Samarjit Kar

Mean-variance-skewness model for portfolio selection with fuzzy returns

Numerous empirical studies show that portfolio returns are generally asymmetric, and investors would prefer a portfolio return with larger degree of asymmetry when the mean value and variance are same. In order to measure the asymmetry of fuzzy portfolio return, a concept of skewness is defined as the third central moment in this paper, and its mathematical properties are studied. As an extension of the fuzzy mean-variance model, a mean-variance-skewness model is presented and the corresponding variations are also considered. In order to solve the proposed models, a genetic algorithm integrating fuzzy simulation is designed. Finally, several numerical examples are given to illustrate the modelling idea and the effectiveness of the proposed algorithm.

Review Article: Applications of neuro fuzzy systems: A brief review and future outline

This paper surveys neuro fuzzy systems (NFS) development using classification and literature review of articles for the last decade (2002-2012) to explore how various NFS methodologies have been developed during this period. Based on the selected journals of different NFS applications and different online database of NFS, this article surveys and classifies NFS applications into ten different categories such as student modeling system, medical system, economic system, electrical and electronics system, traffic control, image processing and feature extraction, manufacturing and system modeling, forecasting and predictions, NFS enhancements and social sciences. For each of these categories, this paper mentions a brief future outline. This review study indicates mainly three types of future development directions for NFS methodologies, domains and article types: (1) NFS methodologies are tending to be developed toward expertise orientation. (2) It is suggested that different social science methodologies could be implemented using NFS as another kind of expert methodology. (3) The ability to continually change and learning capability is the driving power of NFS methodologies and will be the key for future intelligent applications.

Deterministic inventory model with two levels of storage, a linear trend in demand and a fixed time horizon

Abstract A deterministic inventory model is developed for a single item having two separate storage facilities (owned and rented warehouses) due to limited capacity of the existing storage (owned warehouse) with linearly time-dependent demand (increasing) over a fixed finite time horizon. The model is formulated by assuming that the rate of replenishment is infinite and the successive replenishment cycle lengths are in arithmetic progression. Shortages are allowed and fully backlogged. As a particular case, the results for the model without shortages are derived. Results are illustrated with two numerical examples. Scope and purpose Throughout the world, the production of food grains is periodical. Normally, in countries where state control is less, the demand of essential food grains is lowest at the time of harvest and goes up to the highest level just before the next harvest. This phenomenon is very common in developing third world countries where most of the people are landless or marginal farmers. At the time of harvest, they share some grain/product with landowners and as soon as the small inventory is exhausted, they are forced to buy food grains from the open market. As a result, demand for food grains increases with time in a period along with the number of the people whose initial stock of food grains gets exhausted. In this paper, a two-storage inventory model with time-dependent demand and fixed time horizon is developed and solved by a mathematical programme based on gradient method. This methodology of model development and its solution are quite general and it can be applied to inventory models of any product whose production is periodical and demand increases linearly with time.

Fuzzy mean-variance-skewness portfolio selection models by interval analysis

In portfolio selection problem, the expected return, risk, liquidity etc. cannot be predicted precisely. The investor generally makes his portfolio decision according to his experience and his economic wisdom. So, deterministic portfolio selection is not a good choice for the investor. In most of the recent works on this problem, fuzzy set theory is widely used to model the problem in uncertain environments. This paper utilizes the concept of interval numbers in fuzzy set theory to extend the classical mean-variance (MV) portfolio selection model into mean-variance-skewness (MVS) model with consideration of transaction cost. In addition, some other criteria like short and long term returns, liquidity, dividends, number of assets in the portfolio and the maximum and minimum allowable capital invested in stocks of any selected company are considered. Three different models have been proposed by defining the future financial market optimistically, pessimistically and in the combined form to model the fuzzy MVS portfolio selection problem. In order to solve the models, fuzzy simulation (FS) and elitist genetic algorithm (EGA) are integrated to produce a more powerful and effective hybrid intelligence algorithm (HIA). Finally, our approaches are tested on a set of stock data from Bombay Stock Exchange (BSE).

Fixed charge transportation problem with type-2 fuzzy variables

This paper considers two fixed charge transportation problems with type-2 fuzzy parameters. Unit transportation costs, fixed costs in the first problem and unit transportation costs, fixed costs, supplies and demands in the second problem are type-2 fuzzy variables. For the first problem, to get corresponding defuzzified values of the type-2 fuzzy cost parameters, first critical value (CV)-based reduction methods are applied to reduce type-2 fuzzy variables into type-1 fuzzy variables and then centroid method is used for complete defuzzification. Besides this, we also apply geometric defuzzification method to the type-2 fuzzy cost parameters in the first problem to provide a comparison of the results. Coming to the second problem, a chance-constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the CV-based reductions of corresponding type-2 fuzzy parameters. Next, the reduced model is turned into equivalent parametric programming problem. The deterministic problems so obtained are then solved by using the standard optimization solver - LINGO. We have provided numerical examples illustrating the proposed models and techniques. Some sensitivity analyzes for the second model are also presented.

Cross-entropy measure of uncertain variables

ross-entropy is a measure of the difference between two distribution functions. In order to deal with the divergence of uncertain variables via uncertainty distributions, this paper aims at introducing the concept of cross-entropy for uncertain variables based on uncertain theory, as well as investigating some mathematical properties of this concept. Several practical examples are also provided to calculate uncertain cross-entropy. Furthermore, the minimum cross-entropy principle is proposed in this paper. Finally, a study of generalized cross-entropy for uncertain variables is carried out.

A production-inventory model with remanufacturing for defective and usable items in fuzzy-environment

This paper investigates a production-remanufacturing system for a single product over a known-finite time horizon. Here the production system produces some defective units which are continuously transferred to the remanufacturing unit and the constant demand is satisfied by the perfect items from production and remanufactured units. Remanufacturing unit uses the defective items from production unit and the collected used-products from the customers and later items are remanufactured for reuse as fresh items. Some of the used items in the remanufacturing unit are disposed off which are not repairable. The remanufactured units are treated as perfect items. Normally, rate of defectiveness varies in a production system and may be approximated by a constant or fuzzy parameter. Hence, two models are formulated separately with constant and fuzzy defective productions. When defective rate is imprecise, optimistic and pessimistic equivalent of fuzzy objective function is obtained by using credibility measure of fuzzy event by taking fuzzy expectation. Here, it is assumed that remanufacturing system starts from the second production cycle and after that both production and remanufacturing units continue simultaneously. The models are formulated for maximum total profit out of the whole system. Here the decision variables are the total number of cycles in the time horizon, the duration for which the defective items are collected and the cycle length after the first cycle. Genetic Algorithm is developed with Roulette wheel selection, Arithmetic crossover, Random mutation and applied to evaluate the maximum total profit and the corresponding optimum decision variables. The models are illustrated with some numerical data. Results of some particular cases are also presented.

Fuzzy R&D portfolio selection of interdependent projects

Global competition of markets has forced firms to invest in targeted R&D projects so that resources can be focused on successful outcomes. A number of options are encountered to select the most appropriate projects in an R&D project portfolio selection problem. The selection is complicated by many factors, such as uncertainty, interdependences between projects, risk and long lead time, that are difficult to measure. Our main concern is how to deal with the uncertainty and interdependences in project portfolio selection when evaluating or estimating future cash flows. This paper presents a fuzzy multi-objective programming approach to facilitate decision making in the selection of R&D projects. Here, we present a fuzzy tri-objective R&D portfolio selection problem which maximizes the outcome and minimizes the cost and risk involved in the problem under the constraints on resources, budget, interdependences, outcome, projects occurring only once, and discuss how our methodology can be used to make decision support tools for optimal R&D project selection in a corporate environment. A case study is provided to illustrate the proposed method where the solution is done by genetic algorithm (GA) as well as by multiple objective genetic algorithm (MOGA).

Inventory of multi-deteriorating items sold from two shops under single management with constraints on space and investment

Abstract In this study, we propose an inventory model for several continuously deteriorating items, sold from two shops – primary and secondary shops, under single management dealing with limitations on investment and total floor-space area. Initially items are purchased in lots and received at the primary shop, then fresh and deteriorated units are separated, only the fresh units are sold from the primary shop with a profit and its demand is a deterministic linear function of instantaneous stock level and the selling price of the units. The deteriorated units are transferred to the adjacent secondary shop for sale at a reduced price and the demand for these units is linearly proportional to the selling price only. In both the shops, shortages are not allowed. There may be six scenarios depending upon the time periods of two shops and altogether there will be 6 n (n⩾2) different cases for n items. In each case optimum order quantities are evaluated maximizing the corresponding average profit function. Models are illustrated with numerical examples for two items only. Scope and purpose In the case of some goods, specially fruits, vegetables, etc. which are purchased in lots and deteriorate continuously with time, a retailer first separates the deteriorated units from the fresh/good ones. Otherwise the good units will be affected by the spoiled ones. As the items deteriorate continuously, the units considered fresh at a particular point of time, again deteriorate and the deteriorated ones are classified and transferred. Generally, for this type of items, fresh units do have a better demand and are sold at a higher price in the market whereas the spoiled ones have a less market and are sold at a much lower price. Due to these facts, the retailer sells the items separately from two counters/shops at different prices and tries to make a profit out of these two proceeds. This is a very common phenomenon in the case of fruits like mango, orange, apple, etc. and vegetables like potato, onions, etc. This realistic phenomenon is very often observed in the developing countries where some people are very rich and others live below poverty line. The objective of this paper is to formulate and solve a real-life inventory problem for these items. Here, the demand of the fresh units varies with the amount in stock and its selling price and that for the deteriorated ones is assumed to be only selling price dependent. This is a multi-item problem without shortages under space and investment constraints. This model can be made more general including fully backlogged or partially backlogged shortages. In some cases, inventory parameters like, demand, costs, etc. are probabilistic and/or imprecise and uncertain in non-probabilistic sense. The present model can also be formulated in fuzzy, probabilistic and mixed environments assuming the demand, costs, profit goal, available storage space and/or capital for investment as fuzzy or probabilistic.

On distribution function of the diameter in uncertain graph

In uncertain graphs, the existence of some edges is not predetermined. The diameter of an uncertain graph is essentially an uncertain variable, which indicates the suitability for investigation of its distribution function. The main focus of this paper is to propose an algorithm to determine the distribution function of the diameter of an uncertain graph. We first discuss the characteristics of the uncertain diameter, and the distribution function is derived. An efficient algorithm is designed based on Floyds algorithm. Further, some numerical examples are illustrated to show the efficiency and application of the algorithm.