Roberto Ghiselli Ricci

Note on ranking fuzzy triangular numbers

This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision‐making situations. Three new methods are proposed, and a notion of preference between alternatives is suggested. A comparison with other methods is provided in the concluding table.

A characterization of a general class of ranking functions on triangular fuzzy numbers

This paper aims to the discussion of properties for ranking fuzzy numbers. An approach of axiomatic type is followed providing the definition of two groups of requirements which characterize a ranking function through its behaviour on triangular fuzzy numbers. Particularly, the problem of making the evaluations on triangular fuzzy numbers sensitive to their spread has been deeply analyzed.

Multi-attribute aggregation operators

This paper deals with the idea of aggregation. A new, enlarged notion of aggregation operator is given, along with a classification of classical properties into some main groups. The concept of multi-attribute aggregation operator, which incorporates many classical aggregation methods, is provided. An extension of different properties to multi-attribute aggregation operators is proposed.

Economic value added and systemic value added: symmetry, additive coherence and differences in performance

Two measures of excess profit are currently available in the literature: Economic Value Added (EVA) (Stewart, 1991) and Systemic Value Added (SVA) (Magni, 2003a, b, 2004; 2005). This study shows that, unlike EVA, SVA is symmetric and additively coherent. Also, EVA and SVA are not simply different in value but also convey different information about good or bad performances.Two measures of excess profit are currently available in the literature: Economic Value Added (EVA) (Stewart, 1991) and Systemic Value Added (SVA) (Magni, 2003a, b, 2004; 2005). This study shows that, unlike EVA, SVA is symmetric and additively coherent. Also, EVA and SVA are not simply different in value but also convey different information about good or bad performances.

Convexity conditions on t-norms and their additive generators☆

Abstract Let T be an Archimedean (continuous) t-norm and α ∈ ] 0 , 1 2 [ . Fodor and Ovchinnikov have studied a relation between the inequality T ( max ( x - α , 0 ) , min ( x + α , 1 ) ) ⩽ T ( x , x ) and the convexity of the additive generator of T . Here we clarify this relation and answer open problems from previous studies.

Exchangeable copulas

This paper focuses on exchangeable copulas: some necessary and sufficient conditions are provided, together with a characterization result, in differential form. A very flexible model capable to generate a wide range of exchangeable copulas is presented.

FINITELY AND ABSOLUTELY NON IDEMPOTENT AGGREGATION OPERATORS

This paper deals with the problem of establishing a new class of aggregation operators, which are close to the averaging, without being necessarily idempotent. An axiomatic approach is followed thr...

On differential properties of copulas

We clarify the problem of the existence of functions obtained as particular restrictions of the first partial derivatives of a quasi-copula and we show their role for characterizing the 2-increasing property. The question of the existence of the one-sided first partial derivatives of a copula along an affine section of the real unit square is discussed and new results and several examples are provided.

Characterization of non-nilpotent topological interval semigroups

A remarkable subclass of linearly ordered semigroups, called interval semigroups, defined on connected and compact sets is studied. Particularly, a generalized notion of o-isomorphism, called weak o-embedding, of such semigroups into the real numbers with standard operations is given. A representation theorem for the weak o-embedding of topological Archimedean interval semigroups with no zero divisors is provided. Such characterization is shown to be the best one possible.

ASYMPTOTICALLY IDEMPOTENT AGGREGATION OPERATORS

This paper deals with aggregation operators. A new form of idempotency, called asymptotic idempotency, is introduced. A critical discussion of the basic notion of aggregation operator, strictly connected with asymptotic idempotency, is provided. Some general construction methods of symmetric, asymptotically idempotent aggregation operators admitting a neutral element are illustrated.