Some advances in mathematical models for preference relations

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly. The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model. The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency. The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations. The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

The effect of shielding gas feeding method in laser welding of steel

Gas shielding plays an important role in laser welding phenomena. This is because it does not only provide shielding against oxidization but it has an effect in beam absorption and thus welds penetration. The goal of this thesis is to study and compare the effects of different shielding gas feeding methods in laser welding of steel. Research method is a literature survey. It is found that the inclination angle and the arrangement of the gas feeding nozzles affect the phenomena significantly. It is suggested that by designing shielding gas feeding case specifically better welding results can be obtained.

Plant-Herbivore Interaction in a Fragmented Landscape: Local Adaptation and Inbreeding

Reciprocal selection between interacting species is a major driver of biodiversity at both the genetic and the species level. This reciprocal selection, or coevolution, has led to the diversification of two highly diverse and abundant groups of organisms, flowering plants and their insect herbivores. In heterogeneous environments, the outcome of coevolved species interactions is influenced by the surrounding community and/or the abiotic environment. The process of adaptation allows species to adapt to their local conditions and to local populations of interacting species. However, adaptation can be disrupted or slowed down by an absence of genetic variation or by increased inbreeding, together with the following inbreeding depression, both of which are common in small and isolated populations that occur in fragmented environments. I studied the interaction between a long-lived plant Vincetoxicum hirundinaria and its specialist herbivore Abrostola asclepiadis in the southwestern archipelago of Finland. I focused on mutual local adaptation of plants and herbivores, which is a demonstration of reciprocal selection between species, a prerequisite for coevolution. I then proceeded to investigate the processes that could potentially hamper local adaptation, or species interaction in general, when the population size is small. I did this by examining how inbreeding of both plants and herbivores affects traits that are important for interaction, as well as among-population variation in the effects of inbreeding. In addition to bi-parental inbreeding, in plants inbreeding can arise from self-fertilization which has important implications for mating system evolution. I found that local adaptation of the plant to its herbivores varied among populations. Local adaptation of the herbivore varied among populations and years, being weaker in populations that were most connected. Inbreeding caused inbreeding depression in both plants and herbivores. In some populations inbreeding depression in herbivore biomass was stronger in herbivores feeding on inbred plants than in those feeding on outbred ones. For plants it was the other way around: inbreeding depression in anti-herbivore resistance decreased when the herbivores were inbred. Underlying some of the among-population variation in the effects of inbreeding is variation in plant phenolic compounds. However, variation in the modification of phenolic compounds in the digestive tract of the herbivore did not explain the inbreeding depression in herbivore biomass. Finally, adult herbivores had a preference for outbred host plants for egg deposition, and herbivore inbreeding had a positive effect on egg survival when the eggs were exposed to predators and parasitoids. These results suggest that plants and herbivores indeed exert reciprocal selection, as demonstrated by the significant local adaptation of V. hirundinaria and A. asclepiadis to one another. The most significant cause of disruption of the local adaptation of herbivore populations was population connectivity, and thus probably gene flow. In plants local adaptation tended to increase with increasing genetic variation. Whether or not inbreeding depression occurred varied according to the life-history stage of the herbivore and/or the plant trait in question. In addition, the effects of inbreeding strongly depended on the population. Taken together, inbreeding modified plant-herbivore interactions at several different levels, and can thus affect the strength of reciprocal selection between species. Thus inbreeding has the potential to affect the outcome of coevolution.