Louis Aimé Fono

Fuzzy strict preference and social choice

In this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component (indifference) and an asymmetric and regular component (regular fuzzy strict preference). From the above notions, we establish two properties of any regular fuzzy strict preference of a max-*-transitive fuzzy relation, which are then used to obtain new fuzzy versions of Gibbards oligarchy theorem and Arrows impossibility theorem.

Utility function of fuzzy preferences on a countable set under max-*-transitivity

We determine, by means of max-*-transitivity, necessary and sufficient conditions for a fuzzy binary relation R defined on a countable (finite or denumerable) set A to be representable by a utility function. We display one example of its application.

Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison

In this paper, we determine by means of fuzzy implication operators, two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively. The obtained operations allow us to construct as in [B. De Baets, H. De Meyer, Transitivity-preserving fuzzification schemes for cardinality-based similarity measures, European Journal of Operational Research 160 (2005) 726–740], cardinality-based similarity measures which are reflexive, symmetric and transitive fuzzy relations and, to propose two classes of distances (metrics) which are fuzzy versions of the well-known distance of cardinality of the symmetric difference of crisp sets.

Fuzzy arrow-type results without the Pareto principle based on fuzzy pre-orders

In this paper, we introduce appropriate properties of fuzzy preferences and fuzzy aggregation rules. We use them to provide fuzzy counterparts of Malawski and Zhous [A note on social choice theory without the pareto principle, Social Choice and Welfare 16 (1994)] and Wilsons [Social choice theory without the pareto principle, Journal of Economic Theory 5 (1972) 478-486] impossibility results concerning the aggregation of individual preferences, which do not assume the Pareto principle. By weakening conditions on fuzzy social preferences, we obtain a possibility result.

On strict lower and upper sections of weakly complete fuzzy pre-orders based on co-implication

Fono and Gwet [On strict lower and upper sections of fuzzy orderings, Fuzzy Sets and Systems 139 (2003) 583-599] introduced and studied strict lower section, strict upper section and strict order interval of a given weakly complete fuzzy pre-order R when the minimal regular fuzzy strict component of R is defined by the residual coimplicator of the Lukasiewicz t-conorm. And they gave an example of application of fuzzy strict lower sections in economics. In this paper, we generalize their framework for the minimal regular fuzzy strict component of R defined by the residual complicator of a continuous t-conorm. We show that fuzzy strict sections and fuzzy strict order intervals, defined in this general case, generate fuzzy topologies.

A delayed product customization cost model with supplier delivery performance

The concept of delayed product differentiation has received considerable attention in the research literature in recent years. However, few analytical models explain and quantify the benefits of delayed product differentiation strategy with additional consideration of supplier delivery performance. This paper proposes a delayed product differentiation model in which a supply of raw materials is integrated at the beginning of the production process to match uncertain demand in a cost-effective way given the constraint of lead time delivery window. It develops insights regarding a delayed product differentiation strategy and shows that with respect to delivery windows, supplier delivery performance plays an important role in the determination of the optimal point of differentiation. This study also shows that when the “on-time” and the “late” portions of the delivery window are constant, the proposed cost function coincides with similar models found in the literature. An extension of this work also reveals that when the customer service level varies across various production stages, its choice affects the decision to delay or postpone the customization point. A mini industrial case involving the customization of a personal desktop computer is used to illustrate the applicability of the resulting framework.

On strict lower and upper sections of fuzzy orderings

Strict lower sections, strict upper sections and open order intervals (strict order intervals) are classical notions associated to crisp orderings (crisp total preorders). In this paper, we extend these notions to fuzzy orderings. We determine all the fuzzy orderings (they contain all the crisp orderings) which make it possible to compare two fuzzy strict lower sections and two fuzzy strict upper sections. We then deduce the properties (equality, inclusion and intersection) of fuzzy strict order intervals. In this way, we obtain fuzzy extensions of well-known properties of crisp strict sections and crisp strict order intervals, and we display one example of their applications.

Arrow-Type Results Under Intuitionistic Fuzzy Preferences

Fono et al.11 characterized, for an intuitionistic fuzzy t-norm

On The Consistency Of Some Crisp Choice Functions Based On A Strongly Complete Fuzzy Pre-Order

\mathcal{T} = (T, S)

Continuity of utility functions representing fuzzy preferences

, two properties of a given regular intuitionistic fuzzy strict component of a (T,S)-transitive intuitionistic fuzzy preference. In this paper, we examine these characterizations in the particular case where