Download Aggregation Operators: New Trends and Applications by Tomasa Calvo, Anna Kolesárová, Magda Komorníková, Radko PDF

By Tomasa Calvo, Anna Kolesárová, Magda Komorníková, Radko Mesiar (auth.), Professor Tomasa Calvo, Professor Gaspar Mayor, Professor Radko Mesiar (eds.)

ISBN-10: 3662003198

ISBN-13: 9783662003190

1. The expanding variety of study papers seemed within the final years that both utilize aggregation capabilities or give a contribution to its theoretieal examine asses its transforming into significance within the box of Fuzzy Logie and in others the place uncertainty and imprecision play a proper function. on the grounds that those papers are pub­ lished in lots of journals, few books and a number of other complaints of meetings, books on aggregation are partieularly welcome. To my wisdom, "Agrega­ tion Operators. New tendencies and purposes" is the 1st e-book aiming at generality , and that i take it as a honour to jot down this Foreword based on the light call for of its editors, Radko Mesiar, Tomasa Calvo and Gaspar Mayor. My excitement additionally derives from the truth that 20 years aga i used to be one of many first Spaniards attracted to the research of aggregation services, and this ebook comprises paintings via a number of Spanish authors. The booklet includes great and correct unique papers, authored via one of the most striking researchers within the box, and because it could serve, because the editors indicate within the Preface, as a small guide on aggregation, the publication is especially beneficial for these coming into the topic for the 1st time. The booklet additionally comprises aside facing power parts of software, so it may be important in gaining perception at the destiny developments.

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Min(xn, ai)) if ai < b:::; bi , (76) A (iS)( Xl,···, X n ) -_ {Ai b e1se, where a = min(xI, ... , x n ) and b = max(xI, ... , X n ). 37 Observe that admitting formally k = max. 7], A(s)(x,y) else. Observe that the standard ordinal sums of t-norms and t-conorms or copulas (though neither t-norms nor copulas are idempotent operators, in general), as introduced in [114,61], are just our A(iw) ordinal sum, while A(is) describes exactly the standard ordinal sum of t-conorms or of dual copulas, see [114,107,61].

Coming from the arithmetic mean applying some construction method. This chapter is devoted to the presentation of some of these classes of aggregation operators related to the arithmetie mean. 1 Weighted arithmetic means The symmetry of the arithmetie mean does not reflect the possibly different importances of single criteria in multi-criteria decision making. 3, see (69). For n-ary operators, the weights Wl, ... , W n form an n-dimensional weightthink on a n L: Wi = 1. However, if we have to i=l weighted arithmetie mean W: U [0,1]n ---+ [0,1] as an operator ing vector w = (Wb ...

Also observe that G has annihilator a = 0 which corresponds to the annihilator

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