Alfio Giarlotta

Passive and Active Compensability Multicriteria ANnalysis (PACMAN)

Determining intercriteria relations is an important issue in MCDA. In order to handle this problem, this paper presents a new approach to the concept of compensation in multicriteria analysis, named PACMAN (Passive and Active Compensability Multicriteria ANalysis). The notion of compensability introduced here is decision maker oriented, relying only on information provided by him. In PACMAN compensability is analysed by taking into consideration two criteria at a time and distinguishing the compensating criterion from the compensated one. Separating active and passive effects of compensation allows one to point out a possible asymmetry of the notion of compensability. A valued binary relation of compensated preference is introduced. Compensated preference can be used for a modelization of the preference structure.

A Genesis of Interval Orders and Semiorders: Transitive NaP-preferences

A NaP-preference (necessary and possible preference) on a set A is a pair

Representable Lexicographic Products

{\left(\succsim^{^{_N}}\!,\,\succsim^{^{_P}}\!\right)}

Multicriteria compensability analysis

of binary relations on A such that its necessary component

Pointwise Debreu Lexicographic Powers

{\succsim^{^{_N}} \!\!}

Necessary and possible hesitant fuzzy sets: A novel model for group decision making

is a partial preorder, its possible component

Implementations of PACMAN

{\succsim^{^{_P}} \!\!}

The Satisfiability Problem for Boolean Set Theory with a Choice Correspondence.

is a completion of

Perfect Information vs Random Investigation: Safety Guidelines for a Consumer in the Jungle of Product Differentiation

{\succsim^{^{_N}} \!\!}

A Hierarchy of Chains Embeddable into the Lexicographic Power \boldsymbol{({\mathbb{R}}^\omega,\prec_{\rm lex})}

, and the two components jointly satisfy natural forms of mixed completeness and mixed transitivity. We study additional mixed transitivity properties of a NaP-preference