On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.

We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector

Qubit thermometry for micromechanical resonators

We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to non dissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population, and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.Comment: 9 pages, 5 figures, revised version, to appear on PR

On the normalization of a priority vector associated with a reciprocal relation.

In this paper we show that the widely used normalization constraint SUM(i=1,n) wi = 1 does not apply to the priority vectors associated with reciprocal relations, whenever additive transitivity is involved. We show that misleading applications of this type of normalization may lead to unsatisfactory results and we give some examples from the literature. Then, we propose an alternative normalization procedure which is compatible with additive transitivity and leads to better results.reciprocal relation; fuzzy preference relation; priority vector; normalization

OWA-based fuzzy m-ary adjacency relations in Social Network Analysis.

In this paper we propose an approach to Social Network Analysis (SNA) based on fuzzy m-ary adjacency relations. In particular, we show that the dimension of the analysis can naturally be increased and interesting results can be derived. Therefore, fuzzy m-ary adjacency relations can be computed starting from fuzzy binary relations and introducing OWA-based aggregations. The behavioral assumptions derived from the measure and the exam of individual propensity to connect with other suggest that OWA operators can be considered particularly suitable in characterizing such relationships.reciprocal relation; fuzzy preference relation; priority vector; normalization