Fitting generated aggregation operators to empirical data

This paper treats the problem of fitting general aggregation operators with unfixed number of arguments to empirical data. We discuss methods applicable to associative operators (t-norms, t-conorms, uninorms and nullnorms), means and Choquet integral based operators with respect to a universal fuzzy measure. Special attention is paid to k-order additive symmetric fuzzy measures.

Learning weights in the generalized OWA operators

This paper discusses identification of parameters of generalized ordered weighted averaging (GOWA) operators from empirical data. Similarly to ordinary OWA operators, GOWA are characterized by a vector of weights, as well as the power to which the arguments are raised. We develop optimization techniques which allow one to fit such operators to the observed data. We also generalize these methods for functional defined GOWA and generalized Choquet integral based aggregation operators.

Methods of construction of OWA operators from data

This paper investigates the problem of obtaining the weights of the ordered weighted aggregation (OWA) operators from observations. The problem is formulated as a restricted least squares and uniform approximation problems. We take full advantage of the linearity of the problem. In the former case, a well known technique of non-negative least squares is used. In a case of uniform approximation, we employ a recently developed cutting angle method of global optimisation. Both presented methods give results superior to earlier approaches, and do not require complicated nonlinear constructions. Additional restrictions, such as degree of orness of the operator, can be easily introduced

Identification of general and double aggregation operators using monotone smoothing

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and averaging. Recently double aggregation operators have been introduced; they model multistep aggregation process. The choice of aggregation operators depends on the particular problem, and can be done by fitting the operator to empirical data. We examine fitting general aggregation operators by using a new method of monotone Lipschitz smoothing. We study various boundary conditions and constraints which determine specific types of aggregation.

Identification of general aggregation operators by Lipschitz approximation

Aggregation operators model various operations on fuzzy sets, such as conjunction, disjunction and aver aging. The choice of aggregation operators suitable for a particular problem is frequently done by fitting the parameters of the operator to the observed data. This paper examines fitting general aggregation operators by using a new method of Lipschitz approximation.

Handling of absorbent information by aggregation operators

We propose a generalization of the notion of the absorbent element of aggregation operators. Our construction involves tuples of values that are absorbent, that is, that decide the result of aggregation. We analyze some basic properties of this generalization and determine the absorbent tuples of some popular classes of aggregation operators.

Pointwise construction of Lipschitz aggregation operators

This paper establishes tight upper and lower bounds on Lipschitz aggregation operators considering their diagonal, opposite diagonal and marginal sections. Also we provide explicit formulae to determine the bounds. These are useful for construction of these type of aggregation operators, especially using interpolation schemata.

Handling of neutral information by aggregation operators

We generalize the notion of a neutral element of aggregation operators. Our construction involves tuples of values that are neutral with respect to the result of aggregation. Neutral tuples are useful to model situations in which information from different sources, or preferences of several decision makers, cancel each other. We examine many popular classes of aggregation operators in respect to their neutral sets, and also construct new aggregation operators with predefined neutral sets

The ethical outlook of micro business operators

This paper reports the findings of an investigation into the ethical outlook of micro business operators. The study was conducted in Australia and is the first such examination of ethical perspectives in this segment of the business population. Micro business is internationally recognizable, economically significant, and strongly entrepreneurial, and it has a high level of control over the values it enacts. The study indicates that ethical considerations are important to Australian micro business operators. While no one single ethical perspective was dominant, nonreligious beliefs and principles were found to be the most important determinant of their ethical values. Some variation was discovered in operator attitudes based on age, gender, and education.

Handling of neutral information by aggregation operators

We generalize the notion of a neutral element of aggregation operators. Our construction involves tuples of values that are neutral with respect to the result of aggregation. Neutral tuples are useful to model situations in which information from different sources, or preferences of several decision makers, cancel each other. We examine many popular classes of aggregation operators in respect to their neutral sets, and also construct new aggregation operators with predefined neutral sets.

Construction of aggregation operators for automated decision making via optimal interpolation and global optimization

This paper examines methods of point wise construction of aggregation operators via optimal interpolation. It is shown that several types of application-specific requirements lead to interpolatory type constraints on the aggregation function. These constraints are translated into global optimization problems, which are the focus of this paper. We present several methods of reduction of the number of variables, and formulate suitable numerical algorithms based on Lipschitz optimization.

Absorbent tuples of aggregation operators

We generalize the notion of an absorbent element of aggregation operators. Our construction involves tuples of values that decide the result of aggregation. Absorbent tuples are useful to model situations in which certain decision makers may decide the outcome irrespective of the opinion of the others. We examine the most important classes of aggregation operators in respect to their absorbent tuples, and also construct new aggregation operators with predefined sets of absorbent tuples.

Construction of aggregation operators with noble reinforcement

This paper examines disjunctive aggregation operators used in various recommender systems. A specific requirement in these systems is the property of noble reinforcement: allowing a collection of high-valued arguments to reinforce each other while avoiding reinforcement of low-valued arguments. We present a new construction of Lipschitz-continuous aggregation operators with noble reinforcement property and its refinements.

Fitting ST-OWA operators to empirical data

The OWA operators gained interest among researchers as they provide a continuum of aggregation operators able to cover the whole range of compensation between the minimum and the maximum. In some circumstances, it is useful to consider a wider range of values, extending below the minimum and over the maximum. ST-OWA are able to surpass the boundaries of variation of ordinary compensatory operators. Their application requires identification of the weighting vector, the t-norm, and the t-conorm. This task can be accomplished by considering both the desired analytical properties and empirical data.