By Endre Pap (auth.), János Fodor, Janusz Kacprzyk (eds.)
Soft computing, as a set of suggestions exploiting approximation and tolerance for imprecision and uncertainty in commonly intractable difficulties, has develop into very powerful and well known specifically a result of synergy derived from its parts. the combination of constituent applied sciences offers complementary tools that let constructing versatile computing instruments and fixing advanced difficulties. a large quarter of ordinary purposes of soppy computing concepts includes the keep an eye on of dynamic platforms, together with robots. Loosely conversing, regulate could be understood as using a approach to realize a wanted aim. clever keep watch over should be obvious as an extension of this idea, to incorporate self sufficient human-like interactions of a computing device with the surroundings. clever robots should be characterised by means of the power to function in an doubtful, altering surroundings with assistance from acceptable sensing. they've got the facility to autonomously plan and execute movement sequences to accomplish a target laid out in a human consumer with out specified directions. during this quantity top experts deal with a number of theoretical and sensible points in smooth computing, clever robotics and regulate. the issues mentioned are taken from fuzzy structures, neural networks, interactive evolutionary computation, clever cellular robotics, and clever keep an eye on of linear and nonlinear dynamic systems.
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Extra info for Aspects of Soft Computing, Intelligent Robotics and Control
R. Acad. Sci. Paris Ser. : Probabilistic Metric Spaces. : Pseudo-additive measures and integrals. J. Math. Anal. Appl. : Sobre funciones de negacion en la teora de conjuntas difusos. : Fuzzy Measure Theory. : ŏ -Decomposable Measures and Integrals Archimedian t-conorm . J. Math. Anal. Appl. : Uninorm Aggregation Operators. : Fuzzy Sets. Inform. hu Abstract . Aggregation of information represented by membership functions is a central matter in intelligent systems where fuzzy rule base and reasoning mechanism are applied.
Pap Condition (5) is weaker than strictly increasingness of L in each place. So min and max satisfies it, although they are not strictly increasing in each place. Example 9. W T , max is a triangle function for any left continuous t -norm T . It can be proved in a similar way for continuous t-conorm that functions min and © S, where S is W S ( F , H )( x) inf ^S ( F (u ), H (v)) | u v x` , W S , L ( F , H )( x) inf ^S ( F (u ), H (v)) | L(u, v) x` are triangular functions (binary operation L has all properties from previous theorem and F , H ' ).
First we briefly consider essential properties of aggregation functions individually. Then we formulate consistent aggregation as it is usual in the literature. Consistency indicates a functional equation for the aggregation functions involved. We summarize some fundamental results on solutions of particular forms of these equations under some additional properties of the aggregations functions. We show also some non-conventional aggregation functions such as distance-based or entropy-based aggregations.