Moments and Semi-Moments for fuzzy portfolios selection

The aim of this paper is to consider the moments and the semi-moments (i.e semi-kurtosis) for portfolio selection with fuzzy risk factors (i.e. trapezoidal risk factors). In order to measure the leptokurtocity of fuzzy portfolio return, notions of moments (i.e. Kurtosis) kurtosis and semi-moments(i.e. Semi-kurtosis) for fuzzy port- folios are originally introduced in this paper, and their mathematical properties are studied. As an extension of the mean-semivariance-skewness model for fuzzy portfolio, the mean-semivariance-skewness- semikurtosis is presented and its four corresponding variants are also considered. We briefly designed the genetic algorithm integrating fuzzy simulation for our optimization models.Fuzzy moments, Credibility theory, Portfolios, Asset allocation, multi-objective optimization

Prediction of pulmonary tuberculosis treatment outcome in a sub‑Saharan African context

Background: Failure to treat many pathogens is a concern. Identifying a priori, patients with potential failure treatment outcome of a disease could allow measures to reduce the failure rate. Objective: The objectives of this study were to use the Scoring method to identify factors associated with the tuberculosis unsuccessful treatment outcome and to predict the treatment outcome. Methods: A total of 1,529 patients with pulmonary tuberculosis were randomly selected in the city of Douala, Cameroon, this sample was randomly split into two parts: one subsample of 1,200 patients (78%) used as the Development sample, and the remaining of 329 patients (22%) used as the Validation sample. Baseline characteristics associated with unsuccessful treatment outcomes were investigated using logistic regression. The optimal score was based on the Youden’s index. Results: HIV positive status, active smoker and non-belief in healing were the factors significantly associated with unsuccessful treatment outcomes (p < 0.05). A model used to estimate the risk of unsuccessful treatment outcome was derived. The threshold probability which maximize the area under the ROC curve was 18%. Patients for whom the risk was greater than this threshold were classified as unsuccessful treatment outcome and the others as successful. HIV positive and active smoking status were associated with death; the non-belief in healing, youth and male gender associated with lost-to-follow-up, TB antecedent and not having TB contact associated with therapeutic treatment failure. Conclusion: To increase the tuberculosis treatment success rate, targeted follow-up could be taken during the treatment for TB patients with previous characteristics

Continuity of utility functions representing fuzzy preferences

In a previous paper, we established necessary and sufficient conditions for a given binary fuzzy relation to be representable by a utility function. In this article, we construct a crisp order topology associated to a given weakly complete fuzzy pre-order and introduce the notion of “continuous fuzzy pre-order.” We show that this new condition and the conditions introduced in the previous paper are together necessary and sufficient for a numerical representation of a given weakly complete fuzzy pre-order by a continuous utility function

Fuzzy Sets and Systems 155 (2005) 372–389 Fuzzy strict preference and social choice

In this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component (indifference) and an asymmetric and regular component (regular fuzzy strict preference). From the above notions, we establish two properties of any regular fuzzy strict preference of a max-∗-transitive fuzzy relation, which are then used to obtain new fuzzy versions of Gibbard’s oligarchy theorem and Arrow’s impossibility theorem

Fuzzy lower partial moment and Mean-risk Dominance: An application for poverty Measurement

A more general concept of risk in economics consists on the chance of getting an income or a return less than a threshold one. Risk has been studied and generalized more earlier by Fishburn [8] through Mean Partial Lower Moment specially when income can be described by a random variable. In this paper, we present a new concept of partial moment, namely Fuzzy Lower Partial Moment (FLPM) based on credibility measure, to quantify risk of getting a return described by a fuzzy variable and we study its properties. Based on FLPM, we introduce mean risk dominance for fuzzy variables, we characterize the dominance for some specific cases and we determine some of its properties. Furthermore, we study the consistency of mean-risk models with respect to first and second order dominances. We display one application of FLPM by introducing a new poverty index for poverty measurement in the context of fuzzy environment and we examine some of its properties

A Binary Intuitionistic Fuzzy Relation: Some New Results, a General Factorization, and Two Properties of Strict Components

We establish, by means of a large class of continuous t-representable intuitionistic fuzzy t-conorms, a factorization of an intuitionistic fuzzy relation (IFR) into a unique indifference component and a family of regular strict components. This result generalizes a previous factorization obtained by Dimitrov (2002) with the (max,min) intuitionistic fuzzy t-conorm. We provide, for a continuous t-representable intuitionistic fuzzy t-norm , a characterization of the -transitivity of an IFR. This enables us to determine necessary and sufficient conditions on a -transitive IFR under which a strict component of satisfies pos-transitivity and negative transitivity

Dynamic Optimal Hedge Ratio Design when Price and Production are stochastic with Jump

International audienceIn this paper, we focus on the farmer's risk income, by using commodity futures, when price and output processes are correlated random represented by jump-diffusion models. We evaluate the expected utility of the farmer's wealth and we determine, at each instant of time, the optimal consumption rate and hedge position at given the time to harvest and state variables. We find a closed form optimal position of consumption and position rate in case of CARA utility investor. This result (see table 1.5) is a generalization of Ho (1984) result who consider the particular case where price and output are diffusion models

On two parametric probability distributions on crisp complete pre-orders

Mallows and Plackett-Luce parametric probability distributions are the two most used and well-known in the set of complete linear orders of a finite universe. In this paper, we extend those two distributions on the set of complete preorders of the universe. For that purpose, by considering a parametric family of metrics on the set of complete pre-orders generalizing Kemeny Distance on pre-orders and Kendall metric on orders, we determine a parametric probability distribution on pre-orders generalizing Mallows Distribution. By considering pre-orders as orders on blocks of equivalent elements, we generalize the Plackett-Luce distribution on complete pre-orders.Keywords: Complete pre-orders; Generalized Mallows distribution; GeneralizedPlackett-Luce distributionAMS 2010 Mathematics Subject Classification: 06A06, 97K50, 91B1