Abstract: An overview of a variety of methods of agglomerative hierarchical clustering as well as non-hierarchical clustering for semi-supervised classification is given. Methodological aspects are emphasized than experimental results. Two different formulations for semi-supervised classification are introduced: one is with pairwise constraints, while the other does not use constraints. Three families of methods of the mixture of densities, the COP K-means, and fuzzy c-means are contrasted and their theoretical properties are discussed with respect to the two formulations. A number of agglomerative hierarchical algorithms are then discussed. It will be shown that the single linkage has a different characteristic when compared with the complete linkage and average linkage. Moreover the centroid method and the Ward method are discussed. It will also be shown that the must-link constraints and the cannot-link constraints are handled in different manner in these methods.

Abstract: In the real world problems, we may face the cases when parameters of linear programming problems are not known exactly. In such cases, parameters can be treated as random variables or possibilistic variables. The probability distribution which random variables obey are not always easily obtained because they are assumed to be obtained by strict measurement owing to the cardinality of the probability. On the other hand, the possibility distribution restricting possibilistic variables can be obtained rather easily because they are assumed to be obtained from experts perception owing to the ordinality of possibility. Then possibilistic programming approach would be convenient as an optimization technique under uncertainty.
In this talk, we review possibilistic linear programming approaches to robust optimization. Possibilistic linear programming approaches can be classified into three cases: optimizing approach, satisficing approach and two-stage approach. Because the third approach has not yet been very developed, we focus on the other two approaches. First we review the optimization approach. We describe a necessarily optimal solution as a robust optimal solution in the optimization approach. Because a necessarily optimal solution do not always exist, necessarily soft optimal solutions have been proposed. In the necessarily soft optimal solutions, the optimality conditions is relaxed to an approximate optimality conditions. The relation to minimax regret solution is shown and a solution procedure for obtaining a best necessarily soft optimal solution is briefly described.
Next we talk about the modality constrained programming approach. A robust treatment of constraints are introduced. Then the necessity measure optimization model and necessity fractile optimization model are described as treatments of an objective function. They are models from the viewpoint of robust optimization. The simple models can preserve the linearity of the original problems. We describe how much we can generalize the simple models without great loss of linearity. A modality goal programming approach is briefly introduced. By this approach, we can control the distribution of objective function values by a given goal.
Finally, we conclude this talk by giving future topics in possibilistic linear programming.

Abstract: After a short historical overview of the roots of integration theory, dating back to 1850 B.C., an example on optimal performance of a group of workers is given. Under 4 different constraints settings we give motivtion for 4 types of integrals with repsect to monotone measures linked to the standard arithmetic operations, namely Shilkret, Pan, Choquet and concave (Lehrer) integrals. These integrals are further discussed and generalized, cosidering pseudo-arithmetical operations oplus and otimes. Note that all 4 above mentioned constraint settings merge into the unique Sugeno integral once the lattice operations of join and meet are considered.