Businesses deal with different categories of people; some are regular buyers, suppliers, distributors or one-time buyers. They also have several inputs which include products, employees and capital. Some suppliers can be customers to the business as well as some employees. This implies that, in business operations there are a lot of interactions between people and objects. With a good knowledge of sets theory, its rules and operations such as unions, complements and intersections, businesses could find ways to save cost and increase profit. By identifying the products that businesses require, and the persons to supply these requirements, they can be able to make the best bargain thus saving money. By classifying the inputs as one set and the suppliers as another set, businesses can use the set theory (intersection) to get the smallest set of suppliers for all of their required inputs.
Predicting business failure before it actually happens is very important in order to be able to take the necessary preventive measures. Such predictions are mostly important in banking sectors since they are the ones that support the economy of most countries. With the knowledge in set theory, one can use the Rough Set Theory to predict the possibility of bank or business failure. This theory was proposed by Pawlak and since then, it has attracted the attention of many researchers and practitioners across the world. Many scholars have of late contributed to its development and application. Due to its effectiveness, the theory has been used in other fields apart from business. Through this theory, many investigations have been made successfully which includes research in pharmacology and analysis of relationships between the chemical structure and the antimicrobial activity of drugs. Rough sets are considered to be sets with indistinct boundaries and the basic concept here is the whim of approximation space. First a range of minimal subsets of independent attributes is constructed. Next, a reduced decision table is constructed eliminating the redundant attributes. Finally, the set of sorting rules and algorithm is derived on the basis of the decision table with the firms being classified by matching their descriptions to the set of sorting rules (Ruzgar, Unsal, and Ruzgar, 2008, PP.58-9).
Fuzzy set theory has also helped in business production management. Its ability to quantitatively and qualitatively model problems which involve vagueness and imprecision has led to the researchers in production management use it. The theory has been used in areas of production management such as in new product development, production scheduling and control, inventory management, to mention but a few (Bradshaw, 1983, pp.403-08). Karwowski and Evans have given three reasons as to why fuzzy set theory is relevant to production management. First, as imprecision and vagueness are inherent to the decision makers, their experience and judgment may be used to complement established theories to promote a better understanding of the problem. Secondly, in production management, the information used in formulating a model’s objective, decision variables, constraints and parameters may not be precisely measurable. Thirdly, the quality of available information may be weakened by the imprecision and vagueness as a result of personal bias. Hence the theory can be used in filling the gaps between descriptive and perspective models in production management research (Guiffrida & Nagi, 1998, pp. 1-2).
As sets theory has exhibited potential in business management and growth, many business researchers have resulted in developing the existing theories to make them more productive hence help in business running.
Reference
Bradshaw, C.W. (1983). A fuzzy set theoretic interpretation of economic control limits. European Journal of Operational Research, 13(4), 403-408.
Guiffrida, A. L. & Nagi, R. (1998). Fuzzy Set Theory Applications in Production Management Research: A Literature Survey. 2009. Web.
Ruzgar, N. S., Unsal, F. & Ruzgar, B. (2008). Predicting business failures using the rough set theory approach: The case of the Turkish banks. International journal of mathematical models and methods in applied sciences, vol.2 (1), 1-2.