies among the strategy map elements, based on the use of the fuzzy inference database and the Mamdani fuzzy inference method [25].…”

Trend‐cycle Estimation Using Fuzzy Transform and Its Application for Identifying Bull and Bear Phases in Markets

“…Recently, a novel approach to this issue has been introduced using monomial bases that make it possible to compute the components in a way that is simpler than the original one (see Nguyen et al 2017; Holčapek & Nguyen, 2018; Holčapek et al 2018). This simplifies applications of the F‐transform; for applications in time‐series analysis and elsewhere, see, for example, Holčapek and Nguyen (Holčapek & Nguyen, 2016; 2018; Nguyen & Holčapek, 2018) and Novák et al (2016).…”