No abstract

While the international lockdown for the COVID-19 pandemic has greatly influenced the global economy, we are still confronted with the dilemma about the economy recession when the stock market hits record highs repeatedly. As we know, since portfolio selection is often affected by many non-probabilistic factors, it is of not easiness to obtain the precise probability distributions of the return rates. Therefore, fuzzy portfolio model is proposed for solving the efficient portfolio when the economy environment remains in vagueness for the future. To manage such an investment, we revise the Chen and Tsaur’s fuzzy portfolio model by using fuzzy goal programming model. Then, two numerical examples are illustrated by the proposed model which shows that the portfolio selection can be solved by the linguistic imprecise goal of the expected return. With different linguistic descriptions for the imprecise goal of expected return for the future stock market, the optimal portfolio selection that can be solved under different investment risks which is considered better than Chen and Tsaur’s model in real world situations. The sensitivity analysis with some parameter groups can be provided for more invested risk selection in the portfolio analysis.

Based on the concept of high returns as the preference to low returns, this study discusses the adjustable security proportion for excess investment and shortage investment based on the selected guaranteed return rates in a fuzzy environment, in which the return rates for selected securities are characterized by fuzzy variables. We suppose some securities are for excess investment because their return rates are higher than the guaranteed return rates, and the other securities whose return rates are lower than the guaranteed return rates are considered for shortage investment. Then, we solve the proposed expected fuzzy returns by the concept of possibility theory, where fuzzy returns are quantified by possibilistic mean and risks are measured by possibilistic variance, and then we use linear programming model to maximize the expected value of a portfolio’s return under investment risk constraints. Finally, we illustrate two numerical examples to show that the expected return rate under a lower guaranteed return rate is better than a higher guaranteed return rates in different levels of investment risks. In shortage investments, the investment proportion for the selected securities are almost zero under higher investment risks, whereas the portfolio is constructed from those securities in excess investments.

Fuzzy portfolio selection has resulted in many researchers to focus on this field. Based on the risk attitudes, this study discusses the risk attitudes in a decision group for portfolio selection. Therefore, we adopt the risk attitudes to describe the experts’ risk preferences and subjective judgments, and then we suppose that the risk seeker considers a higher return for an excess investment based on the selected guaranteed rate of return; the risk averter considers a shortage in investment for the securities whose return rates are smaller than the selected guaranteed rate of return; and finally, the risk neutral pursues the regular return rate. In order to solve the multi-objective return rate functions under the corresponding investment risks, the SMART-ROC weighting method is used to hybridize the multi-objective programming model to a linear programming model for solving the portfolio selection. Finally, we illustrate a numerical example and two risk scenarios to show the optimal portfolio selection under different investment risks. The results show that the proposed model can obtain a more robust portfolio than the compared models under different risk priorities in a decision group.

In this era of information explosion, smartphones have become a necessary device in our daily life. In order to select a better smartphone, most users try to collect more attributes to help them purchase their own smartphones, including the brand image from the advertisements, features from the specifications, word-of-mouth from their peers, and the average sales from some secondary data webs. In order to assist the users to evaluate the brand performance from the market attributes, in this paper, we selected nine smartphone brands and used multi-criteria decision-making methods to rank the smartphones’ functions. We first use TOPSIS to evaluate word-of-mouth, together with average sales collected from the website of each brand, and the brand image obtained by the use of questionnaires. Finally, we summarize the final rankings of these smartphone brands. The brand performance analysis shows that our proposed hybrid method can significantly derive the overall rankings of smartphone brands.

Fuzzy portfolio models have received many researchers’ focus on the issue of risk preferences. The portfolio based on guaranteed return rates has been developing and considering the dimension of excess investment for the investors in different risk preferences. However, not only excess investment but also shortage investment to the selected portfolio should be considered for risk preferences, including risk-seeking, risk-neutral, and risk-averse, by different degrees of dimensions in excess investment and shortage investment. A comparison to the degree of dimensions for the excess investment and shortage investment indicates that a risk-seeker would like to have excess investment for securities whose return rates are bigger than the guaranteed return rates and shortage investment for securities whose return rates are smaller than the guaranteed return rates. Finally, we present three experiments to illustrate the proposed model. The results show that the different risk preferences derive different fuzzy portfolio selections under s and t dimensions, where a lower value of s is suggested for a risk-seeker as t > s, and we suggest the values of s and t to be smaller than or equal to 3. By contrast, for the risk-neutral investor, we suggest s = t; t < s is suggested to the investor who is risk-averse.