By Edsger W. Dijkstra

Writer Edsger W. Dijkstra introduces A self-discipline of Programming with the assertion, "My unique suggestion was once to post a couple of attractive algorithms in the sort of means that the reader may possibly relish their beauty." during this vintage paintings, Dijkstra achieves this target and accomplishes very much extra. He starts off by way of contemplating the questions, "What is an algorithm?" and "What are we doing after we program?" those questions lead him to a fascinating digression at the semantics of programming languages, which, in flip, ends up in essays on programming language constructs, scoping of variables, and array references. Dijkstra then supplies, as promised, a set of lovely algorithms. those algorithms are some distance ranging, protecting mathematical computations, different types of sorting difficulties, trend matching, convex hulls, and extra. simply because this is often an previous publication, the algorithms provided are occasionally now not the easiest to be had. although, the worth in interpreting A self-discipline of Programming is to soak up and comprehend the way in which that Dijkstra thought of those difficulties, which, in many ways, is extra beneficial than 1000 algorithms.

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Introduction to Fuzzy Sets, Fuzzy Logic and Fuzzy Control Systems. : Debate: Fuzzy Control vs. : A new approach to the design of fuzzy control rules. In: Proceedings of the International Conference on Fuzzy Logic and Applications (Fuzzy 1997), Israel, pp. : Intelligent Control of Dynamical Systems with Type-2 Fuzzy Logic and Stability Study. : Tracking Control For Unicycle Mobile Robot Using A Fuzzy Logic Controller. : Estabilidad en Sistemas de Control con Logica Difusa Tipo-2. : From Type-1 to Type-2 Fuzzy Logic Control: A Stability and Robustness Study.

A simulation where the motor position is the only available measurement for feedback is under study. The fuzzy control output regulator proposed is shown to be eminently suited to locally solve the stabilization problem in question while also attenuating the backlash model discrepancies. : A Tool for Semiglobal Stabilization of Uncertain Non-Minimum-Phase Nonlinear System via Output Feedback. : Nonlinear -Output Regulation of a Nonminimum Phase Servomechanism With Backlash. : A Fuzzy System Compensator for Backlash.

1 Type-2 Fuzzy Reasoning Assuming a fuzzy system with M rules, p input variables and one output variable, we have that the antecedent and consequent are type-2 fuzzy sets. R l : IF x1 is F1l and ... and xp is Fpl THEN y is G l H: x1 is Ax1 and ... xFpl → G l = F1l → G l = Al ΠG l (9) 38 J. Morales, O. Castillo, and J. ΠAx p (10) B l = Ax o R l , Generalized, fuzzy reasoning μ B ( y ) = μ A o R ( y ) = C ∈X [μ A ( x )∏ μ A →G ( x, y )] l l x { [ l x l ]} [ ] μ B ( y ) = μ G ( y )∏ ∏ ip=1 μ A ( xi )∏ μ F ( xi ) = μ B ( y ), μ B ( y ) l l l xi i l l Where ⎡ p ⎤ ~ ~ ⎛ ⎞⎥ ~ ⎢ μ Bl ( y ) = * ⎜ μ A (xi )* μ F l ( xi )⎟ * μ Gl ( y ) ⎢ i ⎝ X1 ⎠⎥ ⎣⎢i = 1 ⎦⎥ ⎡ p ⎤ ~ ~ ⎛ ⎞⎥ ~ ⎢ μ Bl ( y ) = * ⎜ μ AX1 ( xi )* μ Fil ( xi )⎟ * μ G l ( y ) ⎢ ⎝ ⎠⎥ ⎢⎣i = 1 ⎥⎦ Aggregation ( { [ ]}) [ ] μ B ( y ) = C Ml=1 μ B ( y ) = C Mi=1 μ G ( y )∏ ∏ ip=1 μ A ( xi ) = μ B ( y ), μ B ( y ) l l Xi Where ⎛ ⎡ ~p ⎞ ⎤ ~ ⎜⎢ * ⎛ ⎟ ⎞⎥ ~ * μ B ( y ) = ∨ μ Bl ( y ) = ∨ ⎜ i =1 ⎜ μ A ( xi ) μ F l (xi )⎟ * μ G l ( y )⎟ i l =1 l =1 ⎢ ⎠⎥ ⎜ ⎝ xi ⎟ ⎦ ⎝⎣ ⎠ p ⎛ ⎞ ⎤ ~ M ⎡~ M ⎜⎢* ⎛ ⎟ ⎞⎥ ~ * μ B ( y ) = ∨ μ Bl ( y ) = ∨ ⎜ i =1 ⎜ μ Axi ( xi ) μ Fil ( xi )⎟ * μ Gl ( y )⎟ l =1 ⎢ l =1 ⎠⎥ ⎜ ⎝ ⎟ ⎦ ⎝⎣ ⎠ M ( ) ( ) M The interval type-2 fuzzy reasoning is depicted in figure 7.