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Fuzzy Preference Modelling and Multicriteria Decision Support (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Loot Price: R4,343
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Fuzzy Preference Modelling and Multicriteria Decision Support (Paperback, Softcover reprint of hardcover 1st ed. 1995)
Series: Theory and Decision Library D:, 14
Expected to ship within 10 - 15 working days
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The encounter, in the late seventies, between the theory of
triangular norms, issuing frorn stochastic geornetry, especially
the works of Menger, Schweizer and Sklar, on the one band, and the
theory of fuzzy sets due to Zadeh, 10n the other band has been very
fruitful. Triangular norms have proved to be ready-rnade
mathematical rnodels of fuzzy set intersections and have shed light
on the algebraic foundations of fuzzy sets. One basic idea behind
the study of triangular norms is to solve functional equations that
stern frorn prescribed axioms describing algebraic properties such
as associativity. Alternative operations such as rneans have been
characterized in a similar way by Kolmogorov, for instance, and the
rnethods for solving functional equations are now weil established
thanks to the efforts of Aczel, among others. One can say without
overstaternent that the introduction of triangular norms in fuzzy
sets has strongly influenced further developrnents in fuzzy set
theory, and has significantly contributed to its better acceptance
in pure and applied rnathematics circles. The book by Fodor and
Roubens systematically exploits the benefits of this encounter in
the- analysis of fuzzy relations. The authors apply functional
equation rnethods to notions such as equivalence relations, and
various kinds of orderings, for the purpose of preference
rnodelling. Centtal to this book is the rnultivalued extension of
the well-known result claiming that any relation expressing weak
preference can be separated into three cornponents respectively
describing strict preference, indifference and incomparability.
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