Mukesh Kumar Mehlawat

Multiobjective credibilistic portfolio selection model with fuzzy chance-constraints

In this paper, we propose a multiobjective credibilistic model with fuzzy chance constraints of the portfolio selection problem. The key financial criteria used are short-term return, long-term return, risk and liquidity. The model generates portfolios which are optimal to the extent of achieving the highest credibility values for the objective functions. The problem is solved using a hybrid intelligent algorithm that integrates fuzzy simulation with a real-coded genetic algorithm. The approach adopted here has advantage of handling the multiobjective portfolio selection problem where fuzzy parameters are characterized by general functional forms. Numerical examples are provided to demonstrate effectiveness of the solution approach and efficiency of the model.

A hybrid approach to asset allocation with simultaneous consideration of suitability and optimality

In this paper, we develop mathematical models for simultaneous consideration of suitability and optimality in asset allocation. We use a hybrid approach that combines behavior survey, cluster analysis, analytical hierarchy process and fuzzy mathematical programming.

Asset portfolio optimization using support vector machines and real-coded genetic algorithm

This paper presents an integrated approach for portfolio selection in a multicriteria decision making framework. Firstly, we use Support Vector Machines for classifying financial assets in three pre-defined classes, based on their performance on some key financial criteria. Next, we employ Real-Coded Genetic Algorithm to solve a mathematical model of the multicriteria portfolio selection problem in the respective classes incorporating investor-preferences.

Bector--Chandra type duality in fuzzy linear programming with exponential membership functions

In this paper, we study a pair of fuzzy primal-dual linear programming problems and calculate duality results using an aspiration level approach. We use an exponential membership function, which is in contrast to the earlier works that relied on a linear membership function. As the fuzzy environment causes a duality gap, we investigate how choosing the exponential membership function impacts this gap. This issue is particularly important for fuzzy linear programming where, in general, the primal and dual objective values may not be bounded.

Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method

We propose new method for MAGDM problems with trapezoidal intuitionistic fuzzy numbers.The weights of the decision-makers and attributes are considered completely unknown.The method integrates Shannon entropy and Evidence theory with Bayes approximation.A new extended VIKOR method is presented to solve intuitionistic fuzzy MAGDM problems.Utility of the method is demonstrated by solving plant location selection problem. This paper presents a new decision method for multi-attribute group decision-making (MAGDM) problems in general and plant location selection (PLS) problem in particular, with intuitionistic fuzzy information captured through trapezoidal intuitionistic fuzzy numbers (TrIFNs). We assume that the weights of the decision-makers and attributes are completely unknown. The ratings of alternatives with respect to each attribute are considered as linguistic terms, which are mapped to the appropriate TrIFNs. To reduce subjective randomness in the decision-process, we determine attribute weights using the Shannon entropy theory, and weights of the decision-makers by integrating the Evidence theory with Bayes approximation. Furthermore, we extend the classical VIKOR method to solve MAGDM problems under intuitionistic fuzzy environment based on the TrIFNs. Considering that the PLS problem is essentially a MAGDM problem that involves evaluation of the alternatives on several conflicting attributes based on the vague and imprecise assessments of the decision-makers, we demonstrate utility of the proposed decision method by applying it solve the PLS problem. A detailed comparison is presented to demonstrate the advantages of the proposed methodology over the existing methods used for both the intuitionistic fuzzy MAGDM problems and PLS problem.

Hybrid optimization models of portfolio selection involving financial and ethical considerations

In this paper, we propose a comprehensive three-stage multiple criteria decision making framework for portfolio selection based upon financial and ethical criteria simultaneously. It may be noted that the ethical investment movement that began from the USA in 1960s has gained tremendous momentum the world over recently. The growing instances of corporate scams and scandals have made it incumbent upon the investors to consider the quality of governance of corporations and ethicality of their conduct. Indeed, there has been a spate of reforms relating to corporate laws and capital markets all over the world. Also, the investors are becoming conscious of the desirability of ethical evaluation of the assets. The growing influence of institutional investors has reinforced this consciousness. Hence, the research in the area must take cognizance of these developments to construct models that accord due consideration to ethical criteria besides the financial criteria. We use multiple methodologies toward the purpose. Analytical hierarchy process technique is used to obtain the ethical performance score of each asset based upon investor-preferences. A fuzzy multiple criteria decision making method is used to obtain the financial quality score of each asset based upon investor-ratings on the financial criteria. Three hybrid portfolio optimization models are developed to obtain well diversified financially and ethically viable portfolios. These models have maximization of financial goal as main objective and differ in the way the ethical goal is pursued by the investor. Numerical illustrations are included to demonstrate the suitability of the models for obtaining diversified portfolios that meet the investors financial and ethical goals.

COTS selection using fuzzy interactive approach

In this paper, we introduce fuzzy mathematical programming (FMP) for decision-making related to software creation by selecting optimal commercial-off-the-shelf (COTS) products in a modular software system. Each module in such software systems have different alternatives with variations in their properties, for example, quality, reliability, execution time, size and cost. Due to these variations, component-based software developers generally deals with the problem of selecting appropriate COTS products. The development of COTS-based systems largely depends on the success of the selection process. Various crisp optimization models of COTS products selection have been proposed in literature. However, in real COTS products selection problem, it is difficult to estimate precisely the values of various model parameters due to lack of sufficient data and also because of measurement errors. Hence, instead of crisp optimization model, if we use flexible optimization model then we might obtain results which are more preferred by the decision maker. In this study, we use multiple methodologies such as quality model, analytical hierarchy process and FMP to develop fuzzy multiobjective optimization model of the COTS products selection. To determine a preferred compromise solution for the multiobjective optimization problem, an interactive fuzzy approach is used.

Fuzzy Chance-Constrained Multiobjective Portfolio Selection Model

This paper addresses the problem of portfolio selection with fuzzy parameters from a perspective of chance-constrained multiobjective programming. The key financial criteria used here are conventional, namely, return, risk, and liquidity; however, we use short- and long-term variants of return rather than a single measure of an investors expectations in respect thereof. The proposed model aims to achieve the maximal return (short term as well as long term) and liquidity of the portfolio. It does so at a credibility, which is no less than the confidence levels defined by the investor. Further, to capture uncertain behavior of the financial markets more realistically, fuzzy parameters used here are such as those characterized by general functional forms. To solve the problem, we rely on a specially developed algorithm that hybridizes fuzzy simulation and real-coded genetic algorithm. Numerical experiments are included to showcase the applicability and efficiency of the model in a real investment environment.

A MEMBERSHIP FUNCTION APPROACH FOR COST-RELIABILITY TRADE-OFF OF COTS SELECTION IN FUZZY ENVIRONMENT

The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadehs extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.

A Hybrid Approach for Selecting Optimal COTS Products

This paper develops a hybrid approach for selecting the optimal Commercial Off-The-Shelf (COTS) software product among alternatives for each module in the development of modular software systems. We draw on multiple methodologies such as quality models (ISO/IEC 9126), analytical hierarchy process (AHP) and fuzzy mathematical programming (FMP) for developing fuzzy multiobjective optimization models for selecting the optimal COTS software products. The objective functions of the models are to maximize the weighted quality and minimize the cost subject to the limitation of the incompatibility among COTS products. The software system consists of several programs, where a specific function of each program can call upon a series of modules. Each module in a software system has different levels of importance that depends on access frequency. For this reason, this study assign different weights to the modules according to their access frequencies using AHP.