This master thesis deals with the use of fuzzy logic to evaluate the quality customers of the company TILL Ltd. The evaluation is done using Microsoft EXCEL and MathWorks MATLAB, using the main attributes and characteristics of customers. The thesis results are clear and functional fuzzy models that can be used to effectively evaluate potential and existing customers.

Master’s thesis deals with the evaluation and selection of suppliers of products and services for the company Momedica, s.r.o. using fuzzy logic. The resulting fuzzy system will serve as a decision support instrument of company.

Master's thesis deals with a design of models that allow selection of the most suitable contractor for construction of a company's new branch. Models are based on utilization of basic principles of fuzzy logic. Proposed fuzzy models allow evaluation of individual offers and serve as support in decision-making process.

The thesis deals with the evaluation of investments in intangible fixed assets. The company VIKI, spol. s.r.o. is interested in a new storage space acquisition, and therefore the main objective is to choose the best offer by using fuzzy logic. Evaluation is done in Excel, particularly in the Visual Basic environment and in MATLAB. The output of the thesis is an easy to use form that can be reused for other possible offers.

A fuzzy cognitive map (FCM) is made up of factors and direct impacts. In graph theory, a bipolar weighted digraph is used to model an FCM; its vertices represent the factors, and the arcs represent the direct impacts. Each direct impact is either positive or negative, and is assigned a weight; in the model considered in this thesis, each weight is interpreted as the probability of the impact. A directed walk from factor F to factor F' is interpreted as an indirect impact of F on F'. The probabilistic transitive closure (PTC) of an FCM (or bipolar weighted digraph) is a bipolar weighted digraph with the same set of factors, but with arcs corresponding to the indirect impacts in the given FCM. Fuzzy cognitive maps can be used to represent structured knowledge in diverse fields, which include science, engineering, and the social sciences. In [P. Niesink, K. Poulin, M. Sajna, Computing transitive closure of bipolar weighted digraphs, Discrete Appl. Math. 161 (2013), 217-243], it was shown that the transitive closure provides valuable new information for its corresponding FCM. In particular, it gives the total impact of each factor on each other factor, which includes both direct and indirect impacts. Furthermore, several algorithms were developed to compute the transitive closure of an FCM. Unfortunately, computing the PTC of an FCM is computationally hard and the implemented algorithms are not successful for large FCMs. Hence, the Reduction-Recovery Algorithm was proposed to make other (direct) algorithms more efficient. However, this algorithm has never been implemented before. In this thesis, we code the Reduction-Recovery Algorithm and compare its running time with the existing software. Also, we propose a new enhancement on the existing PTC algorithms, which we call the Separation-Reduction Algorithm. In particular, we state and prove a new theorem that describes how to reduce the input digraph to smaller components by using a separating vertex. In the application part of the thesis, we show how the PTC of an FCM can be used to compare different standpoints on the issue of work-integrated learning.

With large-scale implementation of drones having begun and numerous companies competing to be among the original players in the market, there lies a large potential for novel drone designs to be created and flown. These novel designs are the ones that were largely ignored in the previous century due to the physical constraints of having a crewed cockpit, but uncrewed aerial vehicles, or UAVs, have opened a floodgate of potential design spaces that may be explored which were previously impossible. The hybrid vertical take-off and landing, VTOL, UAV is one aircraft that presents a potential solution to the classic trade-off of the traditional VTOL's range and endurance limitations versus the fixed wing's required infrastructure. An aircraft known as the Flite Test Spear is used to examine fuzzy logic control and is one such hybrid VTOL that uses large control surfaces and throttle control to maneuver itself for take-offs and landings in a tail-sitting orientation before transitioning to forward, fixed-wing flight. Current flight controllers used in operation on hybrid VTOL aircraft rely on a control law state machine where given a pre-identified aircraft state, the controller enters a transitioning maneuver that takes the aircraft from a VTOL to fixed wing flight regime, or vice versa. Each flight regime is operated by a PID controller with different gains and control input realizations. A modification to this principle is first examined by using fuzzy logic PID gain modification for increased response time and reduced overshoot. Reducing overshoot is of particular interest in this case as, on an aircraft such as this, it has the potential for entering undesirable and unrecoverable states, especially during its transition. Secondly, a mixing of the two flight controllers using a fuzzy logic system was implemented to combine the two controllers' outputs and potentially smooth this transition for safer, more efficient flight. The fuzzy logic controlled mixing of the two VTOL and fixed wing controllers was not proven to provide a more desirable response within the scope of the simulation, however, performed equally as well to that of the current state machine response. The gain scheduling fuzzy systems implemented in the controller have shown to decrease overshoot of the aircraft when given commands to different states, but respond slower than their conventional counterparts. Promise in the reduction of the overshoot error and their lightweight construction leads to the conclusion that implementation on a prototype aircraft would be worthwhile for further testing. / Master of Science / Drones play a larger role in our daily lives than they ever have before. With the work being performed by Google Wing to begin last-mile delivery of household consumer goods to the success of companies like Zipline and Swoop Aero in delivering emergency medical supplies to remote locations in low-resource areas, drones are being increasingly deployed, and their use will continue to grow if current trends continue. Like all burgeoning markets, competition is driving innovation to seek new market sectors and pushing the stagnant players out. In order to distinguish themselves, many companies have been creating their own drones for whichever sector of the drone market they wish to compete in. Whether that be consumer good delivery or aerial imagery, these challenges create numerous problems that some drones handle better than others. This has led to a large investment into the research and development of drones that best suit the needs of whatever mission has to be performed. Drones that act similarly to conventional aircraft such as planes or helicopters may serve as the best solution for a variety of problem statements, but because the need for a pilot in the cockpit is no longer necessary, solutions that were previously impossible to implement due to human factors can now be explored fully. With such an explosion in the design space of drones, the control algorithms needed to operate them must follow suit. This paper attempts to explain an alternative to one of the most common controllers in use today known as the PID. A modification to this controller using a technique known as fuzzy logic is made to increase the performance of experimental drone types without the need of an extensive, costly research and development phase that is necessary for crewed aircraft.

The fuzzy inference system has been tuned and revamped many times over and applied to numerous domains. New and improved techniques have been presented for fuzzification, implication, rule composition and defuzzification, leaving rule aggregation relatively underrepresented. Current FIS aggregation operators are relatively simple and have remained more-or-less unchanged over the years. For many problems, these simple aggregation operators produce intuitive, useful and meaningful results. However, there exists a wide class of problems for which quality aggregation requires nonditivity and exploitation of interactions between rules. Herein, the fuzzy integral, a parametric non-linear aggregation operator, is used to fill this gap. Specifically, recent advancements in extensions of the fuzzy integral to “unrestricted” fuzzy sets, i.e., subnormal and non-convex, makes this now possible. The roles of two extensions, gFI and the NDFI, are explored and demonstrate when and where to apply these aggregations, and present efficient algorithms to approximate their solutions.

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Finalmente, utilizando la noción de jerarquía de conceptos clásica y fuzzy, damos una aplicación a la economía determinando una función de pertenencia asociada al contexto. / In this dissertation, we give the basic notions of fuzzy sets, as presented by Zadeh, and the we study the underlying algebraic structure. This structure, essentially a lattice endowed with a Galois connection formed by a product and a residuation, appears in many forms, according to the properties of the product and its relation to the lattice structure. We present these cases going from the general to the specific, including the one introduced by Zadeh. For these particular cases we analyze the associated logics. We also expand of the concepts of homomorphisms, subalgebras and products of residuated lattices. Finally, using both, the classic and fuzzy notions of formal concepts analysis, we give an application to Economic Sciences that helps determine membership functions associated to a context.