Wei-Guo Zhang

A goal programming model for incomplete interval multiplicative preference relations and its application in group decision-making

In decision making problems, there may be the cases where the decision makers express their judgements by using preference relations with incomplete information. Then one of the key issues is how to estimate the missing preference values. In this paper, we introduce an incomplete interval multiplicative preference relation and give the definitions of consistent and acceptable incomplete ones, respectively. Based on the consistency property of interval multiplicative preference relations, a goal programming model is proposed to complement the acceptable incomplete one. A new algorithm of obtaining the priority vector from incomplete interval multiplicative preference relations is given. The goal programming model is further applied to group decision-making (GDM) where the experts evaluate their preferences as acceptable incomplete interval multiplicative preference relations. An interval weighted geometric averaging (IWGA) operator is proposed to aggregate individual preference relations into a social one. Furthermore, the social interval multiplicative preference relation owns acceptable consistency when every individual one is acceptably consistent. Two numerical examples are carried out to show the efficiency of the proposed goal programming model and the algorithms.

A possibilistic mean-semivariance-entropy model for multi-period portfolio selection with transaction costs

This paper deals with a multi-period portfolio selection problem with fuzzy returns. A possibilistic mean-semivariance-entropy model for multi-period portfolio selection is presented by taking into account four criteria viz., return, risk, transaction cost and diversification degree of portfolio. In the proposed model, the return level is quantified by the possibilistic mean value of return, the risk level is characterized by the lower possibilistic semivariance of return, and the diversification degree of portfolio is measured by the originally presented possibilistic entropy. Furthermore, a hybrid intelligent algorithm is designed to obtain the optimal portfolio strategy. Finally, the comparison analysis between the possibilistic entropy model and the proportion entropy model is provided by two numerical examples to illustrate the efficiency of the proposed approaches and the designed algorithm.

Portfolio selection under possibilistic mean–variance utility and a SMO algorithm

In this paper, we propose a new portfolio selection model with the maximum utility based on the interval-valued possibilistic mean and possibilistic variance, which is a two-parameter quadratic programming problem. We also present a sequential minimal optimization (SMO) algorithm to obtain the optimal portfolio. The remarkable feature of the algorithm is that it is extremely easy to implement, and it can be extended to any size of portfolio selection problems for finding an exact optimal solution.

Consistency analysis of triangular fuzzy reciprocal preference relations

In order to simulate the uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. Based on the reciprocity property, this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations. The new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by Buckley (1985). The properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail. In addition, the shortcomings of the proof procedure of the proposition given by Wang and Chen (2008) are pointed out. And the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations. Finally, using the (n−1) restricted comparison ratios, a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed, and an algorithm is shown to make a consistent decision ranking. Numerical results are further calculated to illustrate the new definition and the obtained algorithm.

A group decision making model based on a generalized ordered weighted geometric average operator with interval preference matrices

Abstract This paper presents a model for a group decision-making problem with interval preference matrices. First, a new definition of interval additive reciprocal matrices with multiplicative consistency is given. Transformation methods between interval additive and multiplicative reciprocal matrices are proposed and applied to homogenize interval preference matrices. Second, the consistency of interval multiplicative reciprocal matrices is utilized to propose a generalized ordered weighted geometric averaging operator, which permits the aggregation of interval multiplicative reciprocal matrices in such a way that more important weight is given to that with more consistency. In order to avoid a misleading solution, the consistency and acceptable consistency of the collective interval multiplicative reciprocal matrix are studied in detail. Finally, a new algorithm is presented to solve the group decision-making problem with interval preference matrices. Numerical results are carried out to illustrate the given definitions, methods and algorithm, respectively.

Fuzzy multi-period portfolio selection optimization models using multiple criteria

To simulate the real transactions in financial market, multiple decision criteria in portfolio selection should be considered to provide investors with additional choices. This paper deals with multi-period portfolio selection problems in fuzzy environment by considering some or all criteria, including return, transaction cost, risk and skewness of portfolio. Two possibilistic portfolio optimization models by using multiple criteria are first presented for the basic multi-period portfolio selection problem. Then, they are naturally extended to dynamic feedback models with closed-loop control policies. A TOPSIS-compromised programming approach is designed originally to transform the proposed models into single objective models. After that, a genetic algorithm is devised for obtaining optimal solutions. Furthermore, a numerical example is given to illustrate the advantage of the proposed models and the efficiency of the designed algorithm over the existing approaches.

Multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints

Abstract This paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control, in which the returns of assets are characterized by possibilistic mean values. A possibilistic absolute deviation is defined as the risk control of portfolio. A new multiperiod mean absolute deviation fuzzy portfolio selection model with transaction cost, borrowing constraints, threshold constraints and cardinality constraints is proposed. Based on the theory of possibility measure, the proposed model is transformed into a crisp nonlinear programming problem. Because of the transaction cost, the multiperiod portfolio selection is a dynamic optimization problem with path dependence. The discrete approximate iteration method is designed to obtain the optimal portfolio strategy, and is proved convergent. Finally, an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the Shanghai Stock Exchange.

A new fuzzy programming approach for multi-period portfolio optimization with return demand and risk control

Abstract This paper considers a multi-period portfolio selection problem imposed by return demand and risk control in a fuzzy investment environment, in which the returns of assets are characterized by fuzzy numbers. A fuzzy lower semi-deviation is originally defined as the risk control of portfolio. A proportion entropy constraint is added as the divergence measure of portfolio. Based on the theories of possibility and necessity measures, a new multi-period portfolio optimization model with return demand and risk control is proposed. And then, the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach. Furthermore, an improved differential evolution algorithm is designed for obtaining the optimal strategy. Finally, a numerical example is given to illustrate the practicality and efficiency of the proposed model and the corresponding algorithm.

A multi-period fuzzy portfolio optimization model with minimum transaction lots

In this paper, we consider a multi-period fuzzy portfolio optimization problem with minimum transaction lots. Based on possibility theory, we formulate a mean-semivariance portfolio selection model with the objectives of maximizing the terminal wealth and minimizing the cumulative risk over the whole investment horizon. In the proposed model, we take the return, risk, transaction costs, diversification degree, cardinality constraint and minimum transaction lots into consideration. To reflect investor’s aspiration levels for the two objectives, a fuzzy decision technique is employed to transform the proposed model into a single objective mixed-integer nonlinear programming problem. Then, we design a genetic algorithm for solution. Finally, we give an empirical application in Chinese stock markets to demonstrate the idea of our model and the effectiveness of the designed algorithm.

An optimization model of the portfolio adjusting problem with fuzzy return and a SMO algorithm

Based on possibilistic mean and variance theory, this paper deals with the portfolio adjusting problem for an existing portfolio under the assumption that the returns of risky assets are fuzzy numbers and there exist transaction costs in portfolio adjusting precess. We propose a portfolio optimization model with V-shaped transaction cost which is associated with a shift from the current portfolio to an adjusted one. A sequential minimal optimization (SMO) algorithm is developed for calculating the optimal portfolio adjusting strategy. The algorithm is based on deriving the shortened optimality conditions for the formulation and solving 2-asset sub-problems. Numerical experiments are given to illustrate the application of the proposed model and the efficiency of algorithm. The results also show clearly the influence of the transaction costs in portfolio selection.