OWA Aggregation Research Articles

Neutrosophic Sets in Investigating the Right to Genetic Information: A Study using Fuzzy Cognitive Maps and D-OWA

This article provides a comprehensive view of the evolution and ethical implications of genetics, from its historical origins to modern advancements like the Human Genome Project. It emphasizes the importance of genetic information in disease prediction and understanding human diversity while highlighting the need to address associated ethical and privacy issues. It introduces Fuzzy Cognitive Maps (FCM) and the Dependent OWA (D-OWA) aggregation operator as innovative tools for analyzing the complex landscape of the Right to Genetic Information (RGI) in an international context, identifying key factors such as legal frameworks, technological advancements, access to health, culture, ethics, and commercial interests. The research reveals that while legal framework and technology are predominant, other factors also play significant roles in managing RGI. The application of D-OWA provides additional insights, confirming that conventional centrality assessments adequately reflect the priorities and influence of factors in RGI. It concludes by underlining the need for specific strategies to address these challenges, such as strengthening the legal framework, promoting ethics in genetics, improving public education, and respecting cultural diversity, to protect individual rights while leveraging the benefits of genetics for society.

An induced OWA aggregation operator with dual preference setting for DEA cross-efficiency ranking

An induced OWA aggregation operator with dual preference setting for DEA cross-efficiency ranking

Ensemble feature selection using Bonferroni, OWA and Induced OWA aggregation operators

Feature selection becomes inevitable owing to a rapid increase in digital technology which permits the generation of high dimensional data in a large quantity within a short time. Feature selection techniques not only improves classification accuracy but also decreases time complexity as well as computation cost and storage. Ensemble feature selection has lately emerged as a potential approach to data mining. Identifying numerous optimal features is one of the key advantages of ensemble feature selection. The objective of this study is to introduce an ensemble technique based on the rank aggregation procedure. Four operators are used for the purpose of aggregation, namely the induced ordered weighted averaging (IOWA) operator, the normalized Bonferroni weighted mean operator, the Bonferroni-ordered weighted averaging operator and the Bonferroni-induced ordered weighted averaging operator. These operators enable the evaluation of continuous aggregations, multiple assessments between each input and distance measurements in the same formulation. An objective weighting approach denoted as the entropy weight method, is utilized to measure the degree of disorder. A total of 10 benchmark data sets are employed to evaluate the superiority of the proposed methodologies. The effectiveness of the proposed method is evaluated and compared using the accuracy, F-measure, precision and recall performance metrics, and better results than those from other existing techniques are obtained.

A multi-criteria group decision-making method based on OWA aggregation operator and Z-numbers

A multi-criteria group decision-making method based on OWA aggregation operator and Z-numbers

An Iterative Approach for the Solution of the Constrained OWA Aggregation Problem with Two Comonotone Constraints

In this paper, first, we extend the analytical expression of the optimal solution of the constrained OWA aggregation problem with two comonotone constraints by also including the case when the OWA weights are arbitrary non-negative numbers. Then, we indicate an iterative algorithm that precisely indicates whether a constraint in an auxiliary problem is either biding or strictly redundant. Actually, the biding constraint (or two biding constraints, as this case also may occur) are essential in expressing the solution of the initial constrained OWA aggregation problem.

Best approximation of OWA Olympic weights under predefined level of orness

An ideal type of OWA aggregation operator is the one constructed on the so-called Olympic weights. The orness of this operator is 1/2. Therefore, sometimes we need a trade-off between the desire of having an OWA aggregation operator with weights as close as possible to the Olympic ones and the desire of having a predefined level of orness. In this paper, we choose these optimal weights by minimizing the Euclidean distance to the Olympic weights vector under the constraint of preserving a given level of orness. First, in the case n=4, we propose an iterative algorithm where the optimal solution is given for all possible values of the orness, values that are grouped along a partition of the unit interval. This iterative algorithm will inspire us to deduce the optimal weights in the general case. Consequently, we will obtain the analytical solution of the optimal weights as a function depending on the orness level.

OWA aggregation operators and multi-agent decisions with [formula omitted]-soft sets

This work improves the theoretical basis of N-soft sets and insists on their practical applications in a multi-agent context. N-soft sets characterize the alternatives in terms of multinary descriptions by attributes. We argue that unlike the basic example of soft set theory, N-soft sets are amenable to various interesting approaches in relation to aggregation. However the literature has not provided mechanisms for the aggregation of N-soft sets. And there exists no multi-agent decision making procedure based on N-soft sets either.Therefore, the goal of this work is twofold. We present a novel theory of aggregation of N-soft sets. The fundamental tools for this purpose are OWA operators. We produce the first scores of alternatives defined by multi-agent, multinary evaluations. Then we apply this theory to multi-agent decision-making. In this way we produce the first algorithms for multi-agent decisions based on N-soft sets. We support our findings with real examples that illustrate the application and versatility of these flexible approaches.

Some fuzzy measure modeled multi-criteria formulations

ABSTRACTWe first describe an approach to multi-criteria making which makes use of a fuzzy measure over the set of criteria to model the user expressed relationship between the criteria. Under this approach we use the Choquet integral, guided by this fuzzy measure, to aggregate an alternative’s satisfactions to the individual criteria. Our focus in this paper is to look at the formulation, in terms of fuzzy measures, of some interesting and novel relationships between the criteria. After noting that the OWA aggregation can be modeled using a cardinality measure we look at the measure formulation of a rule-based expression of a collection of OWA aggregations. We then focus on the measure representation of a user provided well-formed formula in the language of propositional logic expressed relationship between the criteria.

On the fusion of multiple multi-criteria aggregation functions with focus on the fusion of OWA aggregations

We discuss the concepts of a fuzzy measure and the Choquet integral with respect to a fuzzy measure. We introduce aggregation functions and discus their role in fusing fuzzy measures. We describe the formulation of multi-criteria decision-making using fuzzy measures and explain how the measure is used to capture the relationship between the criteria. We look at some examples of multi-criteria decision-making using a measure-based approach. Two notable examples are the OWA aggregation of the criteria and a propositional logic expression of the relationship between criteria. We next look at the fusion of multiple multi-criteria decision functions. The major objective of this paper is to focus on the problem of the fusion of multiple OWA aggregation functions. A significant benefit of the methodology developed here is that it is based solely on the use of fuzzy measures, this allows us to represent in a unified fashion many different aggregation imperatives.

Extending Set Measures to Pythagorean Fuzzy Sets

We introduce the idea of level sets which are crisp sets associated with a fuzzy set. We show how we can represent a fuzzy set using a collection of level sets; this allows us to extend set functions, such as probability and other set measures, to fuzzy subsets. We emphasize that this extension is itself a fuzzy subset. We next introduce Pythagorean fuzzy subsets and discuss the OWA and Choquet aggregation of these sets. We provide a formulation for level sets associated with a Pythagorean fuzzy subset that we use to provide a representation of a Pythagorean fuzzy set in terms of level sets. With the aid of Zadeh’s extension principle, we use this level set representation to provide for an extension of set measures to Pythagorean fuzzy sets. We then suggest an alternative approach to extending set measures to Pythagorean fuzzy sets using the Choquet integral.

OWA aggregation with an uncertainty over the arguments

We discuss the OWA aggregation operation and the role the OWA weights play in determining the type of aggregation being performed. We introduce the idea of a weight generating function and describe its use in obtaining the OWA weights. We emphasize the importance of the weight generating function in prescribing the type of aggregation to be performed. We consider the problem of performing a prescribed OWA aggregation in the case when we have a probability distribution over the argument values. We show how we use the weight generating function to enable this type of aggregation. Next we consider the situation when we have a more general measure based uncertainty over the argument values. Here again we show how we can use the weight generating function to aid in performing the prescribed OWA aggregation in the face of this more general type of uncertainty. Finally we look at the task of obtaining a weight generating function from a given set of OWA weights.

Dynamic weights allocation according to uncertain evaluation information

ABSTRACTWeights allocation methods are critical in Multi-Criteria Decision Making. Given numerical importances for each involved criterion, direct normalizing those numerical importances to obtain weights for those criteria is plain, lack of flexibility, and thus cannot well model some more types of subjective preferences of different decision makers like Dominance Strength as defined in this study. We show that concave RIM quantifier Q based OWA weights allocation method can well handle and model such preference. However, in real decision making those numerical importances are very often embodied by uncertain information such as independent random variables with discrete or continuous distributions, statistic information and interval numbers. In any of those circumstances, simple RIM quantifier Q based OWA weights allocation cannot work. Therefore, in this study, we will propose some special dynamic weights allocation methods to gradually allocate weights and accumulate allocated parts to each criterion, and finally, obtain a total weights collection. When the uncertain numerical importances become equivalent to general real numbers, the method automatically degenerates into general RIM quantifier based OWA weights allocation. The innovative weight allocations have discrete and continuous versions: the former can be well programmed while the latter has neat and succinct mathematical expression. The method can also be widely used in many other applications like some economic problems including investment quota allocation for one’s favorite stocks, and the dynamic OWA aggregation for interval numbers.

On the constrained OWA aggregation problem with single constraint

In this note we present a simple proof for the constrained OWA aggregation problem with a single constraint but with variable coefficients.

Using linguistic summaries and concepts for understanding large data

We introduce the basic ideas of linguistic summaries. We describe the validation of the summary based upon the compatibility of the data and linguistic terms used in the summary. We next discuss the idea of concepts and describe how to build these concepts from an aggregation of constituent concepts. We discuss the role that hierarchies play in formulating rich concepts. We show how to include these concepts in linguistic summaries and in particular how to validate a summary that contains concepts. We look at the role of aggregation operators in the construction of the rich concepts. We explain how to build concepts using the OWA aggregation operator. Finally we discuss the use of the Choquet integral as means of building rich concepts.

Belief structures, weight generating functions and decision-making

We describe the Dempster---Shafer belief structure and provide some of its basic properties. We introduce the plausibility and belief measures associated with a belief structure. We note that these are not the only measures that can be associated with a belief structure. We describe a general approach for generating a class of measures that can be associated with a belief structure using a monotonic function on the unit interval, called a weight generating function. We study a number of these functions and the measures that result. We show how to use weight-generating functions to obtain dual measures from a belief structure. We show the role of belief structures in representing imprecise probability distributions. We describe the use of dual measures, other then plausibility and belief, to provide alternative bounding intervals for the imprecise probabilities associated with a belief structure. We investigate the problem of decision making under belief structure type uncertain. We discuss two approaches to this decision problem. One of which is based on an expected value of the OWA aggregation of the payoffs associated with the focal elements. The second approach is based on using the Choquet integral of a measure generated from the belief structure. We show the equivalence of these approaches.

Quantifiers induced by subjective expected value of sample information with Bernstein polynomials

A kind of personalized quantifier, the so-called SEVSI-induced quantifier as an acronym for Subjective Expected Value of Sample Information, is developed in this paper by introducing Bernstein polynomials of higher degree. This allows us to provide a novel solution to improve the final representation of the quantifier that generally performed poorly in our previous work, thus enhancing the quality of global approximation of functions and improving the operability of this kind of quantifier for practical use. We show some properties of the developed quantifier. We also prove the consistency of the OWA aggregation under the guidance of this type of quantifier. Finally, we experimentally show that the developed quantifier outperforms the one with the piecewise linear interpolation in many aspects of geometrical characteristics and operability. Thus it could be considered as an effective analytical tool to help handle the complex cases involving people's personalities or behavior intentions that have to be considered in decision making under uncertainty.

Some issues on the OWA aggregation with importance weighted arguments

We introduce the OWA operator and note that it provides a parameterized class of aggregation operators. Here the parameterization is accomplished by the choice of the characterizing OWA weights, different characterizing weights results in different aggregation imperatives. We discuss various ways of providing these characterizing OWA weights. Most notable among these are the use of a vector containing the prescribed weights and the use of a function called the weight generating function from which the characterizing can be extracted. In many applications we are faced with situations in which the arguments being aggregated have different importances. This raises the issue of appropriately combining the individual argument weights with the characterizing weights of the operator to obtain operational weights to be used in the actual aggregation. Our goal here is looking at this issue under different methods of specification of the characterizing weights.

Multi-Criteria, Graph-Based Road Centerline Vectorization Using Ordered Weighted Averaging Operators

In this paper a novel road vectorization methodology based on image space clustering technique and weighted graph theory is presented. The proposed methodology describes a road as a set of optimized points on the centerline which should be connected by defining a number of appropriate criteria. The main contribution of this paper is to design a weighting scheme for combining a small number of road identities using Ordered Weighted Averaging (owa) operators by defining appropriate decision strategy. In this regard, a novel geometric criterion is introduced. Result of the OWA aggregation specifies weight of each edge in the road network graph. Comparing the proposed approach with two state-of-the-art image space clustering-based road vectorization methods proves its efficiency to deal with roads with different widths, parallel roads with different distances, different types of intersections, and also noise clusters. Obtaining improved quality measures for several high-resolution images, demonstrates the successfulness of the vectorization approach.

Two-step method for multiple criteria investment decision making: mutual funds selection using FuzzME software

The paper presents a decision support method for financial investment decision making - an area where uncertainty is inherent. Investment decision support requires understandable tools able to deal with imprecision and provide easily interpretable outputs to the decision makers. We therefore propose a two-step decision support model that employs two different mathematical approaches. The first step represents investment strategy recommendation and is realised on the base of Mamdani's inference using linguistic fuzzy rules. The second step involves a preselection of mutual funds in accordance with the investment strategy proposed in the first step and provides decision support for mutual funds selection based on multiple criteria (fuzzy OWA aggregation is used). The output is presented to the investor as a picture (graphical representation of fuzzy numbers) with linguistic labels and real number representations (defuzzified values) of the fuzzy outputs. A numerical example of mutual funds selection using FuzzME software is presented.

A Note on “Using Trapezoids for Representing Granular Objects: Applications to Learning and OWA Aggregation”

There are lots of errors and misprints in the article by , titled “Using trapezoids for representing granular objects: Applications to learning and OWA aggregation” [Information Sciences, 178(2), pp. 363-380]. The aim of this note is to give some corrections on the article.