Possibilistic Mean Research Articles

An inventory model for single-period products with reordering opportunities under fuzzy demand

This paper analyzes a single-period inventory model of profit maximization with a reordering strategy in an imprecise environment. The entire period is divided into two slots and the customer demand is considered as a fuzzy number in situations where the demand in each slot is linguistic in nature and characterized as ‘ demand is about d ’. The reordering is to be done during the mid-season after the early-season demand has been observed. The objective is to determine the optimal order quantity in maximizing the expected resultant profit by considering the fuzzy demand and reordering strategy in the single-period framework. The solution procedure is presented using ordering of fuzzy numbers with respect to their possibilistic mean values. Numerical examples are given to illustrate the efficiency of this strategy.

Possibilistic mean–variance models and efficient frontiers for portfolio selection problem

In this paper, it is assumed that the rates of return on assets can be expressed by possibility distributions rather than probability distributions. We propose two kinds of portfolio selection models based on lower and upper possibilistic means and possibilistic variances, respectively, and introduce the notions of lower and upper possibilistic efficient portfolios. We also present an algorithm which can derive the explicit expression of the possibilistic efficient frontier for the possibilistic mean-variance portfolio selection problem dealing with lower bounds on asset holdings.

Possibilistic mean–standard deviation models to portfolio selection for bounded assets

Considering the uncertain returns of risky assets in capital markets as fuzzy numbers, we discuss the portfolio selection problem for bounded assets based on upper and lower possibilistic means and variances. The mean–standard deviation model for portfolio selection can be transformed to a linear programming under possibility distributions, so this methodology can be used to solve large-scale portfolio selection problems. A numerical example is used to illustrate our proposed effective means and approaches.

Continuous review inventory model in mixed fuzzy and stochastic environment

In this paper, we consider a continuous review inventory system where fuzziness and randomness appear simultaneously into an optimization setting. Since demand plays an important role in such type of inventory systems, we develop a model in a mixed environment by incorporating fuzzy random variable as customer demand. After fuzzifying the random lead-time demand we consider the annual average demand as a fuzzy random variable. We provide an elegant methodology to determine the optimal order quantity and reorder point such that the total expected annual cost in the fuzzy sense has a minimum value. Since the expected value of a fuzzy random variable is a fuzzy quantity, a method of ranking fuzzy numbers using their possibilistic mean values is adopted to achieve the optimal solution. A numerical example is presented to illustrate the proposed model.

Fuzzy coefficient volatility (FCV) models with applications

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. In this paper, we propose a class of FCV (Fuzzy Coefficient Volatility) models and study the moment properties. The method used here is very similar to the method used in Appadoo et al. [S.S. Appadoo, M. Ghahramani, A. Thavaneswaran, Moment properties of some time series models, Math. Sci. 30 (1) (2005) 50–63]. The proposed models incorporate fuzziness, subjectivity, arbitrariness and uncertainty observed in most financial time series. The usual forecasting method does not incorporate parameter variability. Fuzzy numbers are used to model the parameters to incorporate parameter variability.

Fully fuzzified linear programming, solution and duality

In this paper, we propose a two-phase approach to find the optimal solutions of a class of fuzzy linear programming problems called fully fuzzified linear programming (FFLP), where all decision parameters and variables are fuzzy numbers. Our approach is constructed on the basis of comparison of mean and standard deviation of fuzzy numbers. In this approach, the first phase maximizes the possibilistic mean value of fuzzy objective function and obtains a set of feasible solutions. The second phase minimizes the standard deviation of the original fuzzy objective function, by considering all basic feasible solutions obtained at the end of the first phase. The advantage of the proposed approach is its simplicity in programming and computation. Moreover, we also generalize the concept of linear programming duality and extend the duality as well as the weak duality theory to FFLP.

On the maximum entropy parameterized interval approximation of fuzzy numbers

This paper extends the interval-valued weighted possibilistic mean of a fuzzy number of Fullér and Majlender to a general weighting function without the monotonic increasing assumption. This weighting function determines a weighted average aggregation of the cuts of the fuzzy number according to the preference of a decision-maker. Some properties of the weighting function are provided and a preference index that qualifies this aggregation and can serve as a parameter for the definition of interval approximation of a fuzzy number is proposed. A special class of parameterized weighting functions satisfying the maximal entropy principle is proposed.

A note on weighted possibilistic mean

In this note, we give a remarkably simple proof of the main result of Fullér and Majlender (Fuzzy Sets and Systems 136 (2003) 363) concerning relationship to the weighted possibilistic mean of fuzzy numbers.

A fuzzy approach to real option valuation

To have a real option means to have the possibility for a certain period to either choose for or against making an investment decision, without binding oneself up front. The real option rule is that one should invest today only if the net present value is high enough to compensate for giving up the value of the option to wait. Because the option to invest loses its value when the investment is irreversibly made, this loss is an opportunity cost of investing. The main question that a management group must answer for a deferrable investment opportunity is: How long do we postpone the investment, if we can postpone it, up to T time periods? In this paper we shall introduce a (heuristic) real option rule in a fuzzy setting, where the present values of expected cash flows and expected costs are estimated by trapezoidal fuzzy numbers. We shall determine the optimal exercise time by the help of possibilistic mean value and variance of fuzzy numbers.

On weighted possibilistic mean and variance of fuzzy numbers

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper, we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-valued probabilistic mean. We shall also introduce the notations of crisp weighted possibilistic mean value, variance and covariance of fuzzy numbers, which are consistent with the extension principle. Furthermore, we show that the weighted variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.

On possibilistic mean value and variance of fuzzy numbers

Dubois and Prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions. In this paper introducing the notations of lower possibilistic and upper possibilistic mean values we define the interval-valued possibilistic mean and investigate its relationship to the interval-valued probabilistic mean. We also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions, which are consistent with the extension principle. We also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory.