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By Emmy Landmann; Kurt Böttcher

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In other words, if we show the desired (allowable) output deviation with Ydes , the robustness problem is to find | xi |’s such that the system output, Yout , satisfies the following: | Yout | ≤ | Ydesired |. We formulate this definition as a classical optimization problem: ⎧ ⎪ Maximize : | x1 |, · · · , | xp | ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ | Yout | ≤ | Ydes | ⎪ ⎪ ⎪ ⎪ ⎨ x1min ≤ x1 ≤ x1max ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩Subject to : x2min ≤ x2 ≤ x2max xpmin ≤ xp ≤ xpmax .. 22 M. Biglarbegian Next, we derive an expression for Yout .

Full Type n fuzziness. Type 1 fuzzy sets are obtained in both subjective and objective manners and are well established in this area. Full Type 2 and higher types of fuzziness, on the other hand, are still a very active area of recent research. Here, we present an objective algorithmic Full Type 2 fuzzy systems investigations. 2 Fuzzy System Models Let us first review historically significant fuzzy system model developments in order to identify their unique structures and to point out how they differ from each other.

In Sect. 3, we present a way of constructing information granules on a basis of existing experimental evidence by introducing a principle of justifiable granularity. The generality of the idea is that both the experimental evidence and the resulting information granules can be expressed in different ways not being necessarily confined to fuzzy sets. In the sequel, in Sect. 4, we discuss type-2 and order-2 fuzzy sets in system modeling by articulating a number of compelling reasons behind involving fuzzy sets of type-2.

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