Defuzzification of groups of fuzzy numbers using data envelopment analysis

Defuzzification is a critical process in the implementation of fuzzy systems that converts fuzzy numbers to crisp representations. Few researchers have focused on cases where the crisp outputs must satisfy a set of relationships dictated in the original crisp data. This phenomenon indicates that these crisp outputs are mathematically dependent on one another. Furthermore, these fuzzy numbers may exist as a group of fuzzy numbers. Therefore, the primary aim of this thesis is to develop a method to defuzzify groups of fuzzy numbers based on Charnes, Cooper, and Rhodes (CCR)-Data Envelopment Analysis (DEA) model by modifying the Center of Gravity (COG) method as the objective function. The constraints represent the relationships and some additional restrictions on the allowable crisp outputs with their dependency property. This leads to the creation of crisp values with preserved relationships and/or properties as in the original crisp data. Comparing with Linear Programming (LP) based model, the proposed CCR-DEA model is more efficient, and also able to defuzzify non-linear fuzzy numbers with accurate solutions. Moreover, the crisp outputs obtained by the proposed method are the nearest points to the fuzzy numbers in case of crisp independent outputs, and best nearest points to the fuzzy numbers in case of dependent crisp outputs. As a conclusion, the proposed CCR-DEA defuzzification method can create either dependent crisp outputs with preserved relationship or independent crisp outputs without any relationship. Besides, the proposed method is a general method to defuzzify groups or individuals fuzzy numbers under the assumption of convexity with linear and non-linear membership functions or relationships

Performance Evaluation of Portfolios with Margin Requirements

In financial markets, short sellers will be required to post margin to cover possible losses in case the prices of the risky assets go up. Only a few studies focus on the optimization and performance evaluation of portfolios in the presence of margin requirements. In this paper, we investigate the theoretical foundation of DEA (data envelopment analysis) approach to evaluate the performance of portfolios with margin requirements from a different perspective. Under the mean-variance framework, we construct the optimization model and portfolio possibility set on considering margin requirements. The convexity of the portfolio possibility set is proved and the concept of efficiency in classical economics is extended to the portfolio case. The DEA models are then developed to evaluate the performance of portfolios with margin requirements. Through the simulations carried out in the end, we show that, with adequate portfolios, DEA can be used as an effective tool in computing the efficiencies of portfolios with margin requirements for the performance evaluation purpose. This study can be viewed as a justification of DEA into performance evaluation of portfolios with margin requirements

Introducing faba bean as a new multi-purpose crop for Northeast U.S.A.

Faba bean is a multi-benefit cool-season grain legume that can be integrated into cropping systems of a shorter-growing season regions such as New England. A comprehensive research study was conducted to explore the ecological, nutritional, medicinal, and financial benefits of faba bean as a new multi-purpose crop for Northeast U.S.A. It was revealed that the faba bean genotypes exhibited dramatic variations in thermal units required to reach various phenological stages. Using phenology, morphology and physiological growth pattern of six faba bean varieties showed that larger seeds and later maturity did not necessarily produced higher yield. Aquadulce, the earliest maturity with medium size seed out-yielded other genotypes thus providing the opportunity for double cropping. When planted in August 1, faba bean accumulated up to 192 kg N ha-1. Nitrogen mineralization from faba bean residues had a better synchrony with sweet corn N uptake in no-till system than conventional tillage system. Sweet corn planted into faba bean residues produced higher ear yield and less unfilled ear tip compared with those grown in no faba bean plots. On average, sweet corn planted into faba bean residues responded positively to applications of supplemental N up to 60 kg ha-1. Averaged over two years, sweet corn after faba bean and 50 kg N ha-1, yielded similarly to those that received 100 kg N ha-1 without faba bean cover crop. Faba bean varieties exhibited considerable variations in their macro- and micronutrient contents. Averaged over six varieties, faba bean seeds contained over 19% protein, 0.76% P, 1.78% K, 0.19% Ca, and 0.20% Mg on dry weight basis. Micronutrients content of seeds were Fe 71, Cu 20, B 25, Mn 16, and Zn 40 mg kg-1. Results also revealed that faba bean leaves and pod walls were also rich in protein, macro and micro nutrients. The results of the experiments suggested that the highest L-Dopa concentration was detected at seedling stage however, to maximize the optimum L-Dopa yield, the crop should be harvested prior to the physiological maturity, roughly 70 days after transplanting. It was concluded that the amount of dry matter produced by faba bean was considerable enough to be grown as a viable source of natural L-Dopa that is comparable with synthetic sources. However, given that total extractable L-Dopa is a function of both concentration and biomass, the highest L-Dopa yield was extracted from mature plants. The highest L-Dopa content was detected in fresh leaves followed by flowers, young pods, mature seeds, and roots. It was concluded that all processing methods reduced the L-Dopa content. Among all tested processing methods, immediate freezing of plant tissues preserved more L-Dopa than oven drying, air drying, and boiling. Plants grown in drought stress condition synthesized higher L-Dopa however, their L-Dopa yield was significantly lower due to producing lower biomass. Supplemental N application did not influence L-Dopa synthesis, however L-Dopa yield increased with increased N rate, primarily because of higher biomass production