On the Suitability of the Bandler–Kohout Subproduct as an Inference Mechanism

Fuzzy relational inference (FRI) systems form an important part of approximate reasoning schemes using fuzzy sets. The compositional rule of inference (CRI), which was introduced by Zadeh, has attracted the most attention so far. In this paper, we show that the FRI scheme that is based on the Bandler-Kohout (BK) subproduct, along with a suitable realization of the fuzzy rules, possesses all the important properties that are cited in favor of using CRI, viz., equivalent and reasonable conditions for their solvability, their interpolative properties, and the preservation of the indistinguishability that may be inherent in the input fuzzy sets. Moreover, we show that under certain conditions, the equivalence of first-infer-then-aggregate (FITA) and first-aggregate-then-infer (FATI) inference strategies can be shown for the BK subproduct, much like in the case of CRI. Finally, by addressing the computational complexity that may exist in the BK subproduct, we suggest a hierarchical inferencing scheme. Thus, this paper shows that the BK-subproduct-based FRI is as effective and efficient as the CRI itself

Forecasting seasonal time series with computational intelligence: on recent methods and the potential of their combinations

Accurate time series forecasting is a key issue to support individual and or- ganizational decision making. In this paper, we introduce novel methods for multi-step seasonal time series forecasting. All the presented methods stem from computational intelligence techniques: evolutionary artificial neu- ral networks, support vector machines and genuine linguistic fuzzy rules. Performance of the suggested methods is experimentally justified on sea- sonal time series from distinct domains on three forecasting horizons. The most important contribution is the introduction of a new hybrid combination using linguistic fuzzy rules and the other computational intelligence methods. This hybrid combination presents competitive forecasts, when compared with the popular ARIMA method. Moreover, such hybrid model is more easy to interpret by decision-makers when modeling trended series.The research was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070). Furthermore, we gratefully acknowledge partial support of the project KON- TAKT II - LH12229 of MSˇMT CˇR

A short note on fuzzy relational inference systems

This paper is a short note contribution to the topic of fuzzy relational inference systems and the preservation of their desirable properties. It addresses the two main fuzzy relational inferences – compositional rule of inference (CRI) and the Bandler–Kohout subproduct (BK-subproduct) – and their combination with two fundamental fuzzy relational models of fuzzy rule bases, namely, the Mamdani–Assilian and the implicative models. The goal of this short note article is twofold. Firstly, we show that the robustness related to the combination of BK-subproduct and implicative fuzzy rule base model was not proven correctly in [24]. However, we will show that the result itself is still valid and a valid proof will be provided. Secondly, we shortly discuss the preservation of desirable properties of fuzzy inference systems and conclude that neither the above mentioned robustness nor any other computational advantages should automatically lead to a preference of the combinations of CRI with Mamdani–Assilian models or of the BK-subproduct with the implicative models

Forecasting seasonal time series with computational intelligence: contribution of a combination of distinct methods

Accurate time series forecasting are important for displaying the manner in which the past contin- ues to affect the future and for planning our day to day activities. In recent years, a large litera- ture has evolved on the use of computational in- telligence in many forecasting applications. In this paper, several computational intelligence techniques (genetic algorithms, neural networks, support vec- tor machine, fuzzy rules) are combined in a distinct way to forecast a set of referenced time series. Fore- casting performance is compared to the a standard and method frequently used in practice.Project DAR 1M0572 of the MŠMT ČR

Multi-step time series prediction intervals using neuroevolution

Multi-step time series forecasting (TSF) is a crucial element to support tactical decisions (e.g., designing production or marketing plans several months in advance). While most TSF research addresses only single-point prediction, prediction intervals (PIs) are useful to reduce uncertainty related to important decision making variables. In this paper, we explore a large set of neural network methods for multi-step TSF and that directly optimize PIs. This includes multi-step adaptations of recently proposed PI methods, such as lower--upper bound estimation (LUBET), its ensemble extension (LUBEXT), a multi-objective evolutionary algorithm LUBE (MLUBET) and a two-phase learning multi-objective evolutionary algorithm (M2LUBET). We also explore two new ensemble variants for the evolutionary approaches based on two PI coverage--width split methods (radial slices and clustering), leading to the MLUBEXT, M2LUBEXT, MLUBEXT2 and M2LUBEXT2 methods. A robust comparison was held by considering the rolling window procedure, nine time series from several real-world domains and with different characteristics, two PI quality measures (coverage error and width) and the Wilcoxon statistic. Overall, the best results were achieved by the M2LUBET neuroevolution method, which requires a reasonable computational effort for time series with a few hundreds of observations.This article is a result of the project NORTE-01- 0247-FEDER-017497, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement, through the European Regional Development Fund (ERDF). We would also like to thank the anonymous reviewers for their helpful suggestionsinfo:eu-repo/semantics/publishedVersio

Interpolativity of at-least and at-most models of monotone fuzzy rule bases with multiple antecedent variables ☆

Of the many desirable properties of fuzzy inference systems, not all are known to co-exist. For instance, a fuzzy inference system should be interpolative, i.e., if a fuzzy set equivalent to one of the antecedent fuzzy sets appears on the input of such a system, the inferred output should be equivalent to the respective consequent fuzzy set. Similarly, the defuzzified output obtained from a system based on a monotone fuzzy rule base should be monotone, i.e., if x,x′x,x′ are crisp inputs to the system that are ordered x≤x′x≤x′, then, the corresponding defuzzified outputs from the system y,y′y,y′ should also be ordered accordingly, i.e., y≤y′y≤y′. However, the particular setting that ensures monotonicity need not simultaneously ensure interpolativity. Recently, Štěpnička and De Baets have investigated and demonstrated the co-existence of the above two properties in the case of fuzzy relational inference systems and single-input-single-output (SISO) rule bases. An extension of these results to the multiple-input-single-output (MISO) case is not straightforward due to the lack of a natural ordering in higher dimensions. In this work, we study the MISO case and show that similar results can be obtained when the monotone rule base is modeled based on at-most and at-least modifiers

Interpolativity of "at least-at most" models of monotone fuzzy rule bases: Multiple-input case

Among the many desirable properties of fuzzy inference systems not all of them are known to co-exist. For instance, a system based on a monotone fuzzy rule base need not be monotonic and interpolative simultaneously. Recently, Štěpnička and De Baets have investigated and shown the co-existence of the above two properties in the case of a fuzzy relational inference systems and the single-input-single-output (SISO) rule bases. An extension of these results to the multiple-input-single-output (MISO) case is not straight-forward owing to the lack of a natural ordering in higher dimensions. In this work, we study the MISO case and show that similar results are available when the monotone rule base is modeled based on at-most and at-least modifiers

Modelling competing theories

We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the context of the formal analysis of the interaction between (competing) scientific theories

Modelling competing theories

We introduce a complete many-valued semantics for two normal lattice-based modal logics. This semantics is based on reflexive many-valued graphs. We discuss an interpretation and possible applications of this logical framework in the context of the formal analysis of the interaction between (competing) scientific theories.Ethics & Philosophy of Technolog