Elsevier

Information Sciences

Volume 180, Issue 9, 1 May 2010, Pages 1582-1590
Information Sciences

Application of fuzzy calculations for improving portfolio matrices

https://doi.org/10.1016/j.ins.2010.01.012Get rights and content

Abstract

In this paper, we draw upon portfolio analysis to develop and implement a strategic decision making model. We consider the limitations and problems of classic portfolio analysis approach and resolve these problems by using fuzzy set theory. In the proposed method, both internal and external factors are evaluated in linguistic terms and in terms of fuzzy triangular numbers. The fuzzy numbers are fed into an industry attractiveness-business analysis matrix. The novelty of the proposed approach comes from the fact that fuzzy numbers are processed without using conventional methods, allowing for strategies to be ranked.

Introduction

Strategic management is defined as the science of formulating, executing, and assessing those decisions that enable organizations to achieve their long-term goals [4]. The most important stage in this process deals with strategy formulation. In this stage, the organization’s mission is determined, and threats and opportunities are identified. Strengths and weaknesses are identified, long-term goals are determined, various strategies are proposed, and specific strategies are selected.

One of the most important instruments used in this stage is the business portfolio analysis matrix [3], [4], [8], [13]. The matrix is composed of zones, which represent predefined sets of strategies. The evaluation of the firm’s internal and external conditions results in a position (usually a point) in one of the strategy zones. The industry attractiveness-business strength matrix is the variation of the business portfolio analysis matrix that we have selected for the purposes of this research (see Fig. 1) [4].

The strategies represented by each zone are as follows:

  • (1)

    Cells 1, 2 and 4 (zone A) comprise strategies of growth and building, and also offensive strategies. These strategies are known as “intensive strategies,” i.e., market penetration, market development, product development, forward integration, backward integration and horizontal integration.

  • (2)

    Cells 3, 5 or 7 (zone B) call for the preservation of the status quo. In this zone, common strategies are market penetration and product development.

  • (3)

    Units located in cells 6, 8 or 9 (zone C) should divest.

In the above matrix, point calculations are usually based on inexact terms, but fuzzy-based methodologies have seldom been used. The application of fuzzy theory to the interpretation of portfolio matrices is recommended in [11], [12]. In [11], the industry attractiveness-business strength matrix is fuzzified. In [12] a fuzzy rule-based method is used to handle the growth-share matrix. The fuzzy concept also has been applied in optimal portfolio selection problems. For instance, in [9], the portfolio selection problem is investigated when the security returns contain both randomness and fuzziness. In [7], a fuzzy mathematical model is applied to a similar problem. In [1], a fuzzy random multi-objective quadratic programming method is examined and applied to the portfolio optimization problem. Finally, in [14], the analytic hierarchy process is applied to the portfolio selection problem.

Despite this extensive research, difficulties still persist: portfolio analysis recommends a strategy for each business unit based on its position in the company’s overall portfolio of businesses, according to known and accepted rules. This could lead to different strategy recommendations for business units that are very close to each other but on the opposite sides of boundaries in matrices. This last point can be construed as the first drawback of portfolio analysis. Also, the portfolio analysis suggests the same strategy choice for all business units in the same quadrant, regardless of their exact positions in the matrix. For example, one of the legitimate shortcomings of the growth-share matrix is that a “four-cell matrix based on high/low classification hides the fact that many businesses are in markets with an average growth rate and have relative market shares that are neither high nor low but in-between or intermediate. In which cells do these average businesses belong?” [12].

The expression of internal and external factors in the form of fuzzy numbers, instead of crisp numbers, provides a convenient answer to that question [5]. Therefore, one should consider an environment for the expression of strategies based on areas instead of points. Although some researchers have attempted to fuzzify the inputs of process of strategic planning [11], [12], this paper considers both inputs and outputs of this process. Whereas the real nature of the environment for the implementation of strategies is ambiguous, we pursue an approach towards the expression of strategies in uncertain states. The ability to prioritize strategies is one of the outcomes of such an approach. Furthermore, by quantifying the factors as fuzzy triangular numbers, the evaluation of the factors is made more flexible, and both qualitative and quantitative aspects of the factors can be considered. The ambiguity and uncertainty of the factors can also be taken into account during the process of decision making. Therefore, our aim in this paper is to develop a flexible, adaptive, and realistic system to support the process of decision making.

Section snippets

Fuzzy sets application in industry attractiveness-business strength matrix

There are three main problems with the classical method of strategy extraction using the industry attractiveness-business strength matrix:

  • (1)

    The internal factor evaluation (IFE) matrix is used to evaluate the internal conditions of an organization. The IFE matrix comprises factors (strengths and weaknesses), weights (0.0–1.0), ratings (1–4: One for high weakness, two for low weakness, three for low strength, and four for high strength), and the final weighted score is obtained by multiplying the

Factors evaluation

Suppose that there are n SBUs to be evaluated considering m internal and k external factors. Suppose that Wi is the fuzzy weight number representing the importance of the internal factor Fi and Dij is the desirability of the jth SBU regarding that factor, for all iI{1,2,,m} and for all jJ{1,2,,n}. The overall internal desirability of the SBU j is denoted by IDj.

The α-cut of the overall internal desirability IDj of a SBUj is calculated through fuzzy weight average (FWA) [15] for m

A case illustration

In order to evaluate the applicability of the proposed algorithm, we implemented it in a strategic planning process for a food company in Iran [19]. The company is a successful player in the food industry in the Middle East.

Conclusion

Portfolio analysis using a fuzzy approach has been the main focus of this paper. We have drawn on fuzzy methodology to extract strategies. Fuzzy methodology allows us to incorporate uncertainty into historical data and also to incorporate subjective/intuitive characteristics into the portfolio analysis models. Furthermore, the ambiguity and uncertainty of the factors can be taken into account during the process of decision making.

The industry attractiveness-business strength matrix is a

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