Fuzzy ES - Fuzzy množiny_ stručný náhľad Približne dva alebo aj trochu viac /matematizácia neurčitosti/ Fuzzy logic is a very powerful technique that enables you to build expert systems that more closely reflect the real world. If you look at many books on fuzzy logic, they are filled with arcane set theory notation and are quite difficult to read and understand. As with many complex subjects, there is a core portion of fuzzy logic that can be easily explained and implemented. This is surrounded by the much more complex, rigorous mathematics of the subject, that are not necessary for the average user. / / EXSYS Professional for Windowed Environments, © Copyright EXSYS Inc./

Fuzzy expertné systémy Suppose you are building an expert system to control the temperature of hot water fed to a machine /equipment/. In a non-fuzzy system, you might have a rule IF The input water is too hot THEN Mix cold water with the input stream When this rule is run, it will ask the end user if the input water is "too hot". Since this is a somewhat ambiguous question, you could add a rule to derive more specific information. IF [INPUT TEMP] > 180 THEN The input water is too hot Now the system will ask about the water temperature. This information might come from the end user or directly from instrumentation. The problem with this approach, is nothing happens at a temperature of and the system may add too much cold water at This can result in the temperature being put into oscillation rather than being brought to the desired temperature smoothly. Nepriaznivé kolísanie požadovanej teploty chladiaceho média Informácie by mohli prísť od konečného užívateľa, alebo priamo z prístroja.

Fuzzy expertné systémy IF The input water is a little too hot THEN The amount of cold water to add to the input is a little IF The input water is too hot THEN The amount of cold water to add to the input is medium IF The input water is way too hot THEN The amount of cold water to add to the input is a lot with temperature rules to derive the values: IF [INPUT TEMP] <= 160 THEN The input water is OK IF [INPUT TEMP] > 160 and [INPUT TEMP] < 180 THEN The input water is a little too hot IF [INPUT TEMP] >= 180 and [INPUT TEMP] < 200 THEN The input water is too hot IF [INPUT TEMP] >= 200 THEN The input water is way too hot

Fuzzy expertné systémy This breaks up the single step function into three steps. As the input water gets a little too hot, you try adding a little cold water. If this is not enough, and the temperature of the input water continues to rise, at 180 you increase the amount of cold water added. If the temperature reaches 200, you increase the amount of cold water again. The three step system clearly is better at controlling the process and more closely reflects the way a human operator would react. A hard break point at 180 in the first system has been made slightly "fuzzier„ by breaking it into three steps. But you had to write three times as many rules to do it. Suppose you want to break the process into 100 steps and have many functions to control. The number of rules needed would become enormous and impractical. What would be best, is to make it a continuous function rather than a series of steps. The solution is Fuzzy Logic. Rozdelenie jedného kroku funkcie do troch krokov. Ak je chladiace médium príliš horúce, nasleduje pridanie trochu studenej vody. Ak to nie je dosť, a teplota stúpa, pri 180 zvýšite množstvopridanej studenej vody,. Ak teplota dosiahne 200, zvýšite množstvo studenej vody znovu. „Trojkrokový“systém je jednoznačne vhodnejší na riadenie procesu a lepšie odráža spôsob, akým „ľudský„ operátor reaguje. Kľúčová teplota na 180 sa aspoň trochu stáva „fuzzier“ ; tým, že sa rozdelí to do troch krokov. Ale je potrebné zadefinovať trikrát toľko pridukčných pravidiel. Predpokladajme rozdelenie procesu do 100 krokov a mnoho funkcií pre riadenie. Počet potrebných pravidiel by sa stal obrovským a nepraktickým. Najlepšie je aplikovanie spojitej funkcia, a nie rad krokov.

Fuzzy expertné systémy Fuzzy logic is a technique of assigning degrees of confidence to various possible options, based on the value of a variable. In your rules you did this in a crude way that could be diagrammed in a graph as: The confidence for each of the three possible values is either 0 or 1 depending on the temperature. There is no overlap and the confidence changes abruptly at a specific break point.

Fuzzy expertné systémy It would be better to gradually increase the confidence in each of the values as the temperature increases. As a graph, this would look more like: In this system, as the temperature increases, the confidence in each of the three ranges will gradually increase (and in some cases, fall off) smoothly. At a temperature of 152, the confidence in "a little too hot" starts to increase from 0 and reaches 1 at 162. The temperatures between 152 and 162 give a continuous smoothly increasing confidence value. For any temperature, the graph shows the confidence in each of the values. Notice that for some temperatures, you have some confidence in two different values. At 175, "a little too hot" has a confidence of.8 and "too hot" has a confidence of.4. This is a great advantage, since you want the rules based on "too hot" to kick in gradually, rather than suddenly at a threshold value.

Fuzzy expertné systémy It is very important to remember that in a fuzzy system, there is a confidence associated with EACH VALUE of a qualifier - not just the qualifier as a whole. These graphs of confidence in a qualifier value, versus a variable (temperature) are called "membership functions" and are the key to making an expert system "fuzzy". For a simple case like this, it would be possible to write a series of rules that calculated the confidence, but it would be very cumbersome, even for this simple problem. Zdroj: EXSYS Professional for Windows Environments - manual

Fuzzy expertné systémy Determinácia tvarovej zložitosti na základe tvarovej zložitosti: Modelové súčiastky

Fuzzy expertné systémy

Determinácia tvarovej zložitosti na základe tvarovej členitostii: T( tvarová členitosť ) = 1 + (1 – V s / V ot )