Developing environmental indices using fuzzy numbers ordered weighted averaging (FN-OWA) operators

Interval numbers multiple attribute decision-making (MADM) is an important branch of uncertainty decision theory, and the decision result largely depends on the selection of the aggregation operator. In this paper, we analyze the ordered weighted average (OWA) operator, which is an averaging aggregation operator. The OWA operator provides an aggregation method between the minimum and maximum operators. Moreover, we further analyze some of extensions about OWA operator, and pay special attention to the Bonferroni means and OWA (BON-OWA) operator. Note that the BON-OWA operator only aggregate the input arguments which are exact numbers. Under normal circumstances, decision makers is difficult to provide a clear evaluation value for attribute and most of them are described by vague information. When the decision information is an interval numbers, the BON-OWA operator cannot describe decision result accurately. Under these environments, we proposed the interval numbers BON-OWA (IBr,q-OWA) operator to deal with the vague decision information in this paper. Then we consider their main properties, such as idempotence, monotonicity, and boundedness and prove them. Besides, a wide range of special aggregation operators are found in changing parameter values, such as the square mean and max operator, and so on. We also compare the ranking method of the interval numbers based on Boolean matrix. As a result, the combination of IBr,q-OWA operator makes the decision result more scientific. Finally, a new approach for decision-making problem is developed based on the IBr,q-OWA operator, which shows the effectiveness in practical examples.

Determination of the weights of an ordered weighted averaging (OWA) operator is a vital constituent of the operator's aggregation procedure. Consequently, several weight generation techniques have evolved in the literature. Here, using inverse hypergeometric distribution, we use a novel parametric function to generate the weight vector of an OWA operator. The proposed inverse hypergeometric OWA (InHyp-OWA) operator generates a unique weight vector for every choice of its parameter. Also, using the proposed weight function, OWA weight vectors can be generated without solving any complicated optimization problem. An important property of InHyp-OWA operator is that for a given parameter value, its orness value remains constant, regardless of the number of objectives aggregated. Hence, InHyp-OWA operator is a new member of the family of OWA operators with constant orness. This class of OWA operators can utilize a prejudiced preference to determine the corresponding weight vector. The proposed approach provides a number of advantages over existing weight generating methods for OWA operators. One of the remarkable advantages of the InHyp-OWA operator is the fact that it generates weight vectors with strictly monotonic components. It also generalizes the well-known Borda-Kendall OWA operator.

Some properties and representation methods for Ordered Weighted Averaging operators

Ordered Weighted Averaging (OWA) operators are a family of aggregation functions for data fusion. If the data are real numbers, then OWA operators can be characterized either as a special kind of discrete Choquet integral or simply as an arithmetic mean of the given values previously ordered. This paper analyzes the possible generalizations of these characterizations when OWA operators are defined on a complete lattice. In addition, the set of all n-ary OWA operators is studied as a sublattice of the lattice of all the n-ary aggregation functions defined on a distributive lattice.

The result of aggregation performed by the ordered weighted averaging (OWA) operator heavily depends upon the weighting vector used. A number of methods have been presented for obtaining the associated weights. In this paper, we present analytic forms of OWA operator weighting functions, each of which has properties of rank-based weights and a constant level of orness, irrespective of the number of objectives considered. These analytic forms provide significant advantages for generating the OWA weights over previously reported methods. First, the OWA weights can be efficiently generated by using proposed weighting functions without solving a complicated mathematical program. Moreover, convex combinations of these specific OWA operators can be used to generate the OWA operators with any predefined values of orness once specific values of orness are a priori stated by the decision maker. Those weights have a property of constant level of orness as well. Finally, the OWA weights generated at a predefined value of orness make almost no numerical difference with maximum entropy OWA weights in terms of dispersion.

Decision-making in sport management based on the OWA operator

A minimax disparity approach for obtaining OWA operator weights

How well does the OWA operator represent real preferences?

This paper forwards an ordered weighted average (OWA) operator of linguistic label vague (LLV) set. The OWA operator evaluates the degrees to which the object described by linguistic label vague set satisfies, docs not satisfy and does not know whether it satisfies or not most individuals of universe. Secondly, it converts the vague value expressed by triangular fuzzy numbers (TFNs) into the ordinary vague value. Thirdly, it uses the score function of LLV set to measure the suitable degree of the object described by LLV set, and takes the score as an index for sorting. Lastly, it applies the OWA operator of LLV to our simulation example of decision making. The result shows the efficiency of OWA operator of LLV set.

The most important thing in using the ordered weighted averaging (OWA) operator which can easily describe the mental model of an Decision Maker (DM), is to characterize OWA weights. Determination of OWA weights cannot provide a characterization by itself. If we want to generalization and reusability of the OWA weights to aggregate various sized objects, we have to be determine more general form. In this paper, we propose a new approach for learning a stress function, which can be characterized as a DM strategy of OWA operator. For this aim the Kolmogorov-Smirnov test for similarity probability density functions is used.

The classification accuracy of a classifier depends largely on the aggregation operator it uses in fusion of information. This paper presents a similarity classifier that utilizes a weighted ordered weighted averaging (WOWA) operator. The applicability of the WOWA operator for aggregation of similarities is studied and tested with several Regular Increasing Monotonic (RIM) type weight generators. The RIM quantifiers used here are of the basic, polynomial, trigonometric, exponential, and of the logarithmic type. The proposed approach is tested on three real world data sets. Results obtained with the new method are compared with those obtained using two previously presented similarity classifiers. The proposed new classifier shows better performance on the data sets studied, which indicates that benefits can be gained from using a WOWA operator in the aggregation.

Yager's ordered weighted averaging (OWA) operator has been widely used in soft decision making to aggregate experts' individual opinions or preferences for achieving an overall decision.The traditional Yager's OWA operator focuses exclusively on the aggregation of crisp numbers.However, human experts usually tend to express their opinions or preferences in a very natural way via linguistic terms.Type-2 fuzzy sets provide an efficient way of knowledge representation for modeling linguistic terms.In order to aggregate linguistic opinions via OWA mechanism, we propose a new type of OWA operator, termed type-2 OWA operator, to aggregate the linguistic opinions or preferences in human decision making modeled by type-2 fuzzy sets.A Direct Approach to aggregating interval type-2 fuzzy sets by type-2 OWA operator is suggested in this paper.Some examples are provided to delineate the proposed technique.

The objective of the paper is to present an extension of the ordered weighted average (OWA) operator, probability OWA (POWA) operator, distance measures and Pythagorean membership grades. These new operators are called the Pythagorean membership grade OWA distance (PMGOD) operator and the probabilistic Pythagorean membership grade OWA distance (PPMGOD) operator. This extension includes in one formulation the ability to measure the ideal vs. real situation of the distance operators, the weighting vector and reordering step of the OWA operator and the way in which it includes uncertainty based on the satisfaction of the criteria of the Pythagorean membership degree. These propositions are applied to new business ventures in the city of Colombia, where the decision maker can express his/her concerns about the uncertainty and probabilities of the current business environment and, thus, generate a better decision-making process.

An automated methodology for combining Ground Penetrating Radar features from different depths is presented and analyzed. GPR data from the NIITEK system are processed by a depth-dependent, adaptive whitening algorithm. Shape and contrast features, including compactness, solidity, eccentricity, and relative area are computed at the different depths. These features must be combined to make a decision as to the presence of a landmine at a specific location. Since many of the depths contain no useful information and the depths of the mines are unknown, a strategy based on sorting is used. In a previous work, sorted features were combined via a rule-based system. In the current paper, an automated algorithm that builds a decision rule from sets of Ordered Weighted Average (OWA) operators is described. The OWA operator sorts the feature values, weights them, and performs a weighted sum of the sorted values, resulting in a nonlinear combination of the feature values. The weights of the OWA operators are trained off-line in combination with those of a decision-making network and held fixed during testing. The combination of OWA operators and decision-making network is called a FOWA network. The FOWA network is compared to the rule-based method on real data taken from multiple collections at two outdoor test sites.

Admissible OWA operators for fuzzy numbers