Axiomatic Theory of Complex Fuzzy Logic and Complex Fuzzy Classes

Complex fuzzy sets, classes, and logic have an important role in applications, such as prediction of periodic events and advanced control systems, where several fuzzy variables interact with each other in a multifaceted way that cannot be represented effectively via simple fuzzy operations such as union, intersection, complement, negation, conjunction and disjunction. The initial formulation of these terms stems from the definition of complex fuzzy grade of membership. The problem, however, with these definitions are twofold: 1) the complex fuzzy membership is limited to polar representation with only one fuzzy component. 2) The definition is based on grade of membership and is lacking the rigor of axiomatic formulation. A new interpretation of complex fuzzy membership enables polar and Cartesian representation of the membership function where the two function components carry uncertain information. Moreover, the new interpretation is used to define complex fuzzy classes and develop an axiomatic based theory of complex propositional fuzzy logic. Additionally, the generalization of the theory to multidimensional fuzzy grades of membership has been demonstrated. In this paper we propose an axiomatic framework for first order predicate complex fuzzy logic and use this framework for axiomatic definition of complex fuzzy classes. We use these rigorous definitions to exemplify inference in complex economic systems. The new framework overcomes the main limitations of current theory and provides several advantages. First, the derivation of the new theory is based on axiomatic approach and does not assume the existence of complex fuzzy sets or complex fuzzy classes. Second, the new form significantly improves the expressive power and inference capability of complex fuzzy logic and class theory. The paper surveys the current state of complex fuzzy sets, complex fuzzy classes, and complex fuzzy logic; and provides an axiomatic basis for first order predicate complex fuzzy logic and complex class theory

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

Fuzzy investment decision support for brownfield redevelopment

Tato disertační práce se zaměřuje na problematiku investování a podporu rozhodování pomocí moderních metod. Zejména pokud jde o analýzu, hodnocení a výběr tzv. brownfieldů pro jejich redevelopment (revitalizaci). Cílem této práce je navrhnout univerzální metodu, která usnadní rozhodovací proces. Proces rozhodování je v praxi komplikován též velkým počet relevantních parametrů ovlivňujících konečné rozhodnutí. Navržená metoda je založena na využití fuzzy logiky, modelování, statistické analýzy, shlukové analýzy, teorie grafů a na sofistikovaných metodách sběru a zpracování informací. Nová metoda umožňuje zefektivnit proces analýzy a porovnávání alternativních investic a přesněji zpracovat velký objem informací. Ve výsledku tak bude zmenšen počet prvků množiny nejvhodnějších alternativních investic na základě hierarchie parametrů stanovených investorem.This dissertation focuses on decision making, investing and brownfield redevelopment. Especially on the analysis, evaluation and selection of previously used real estates suitable for commercial use. The objective of this dissertation is to design a method that facilitates the decision making process with many possible alternatives and large number of relevant parameters influencing the decision. The proposed method is based on the use of fuzzy logic, modeling, statistic analysis, cluster analysis, graph theory and sophisticated methods of information collection and processing. New method allows decision makers to process much larger amount of information and evaluate possible investment alternatives efficiently.

Meta-analysis of stomatitis in clinical studies of everolimus: incidence and relationship with efficacy.

BackgroundEverolimus, an oral mammalian target of rapamycin (mTOR) inhibitor, is used to treat solid tumors and tuberous sclerosis complex (TSC). Stomatitis, an inflammation of the mucous membranes of the mouth, is a common adverse event associated with mTOR inhibitors, including everolimus. We conducted a meta-analysis of data from seven randomized, double-blind phase 3 clinical trials of everolimus to determine the clinical impact of stomatitis on efficacy and safety.Patients and methodsData were pooled from the safety sets of solid tumor [breast cancer (BOLERO-2 and BOLERO-3), renal cell carcinoma (RECORD-1), carcinoid tumors (RADIANT-2), and pancreatic neuroendocrine tumors (RADIANT-3)] and TSC studies (EXIST-1 and EXIST-2). Data from solid tumor trials and TSC trials were analyzed separately.ResultsThe rate of stomatitis was 67% in the solid tumor trials (973/1455 patients) and 70% in the TSC trials (110/157 patients). Most stomatitis events were grade 1/2, with grade 3/4 events reported in only 9% (solid tumor trials) and 8% (TSC trials) of patients. Low TSC patient numbers prevented an in-depth evaluation of stomatitis and response. In the solid tumor trials, most first stomatitis episodes (89%; n = 870) were observed within 8 weeks of starting everolimus. Patients with stomatitis occurring within 8 weeks of everolimus initiation had longer progression-free survival (PFS) than everolimus-treated patients without stomatitis in BOLERO-2 {8.5 versus 6.9 months, respectively; hazard ratio (HR), 0.78 [95% confidence interval (CI), 0.62-1.00]} and RADIANT-3 [13.9 versus 8.3 months, respectively; HR, 0.70 (95% CI, 0.48-1.04)]. A similar trend was observed in RECORD-1 [HR, 0.90 (95% CI, 0.66-1.22)] and RADIANT-2 [HR, 0.87 (95% CI, 0.61-1.22)] but not in BOLERO-3 [HR, 1.01 (95% CI, 0.75-1.36)].ConclusionsStomatitis did not adversely affect PFS, supporting the administration of everolimus in accordance with standard management guidelines

A hierarchical Mamdani-type fuzzy modelling approach with new training data selection and multi-objective optimisation mechanisms: A special application for the prediction of mechanical properties of alloy steels

In this paper, a systematic data-driven fuzzy modelling methodology is proposed, which allows to construct Mamdani fuzzy models considering both accuracy (precision) and transparency (interpretability) of fuzzy systems. The new methodology employs a fast hierarchical clustering algorithm to generate an initial fuzzy model efficiently; a training data selection mechanism is developed to identify appropriate and efficient data as learning samples; a high-performance Particle Swarm Optimisation (PSO) based multi-objective optimisation mechanism is developed to further improve the fuzzy model in terms of both the structure and the parameters; and a new tolerance analysis method is proposed to derive the confidence bands relating to the final elicited models. This proposed modelling approach is evaluated using two benchmark problems and is shown to outperform other modelling approaches. Furthermore, the proposed approach is successfully applied to complex high-dimensional modelling problems for manufacturing of alloy steels, using ‘real’ industrial data. These problems concern the prediction of the mechanical properties of alloy steels by correlating them with the heat treatment process conditions as well as the weight percentages of the chemical compositions

RAPID ANALYTICAL VERIFICATION OF HANDWRITTEN ALPHANUMERIC ADDRESS FIELDS

Microsoft, Motorola, Siemens, Hitachi, IAPR, NICI, IUF This paper presents a combination of fuzzy system and dynamic analytical model to deal with imprecise data derived from feature extraction in handwritten address images which are compared against postulated addresses for address verification. A dynamic building­number locator is able to locate and recognise the building­number, without knowing exactly where the building­number starts in the candidate address line. The overall system achieved a correct sorting rate of 72.9%, 27.1% rejection rate and 0.0% error rate on a blind test set of 450 cursive handwritten addresses.