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This paper focuses on the problem of constructing aggregation functions which support the concept of partial agreement when only one or more sub-group(s) of decision makers and criteria, not necessarily all of them, is (are) involved to take the final action. The proposed method is started with computing all different α -combinations from an n -element set of inputs, according to the binomial coefficient, and then completed by combining their aggregations. This approach, so-called combination operator-based aggregation function, guarantees to consider various agreement scenarios at different consensus levels in contrary with the traditional composition-based construction methods that act as a full agreement. The attention is then given to the weighted case specially the conditions of weighting vectors for ensuring the well-defined property of the proposed method. As an application, the combination operator-based aggregation function is generalized over the Cartesian product of unit intervals [0,1] to deal with multi-polar information. The proposed aggregating methodology is then used to reach consensus in a group decision-making problem. [ABSTRACT FROM AUTHOR]

Abstract In this contribution we consider methods for improving the quality of classification by the k nearest neighborhood classifiers in the case of large number of missing values. The classical version of such classifier is applied, moreover the classifier with the aggregation of certainty coefficients of the individual classifiers with the use of the arithmetic mean, as well as new versions of the classifier with the use of diverse interval-valued aggregation functions are considered. After adding missing values to the data, the quality of the classical method decreases. By contrast, the interval modeling of missing values and application of interval-valued aggregation functions in the classifiers entail a much slower decrease of their quality. The paper includes the results of experiments performed on the data sets from the machine learning repository UCI. [ABSTRACT FROM AUTHOR]

Ordered qualitative scales formed by linguistic terms are frequently used for evaluating sets of alternatives in different decision-making problems. These scales are usually implicitly considered as uniform in the sense that the psychological proximity between consecutive terms is perceived as identical. However, sometimes agents can perceive different proximities between the linguistic terms of the scale, and an appropriate method is required for aggregating these perceptions. In this paper we introduce the notion of metrizable ordinal proximity measure, discuss some aggregation procedures and propose a method based on metrics for aggregating experts’ opinions on proximities between linguistic terms on ordered qualitative scales. [ABSTRACT FROM AUTHOR]

Overlap and grouping functions, as two kinds of special binary aggregation functions, have been investigated for applications in image processing, classification problems and decision making based on fuzzy preference relations. In addition, after the distributive laws related to fuzzy implications and some special binary aggregation functions have been proposed, there arise many discussions on this research topic. In this paper, we continue studying this topic and discuss the four basic distributive laws of fuzzy implications over overlap and grouping functions. At first, we investigate the four basic distributive laws of fuzzy implications over overlap and grouping functions for the residual implications derived from overlap functions, ( G, N )-implications obtained from grouping functions G and fuzzy negations N , and QL -operations derived from overlap functions, grouping functions and fuzzy negations, respectively. And then, we extend the related results when we take into account the residual implications, ( G, N )-implications or QL -operations in the four basic distributive laws of fuzzy implications over overlap and grouping functions to arbitrary fuzzy implications satisfying some desirable algebraic properties in the preceding four basic distributive laws. [ABSTRACT FROM AUTHOR]

In this contribution new types of aggregation functions for interval-valued fuzzy setting are introduced. They are called necessary and possible aggregation functions, respectively. In the monotonicity conditions for these aggregation functions the classical monotonicity for intervals is replaced with the new comparability relations. These relations follow naturally from the interpretations of interval-valued fuzzy sets and together with the classically used monotonicity for intervals, form a family of all possible approaches to define relations of comparability for intervals. Moreover, in this paper dependencies between considered families of aggregation functions are presented. Furthermore, transitivity properties of interval-valued fuzzy relations, based on these new comparability relations, are studied and preservation of them by possible and necessary aggregation functions are considered. [ABSTRACT FROM AUTHOR]

In this paper, conditions for n -argument functions to preserve diverse types of fuzzy orders during aggregation process are presented. Namely, the following fuzzy orders are studied: total preorder, total order, strict total order, partial preorder, partial order, strict partial order, interval order or semiorder and their preservation in aggregation process along with other connections between input fuzzy relations and the aggregated one are presented. Moreover, dependencies between diverse classes and also among the given class of fuzzy orders are presented. The considered fuzzy orders are compound properties depending in their definitions on arbitrary binary operations on [0, 1], including fuzzy conjunctions and disjunctions (with special cases of triangular norms and triangular conorms). Finally, an application of the obtained result is presented by the given algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes some new geometric operations on intuitionistic fuzzy sets (IFSs) based on probability non-membership (PN) function operator, probability membership (PM) function operator and probability hetergeneous (PH) operator, which are constructed from the probability point of view. The geometric interpretations of these operations are given. Moreover, we develop some intuitionistic fuzzy geometric interaction averaging (IFGIA) operators. The properties of these aggregation operators are investigated. The key advantage of the IFGIA operators is that the interactions between non-membership function and membership function of different IFSs are considered. Finally, an approach to multiple attributes decision making is given based on the proposed aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of the proposed approach. [Copyright &y& Elsevier]