| The financial aspect is essential to any kind of | | | | Excel DB-like data sets etc.) containing info on invoices, |
| business. How a company receives funding and | | | | their birth dates, adjournment periods for each of the |
| incomes determines its overall welfare. For any B2B | | | | debtors, actual dates of debtors' payments that have |
| company, one of the major concerns is the control | | | | occurred in the past, we can view the statistics "Past |
| over the payments of the non-bank debtors, i.e. the | | | | payment delays". The density function of this statistics |
| payments resulting from sales of goods and/or | | | | can be viewed as a subnormal fuzzy set. This set, |
| services. Indeed, this inflow enables the company to | | | | labeled "A", will be the first of the three fuzzy sets to |
| assess its efficiency, playing the role of the factor | | | | be components of the resulting fuzzy set "payment |
| underlying the company's profits. Having produced | | | | date forecast". The density function can give us a |
| some goods or services, the company sells the ware, | | | | general idea about the "payment discipline" of a |
| receiving money for the ware -- which becomes | | | | specific debtor in the past. The density function, in a |
| income. The company crucially needs this income in | | | | general case, will be containing several "waves" |
| order to be able to buy some raw materials and | | | | because it's usually not a trend-containing characteristic |
| equipment needed to produce new portions of goods. | | | | as to how many days a debtor will be evading from |
| Thus, it is essential that the company receives income | | | | paying the debt.Firstly, in most cases the amount of |
| regularly. What is regularity, in this case? It's in fact | | | | days of a payment delay is a random variable. It can |
| receiving the money on a predetermined schedule. The | | | | be fluctuating within a couple days' limits. Secondly, |
| one that has been formed with a necessity in mind to | | | | statistical forecasts of delays may be differing |
| meet the company's needs in financing its | | | | significantly for different periods of time. This is |
| expenditures. However, we are living in a REAL world, | | | | because B2B relationships are not static, they are |
| which means that, inevitably, there are delays in | | | | developing all the time. Sometimes, the selling company |
| debtors' payments. This, in turn, can lead to a complete | | | | comes to "shaking hands" with the buying company |
| breakdown of the financial plan. The latter may cause | | | | for the latter to pay a couple days earlier, whereas |
| a non-reversible failure of the company. Effective | | | | sometimes the buying company may be facing |
| planning of these delays is the key to successful | | | | temporary financial problems (e.g., resulting from a |
| financial management.Given the stated facts, we | | | | huge credit to be returned to a bank by the buying |
| arrive at the importance of a system that would be | | | | company), so that the buying company warns the |
| able to forecast potential delays in debtors' payments. | | | | selling company that there may be slight delays of |
| Errors (deviations of the actual payment dates from | | | | payments. This is reflected in another component of |
| forecasted dates) should be minimal in order for such | | | | the resulting fuzzy forecast, -- fuzzy set "C". It is in |
| a system to be considered effective. Now this is a | | | | fact a linguistic variable "Payment delay most likely" |
| tough point. Existing works show that ordinary | | | | fuzzy set. The linguistic variable may take one of the |
| statistical models cannot bear really effective results | | | | following values: "Neutral" (which means that there are |
| that would be stable in time. From our viewpoint, the | | | | no specific anticipations of the payments delay value |
| best way to solve this issue is to use the so-called | | | | for the specific debtor), "A slight delay is possible", "A |
| "fuzzy approach", which is based on the fuzzy set | | | | slight delay is most likely", "A large delay is most likely", |
| theory, originally suggested by L. Zadeh.The basics of | | | | "An on-time payment is most likely", "Payment in |
| the fuzzy sets are explained in a huge amount of | | | | advance is most likely". Each of these term-values has |
| articles and books -- use web search engines to find | | | | its own membership function. A corresponding |
| out what fuzzy logic is and how it all works, if there's | | | | membership function is used each time when building a |
| such a need. Here, we only suggest a ready-to-use | | | | forecast for a specific debtor. The membership |
| principle of forecasting debtors' payments, basing on | | | | functions for the term-values of the linguistic variable |
| the fuzzy approach. The principle suggested in this | | | | "Payment delay most likely" are given below:"An |
| article has been realized in the form of a computer | | | | on-time payment is most likely": y=SQRT(1-ABS(x)/2), |
| program. The program has been tested on real data | | | | x belongs to [-2;2]"A slight delay is most likely": |
| of a real company. The mean-square deviation thus | | | | y=SQRT(1-ABS(x-4)/3), x belongs to [1;7]"A slight delay |
| calculated estimated 3, which suggests the idea that | | | | is possible": y=(1-ABS(x-4)/3)**2, x belongs to [1;7]"A |
| the principle presented herein is rather effective, but | | | | large delay is most likely": y=SQRT(0.25-(12-x)/24)+0.5, |
| can be subject to further improvement.Given a | | | | x belongs [6;12]y=(0.71-(6-x)/4.23)**2, x belongs to |
| relational database (which may be in fact realized in | | | | [3;6)y=0, x12"Neutral": y=0. |
| any way, including but not limited to, MS Access, MS | | | | |