In this paper we consider some properties of intuitionistic fuzzy preference relations. We pay attention to preservation of intuitionistic fuzzy preference relations by aggregation operations. In particular, we know, that a special kind of aggregation operations (lattice operations) do not preserve intuitionistic fuzzy preference relations. We describe the operations which preserve intuitionist...

We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...

Decomposable mappings from the space of symmetric k-fold tensors over E, ⊗ s,k E, to the space of k-fold tensors over F , ⊗ s,k F , are those linear operators which map nonzero decomposable elements to nonzero decomposable elements. We prove that any decomposable mapping is induced by an injective linear operator between the spaces on which the tensors are defined. Moreover, if the decomposable...

We discuss the use of the fuzzy measure for representing information about uncertain variables. We describe the relationship between the fuzzy measure and the Dempster-Shafer belief structure. A method for generating the fuzzy measures associated with a D-S belief structure is described. We discuss the use of the Shapley index as a means for providing an entropy for fuzzy measures. We introduce...

This paper describes a fuzzy union based approach for automatically evaluating machine generated extract summaries. The proposed method represents every sentence within a machine generated summary as a fuzzy set. Sentences in the reference summary are assigned membership grades in each of these fuzzy sets using cosine distance measure. Finally Fuzzy union (s-norm operation) is used to compute a...

In a recent paper (European Journal of Operational Research, 158, 271–292, 2004), S. Greco, B. Matarazzo and R. S lowiński have stated without proof a result characterizing binary relations on product sets that can be represented using a discrete Sugeno integral. To our knowledge, this is the first result about a fuzzy integral that applies to non-necessarily homogeneous product sets and only u...

In this work, we present a Fuzzy Constraint Networks model for discrete domains, which generalizes the Disjunctive Fuzzy Temporal Constraint Networks model for temporal reasoning, and we propose the use of the seriesparallel and tree-decomposition approaches for simplifying its processing. After a separate empirical evaluation process of both techniques, a combined evaluation process over the s...