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.)

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 becoming significance within the box of Fuzzy Logie and in others the place uncertainty and imprecision play a correct position. seeing that those papers are pub­ lished in lots of journals, few books and several other lawsuits of meetings, books on aggregation are partieularly welcome. To my wisdom, "Agrega­ tion Operators. New traits and functions" is the 1st e-book aiming at generality , and that i take it as a honour to jot down this Foreword in line with the light call for of its editors, Radko Mesiar, Tomasa Calvo and Gaspar Mayor. My excitement additionally derives from the truth that two decades aga i used to be one of many first Spaniards drawn to the learn of aggregation features, and this ebook comprises paintings by way of numerous Spanish authors. The ebook includes great and correct unique papers, authored through probably the most impressive researchers within the box, and because it may well serve, because the editors indicate within the Preface, as a small instruction manual on aggregation, the ebook is especially helpful for these coming into the topic for the 1st time. The e-book additionally includes aside facing power components of software, so it may be beneficial in gaining perception at the destiny developments.

Show description

Read Online or Download Aggregation Operators: New Trends and Applications PDF

Best nonfiction_7 books

Secure Data Management: 6th VLDB Workshop, SDM 2009, Lyon, France, August 28, 2009. Proceedings

This publication constitutes the refereed complaints of the sixth VLDB Workshop on safe info administration, SDM 2009, held in Lyon, France, on August 28, 2009, along side VLDB 2009. the ten revised complete papers provided have been conscientiously reviewed and chosen from 24 submissions for ebook within the publication.

Morphogenesis: Origins of Patterns and Shapes

What are the kinfolk among the form of a procedure of towns and that of fish tuition? Which occasions may still take place in a telephone so that it participates to at least one of the finger of our arms? how one can interpret the form of a sand dune? This collective publication written for the non-specialist addresses those questions and extra commonly, the elemental factor of the emergence of varieties and styles in actual and dwelling structures.

Additional info for Aggregation Operators: New Trends and Applications

Example text

As an example, suppose that a sequence A = (an)nEN E [0, IF~ with al = 1 is given and let A(n)(x, ... , X, y) = (1 - an)x + any, for each n E N. Then the relevant decomposable aggregation operator AA: U [0, l]n -+ [0,1] is given by nEN (60) 28 where n TI j=n+l (1 - aj) = 1, by convention. Evidently, if all an = p, n ~ 2, then AA = A * as given in (20) with y) = (l-p)x+py. 1, compare with (95). For more details on decomposable aggregation operators we recommend [34]. A(2) (x, 3 Some construction methods for aggregation operators There is a wide known demand for an ample variety of aggregation operators having predietable and tailored properties to be used in modelling processes.

U [0, l]n ~ [0,1] be an aggregation operator. A nEJ'II is said to have the temporary breakdown property if there is an element tE [0,1] such that Definition 11. Let A: Vn,m E Nu {O}, VXI, ... ,Xn,Yb ... ,Ym E [0,1] : A(Xl' ... ·· ,Ym) Note that if m = = A(t,Yb .. · ,Ym). (46) °we have A(Xl, ... , t acts as the annihilator. Moreover, if an aggregation operator A has annihilator athen A has the temporary breakdown property with t = a. The temporary breakdown property reflects the renewal of cumulated output after a total collapse.

Moreover, for any symmetrie idempotent aggregation operator A we have Ar = A, independently of B. Example 5 (i) Put A = M and B = max. 2, (81) where (x~, ... , x~) is a non-decreasing permutation of (Xl, ••• , X n ). (ii) Similarly to (i), D k = Mk'in is an OWA operator related to a decreasing quantifier q(x) = (1- x)k, n Dk(X1, ... )k - (I_t~ . I)k Ix~, I-~ = M? 3. (iv) The operator G~, k > 1, is a new operator not belonging to any of classes discussed in next sections. For example, for n = 2 we obtain while In general, 41 Proposition 6 describes two-step aggregation.

Download PDF sample

Rated 4.57 of 5 – based on 5 votes