Fuzzy real option analysis in patent related decision making and patent valuation

The shift towards a knowledge-based economy has inevitably prompted the evolution of patent exploitation. Nowadays, patent is more than just a prevention tool for a company to block its competitors from developing rival technologies, but lies at the very heart of its strategy for value creation and is therefore strategically exploited for economic pro t and competitive advantage. Along with the evolution of patent exploitation, the demand for reliable and systematic patent valuation has also reached an unprecedented level. However, most of the quantitative approaches in use to assess patent could arguably fall into four categories and they are based solely on the conventional discounted cash flow analysis, whose usability and reliability in the context of patent valuation are greatly limited by five practical issues: the market illiquidity, the poor data availability, discriminatory cash-flow estimations, and its incapability to account for changing risk and managerial flexibility. This dissertation attempts to overcome these impeding barriers by rationalizing the use of two techniques, namely fuzzy set theory (aiming at the first three issues) and real option analysis (aiming at the last two). It commences with an investigation into the nature of the uncertainties inherent in patent cash flow estimation and claims that two levels of uncertainties must be properly accounted for. Further investigation reveals that both levels of uncertainties fall under the categorization of subjective uncertainty, which differs from objective uncertainty originating from inherent randomness in that uncertainties labelled as subjective are highly related to the behavioural aspects of decision making and are usually witnessed whenever human judgement, evaluation or reasoning is crucial to the system under consideration and there exists a lack of complete knowledge on its variables. Having clarified their nature, the application of fuzzy set theory in modelling patent-related uncertain quantities is effortlessly justified. The application of real option analysis to patent valuation is prompted by the fact that both patent application process and the subsequent patent exploitation (or commercialization) are subject to a wide range of decisions at multiple successive stages. In other words, both patent applicants and patentees are faced with a large variety of courses of action as to how their patent applications and granted patents can be managed. Since they have the right to run their projects actively, this flexibility has value and thus must be properly accounted for. Accordingly, an explicit identification of the types of managerial flexibility inherent in patent-related decision making problems and in patent valuation, and a discussion on how they could be interpreted in terms of real options are provided in this dissertation. Additionally, the use of the proposed techniques in practical applications is demonstrated by three fuzzy real option analysis based models. In particular, the pay-of method and the extended fuzzy Black-Scholes model are employed to investigate the profitability of a patent application project for a new process for the preparation of a gypsum-fibre composite and to justify the subsequent patent commercialization decision, respectively; a fuzzy binomial model is designed to reveal the economic potential of a patent licensing opportunity.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. Even mathematicians like H. Poincare worried about this. He observed that mathematical models are over idealizations, for instance, he said that only in Mathematics, equality is a transitive relation. A first attempt to save this situation was perhaps given by K. Menger in 1951 by introducing the concept of statistical metric space in which the distance between points is a probability distribution on the set of nonnegative real numbers rather than a mere nonnegative real number. Other attempts were made by M.J. Frank, U. Hbhle, B. Schweizer, A. Sklar and others. An aspect in common to all these approaches is that they model impreciseness in a probabilistic manner. They are not able to deal with situations in which impreciseness is not apparently of a probabilistic nature. This thesis is confined to introducing and developing a theory of fuzzy semi inner product spaces.

A study on fuzzy semi inner product spaces

Mathematical models are often used to describe physical realities. However, the physical realities are imprecise while the mathematical concepts are required to be precise and perfect. The 1st chapter give a brief summary of the arithmetic of fuzzy real numbers and the fuzzy normed algebra M(I). Also we explain a few preliminary definitions and results required in the later chapters. Fuzzy real numbers are introduced by Hutton,B [HU] and Rodabaugh, S.E[ROD]. Our definition slightly differs from this with an additional minor restriction. The definition of Clementina Felbin [CL1] is entirely different. The notations of [HU]and [M;Y] are retained inspite of the slight difference in the concept.the 3rd chapter In this chapter using the completion M'(I) of M(I) we give a fuzzy extension of real Hahn-Banch theorem. Some consequences of this extension are obtained. The idea of real fuzzy linear functional on fuzzy normed linear space is introduced. Some of its properties are studied. In the complex case we get only a slightly weaker analogue for the Hahn-Banch theorem, than the one [B;N] in the crisp case

The real number system,

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Aplicação da Lógica Fuzzy para avaliação do faturamento do consumo de energia elétrica e demanda de uma empresa de avicultura de postura

Pós-graduação em Agronomia (Energia na Agricultura) - FCA

Multi-argument fuzzy measures on lattices of fuzzy sets

In this paper, we axiomatically introduce fuzzy multi-measures on bounded lattices. In particular, we make a distinction between four different types of fuzzy set multi-measures on a universe X, considering both the usual or inverse real number ordering of this lattice and increasing or decreasing monotonicity with respect to the number of arguments. We provide results from which we can derive families of measures that hold for the applicable conditions in each case.

Generalizações do conceito de distância, i-distâncias, distâncias intervalares e topologia

In this dissertation we present some generalizations for the concept of distance by using more general value spaces, such as: fuzzy metrics, probabilistic metrics and generalized metrics. We show how such generalizations may be useful due to the possibility that the distance between two objects could carry more information about the objects than in the case where the distance is represented just by a real number. Also in this thesis we propose another generalization of distance which encompasses the notion of interval metric and generates a topology in a natural way. Several properties of this generalization are investigated, and its links with other existing generalizations

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Desenvolvimento e aplicação do índice de desempenho energético da iluminação pública utilizando lógica nebulosa: estudo de caso da Cidade Universitária \"Armando de Salles Oliveira\" da Universidade de São Paulo.

A eficiência e a racionalidade energética da iluminação pública têm relevante importância no sistema elétrico, porque contribui para diminuir a necessidade de investimentos na construção de novas fontes geradoras de energia elétrica e nos desperdícios energéticos. Apresenta-se como objetivo deste trabalho de pesquisa o desenvolvimento e aplicação do IDE (índice de desempenho energético), fundamentado no sistema de inferência nebulosa e indicadores de eficiência e racionalidade de uso da energia elétrica. A opção em utilizar a inferência nebulosa deve-se aos fatos de sua capacidade de reproduzir parte do raciocínio humano, e estabelecer relação entre a diversidade de indicadores envolvidos. Para a consecução do sistema de inferência nebulosa, foram definidas como variáveis de entrada: os indicadores de eficiência e racionalidade; o método de inferência foi baseado em regras produzidas por especialista em iluminação pública, e como saída um número real que caracteriza o IDE. Os indicadores de eficiência e racionalidade são divididos em duas classes: globais e específicos. Os indicadores globais são: FP (fator de potência), FC (fator de carga) e FD (fator de demanda). Os indicadores específicos são: FU (fator de utilização), ICA (consumo de energia por área iluminada), IE (intensidade energética) e IL (intensidade de iluminação natural). Para a aplicação deste trabalho, foi selecionada e caracterizada a iluminação pública da Cidade Universitária \"Armando de Salles Oliveira\" da Universidade de São Paulo. Sendo assim, o gestor do sistema de iluminação, a partir do índice desenvolvido neste trabalho, dispõe de condições para avaliar o uso da energia elétrica e, desta forma, elaborar e simular estratégias com o objetivo de economizá-la.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

On the minimality of the p-harmonic map - x/vertical bar x vertical bar : B-n -> Sn-1

We prove that for any real number p with 1 p less than or equal to n - 1, the map x/\x\ : B-n --> Sn-1 is the unique minimizer of the p-energy functional integral(Bn) \delu\(p) dx among all maps in W-1,W-p (B-n, Sn-1) with boundary value x on phiB(n).

HTLV-1/2 seroprevalence and coinfection rate in Brazilian first-time blood donors: an 11-year follow-up

The seroprevalence and geographic distribution of HTLV-1/2 among blood donors are extremely important to transfusion services. We evaluated the seroprevalence of HTLV-1/2 infection among first-time blood donor candidates in Ribeirão Preto city and region. From January 2000 to December 2010, 1,038,489 blood donations were obtained and 301,470 were first-time blood donations. All samples were screened with serological tests for HTLV-1/2 using enzyme immunoassay (EIA). In addition, the frequency of coinfection with hepatitis B virus (HBV), hepatitis C virus (HCV), human immunodeficiency virus (HIV), Chagas disease (CD) and syphilis was also determined. In-house PCR was used as confirmatory test for HTLV-1/2. A total of 296 (0.1%) first-time donors were serologically reactive for HTLV-1/2. Confirmatory PCR of 63 samples showed that 28 were HTLV-1 positive, 13 HTLV-2 positive, 19 negative and three indeterminate. Regarding HTLV coinfection rates, the most prevalent was with HBV (51.3%) and HCV (35.9%), but coinfection with HIV, CD and syphilis was also detected. The real number of HTLV-infected individual and coinfection rate in the population is underestimated and epidemiological studies like ours are very informative.

Caracterização das Comunidades Subtidais de Macroinvertebrados Bentónicos de Substrato Rochoso da Ilha de São Vicente, Cabo Verde

The Cape Verde Archipelago location and its biogeographical features are of special interest for Marine Ecology. However, there’s a lack of knowledge regarding the composition of the coastal ecosystems in this region, especially about benthic macroinvertebrates subtidal communities. Between August and October of 2007, eight locations around the island of São Vicente were sampled. Within each of those spots, fragments of substratum were collected and throughout the processing of the collected data, a total of 4032 individuals were counted, which belong to 81 different species. Shannon’s Entropy and Gini-Simpson’s diversity index were calculated, as the real number of species each one represented. By comparing the results, differences between sampling stations and between indices within the same sampling station were found. With the purpose of clustering the sampled locations according to the number of collected organisms by species, a dendrogram was elaborated and a principal component analysis was carried out. The considered sampling stations didn’t reveal significant differences according to the composition of their benthic macroinvertebrates subtidal communities in terms of great taxonomic groups or functional groups. It’s assumed that they differ only by minute traits.

Riesz-Nágy singular functions revisited

In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their example was built as the limit of a sequence of deformations of the identity function. As an easy consequence of the definition, the derivative, when it existed and was finite, was found to be zero. In this paper we revisit the Riesz-N´agy family of functions and we relate it to a system for real numberrepresentation which we call (t, t-1) expansions. With the help of these real number expansions we generalize the family. The singularity of the functions is proved through some metrical properties of the expansions used in their definition which also allows us to give a more precise way of determining when the derivative is 0 or infinity.

A new light on Minkowski's? $(x)$ function

The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ?$(x)$ is clearly proved in two ways: by exhibiting a set of measure one in which ?ï$(x)$ = 0; and again by actually finding a set of measure one which is mapped onto a set of measure zero and viceversa. These sets are described by means of metrical properties of different systems for real number representation.