OWA Operator Research Articles

Upper bound of fractional differential operator related to univalent functions

In this article, we defined the generalized fractional differential Tremblay operator in the open unit disk that by usage the definition of the generalized Srivastava–Owa operator. In particular, we established a new operator denoted by \( \Theta ^{\beta ,\tau , \gamma }_{z}\) based on the normalized generalized fractional differential operator and represented by convolution product. Moreover, we studied the coefficient criteria of univalence, starlikeness and convexity for the last operator mentioned.

Bonferroni means with distance measures and the adequacy coefficient in entrepreneurial group theory

The aim of the paper is to develop new aggregation operators using Bonferroni means, OWA operators and some distance measure. We introduce the BON-OWAAC and BON-OWAIMAM operators. We are able to include coefficient adequacy and the maximum and minimum levels in the same formulation with Bonferroni means and an OWA operator. The main advantages of using these operators are that they allow consideration of continuous aggregations, multiple comparisons between each argument and distance measures in the same formulation. An application is developed using these new algorithms in combination with Moore's families and Galois lattices to solve group decision-making problems. The professional and personal interests of the entrepreneurs who share co-working spaces are taken as an example for establishing relationships and groups. According to the professional and personal profile affinities for each entrepreneur, the results show dissimilarity and fuzzy relationships and the maximum similarity sub-relations to establish relationships and groups using Moore's families and Galois lattice. Finally, this new type of distance family can be used for applications in areas such as sports teams, strategy marketing and teamwork.

Decision Making in Reinsurance with Induced OWA Operators and Minkowski Distances

ABSTRACTThe decision to choose a reinsurance program has many complexities because it is difficult to simultaneously achieve high levels in different optimal criteria including maximum gain, minimum variance, and probability of ruin. This article suggests a new method by which, through membership functions, we can measure the distance of each alternative to an optimal result and aggregate it by using different types of aggregations. In this article, particular attention is given to the induced Minkowski ordered weighted averaging distance operator and the induced Minkowski probabilistic ordered weighted averaging distance operator. The main advantage of these operators is that they include a wide range of special cases. Thus, they can adapt efficiently to the specific needs of the calculation processes. By doing so, the reinsurance system can make better decisions by using different scenarios in the uncertain environment considered.

OWA operator for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making

OWA operator for discrete gradual intervals: implications to fuzzy intervals and multi-expert decision making

S-H OWA Operators with Moment Measure

Step-like or Hurwicz-like ordered weighted averaging OWA S-H OWA operators connect two fundamental OWA operators, step OWA operators and Hurwicz OWA operators. S-H OWA operators also generalize them and some other well-know OWA operators such as median and centered OWA operators. Generally, there are two types of determination methods for S-H OWA operators: One is from the motivation of some existed mathematical results; the other is by a set of nonstrict definitions and often via some intermediate elements. For the second type, in this study we define two sets of strict definitions for Hurwitz/step degree, which are more effective and necessary for theoretical studies and practical usages. Both sets of definitions are useful in different situations. In addition, they are based on the same concept moment of OWA operators proposed in this study, and therefore they become identical in limit forms. However, the Hurwicz/step degree HD/SD puts more concerns on its numerical measure and physical meaning, whereas the relative Hurwicz/step degree rHD/rSD, still being accurate numerically, sometimes is more reasonable intuitively and has larger potential in further studies and practical applications.

An application of OWA operators in fuzzy business diagnosis

The paper aims to develop an adjustment index based on OWA operators to enrich the results of diagnostic fuzzy models of business failure. A proposal to verify the diseases prediction accuracy of the models is also added. This allows a reduction of the map of causes or diseases detected in strategic defined areas. At the same time, these key areas can be disaggregated when an alert indicator is identified, and shows which of the causes need special attention. This application of OWA can encourage the development of suitable computer systems for monitoring companies’ problems, warn of failures and facilitate decision-making. In addition, taking Vigier and Terceño’s 2008 model as a benchmark, causes aggregation operators are introduced to evaluate alternative groupings, and the adjustment measure using approximate solutions is proposed to test the model’s prediction.The empirical estimation and the verification of the improvement proposals in a set of small and medium- sized enterprises (SMEs) in the construction industry are also presented. The functionality and the prediction capacity are thus measured and detected by monitoring key areas that warn about insolvency situations in the firm.

On Algebraic Properties and Linearity of Owa Operators for Fuzzy Sets

Abstract We deal with an ordered weighted averaging operator (OWA operator) on the set of all fuzzy sets. Our starting point is OWA operator on any lattice introduced in Lizasoain, I.-Moreno,C.: OWA operators defined on complete lattices, Fuzzy Sets and Systems 224 (2013), 36-52; Ochoa, G.-Lizasoain, I.- -Paternain, D.-Bustince, H.-Pal, N. R.: Some properties of lattice OWA operators and their importance in image processing, in: Proc. of the 16th World Congress of the Internat. Systems Assoc.-IFSA ’15 and the 9th Conf. of the European Soc. for Fuzzy Logic and Technology-EUSFLAT ’15 (J. M. Alonso et al., eds.), Atlantis Press, Gijón, Spain, 2015, pp. 1261-1265. We focus on a particular case of lattice, namely that of all normal convex fuzzy sets in [0,1], and study algebraic properties and linearity of the proposed OWA operator. It is shown that the operator is an extension of standard OWA operator for real numbers and it possesses similar algebraic properties as standard one, however, it is neither homogeneous nor shift-invariant, i.e., it is not linear in contrast to the standard OWA operator.

Application of Optimistic and Pessimistic OWA and DEA Methods in Stock Selection

One of the main objectives of fund managers in financial service industry is to select superior stocks by analyzing financial ratios. This paper proposes a novel methodology for stock selection by integrating optimistic and pessimistic ordered weighted averaging OWA and data envelopment analysis DEA methods. The paper first reveals the drawback of using the standard DEA models for stocks evaluation and then proposes a new method by using the OWA operator. Unlike the classical DEA, the proposed method in this paper does not involve the specification of inputs and outputs. The paper incorporates optimistic and pessimistic scenarios and generates interval OWA scores for all stocks. This is followed by using appropriate interval DEA models for selecting superior stocks. The proposed method in this paper is applied to identify high financial performance stocks in the Tehran stock market.

Discrete and continuous recursive forms of OWA operators

We firstly present an evaluation problem for online shop based on gradually increasing number of inputs. Then we propose a model using Recursive OWA operator with constant orness/andness grade involved. Next, we analyze properties of discrete Recursive OWA operators, show their relationship with Pascal Triangle and further generalize this relationship to Γ function. For the continuous case, we propose a concept of self-similar ordered weighting functions (OWF) and analyze some properties of OWF. Using these concepts, we present the recursive aggregation method of continuous arguments under continuous OWF. We show a relationship of OWF with the Regular Increasing (RIM) quantifier. Furthermore, based on an isomorphism relation between discrete and continuous recursive OWA operators, Left Recursive OWA can be seen as the discrete form of continuous OWF.

The decompositions of rank-dependent poverty measures using ordered weighted averaging operators

This paper is concerned with rank-dependent poverty measures and shows that an ordered weighted averaging, hereafter OWA, operator underlies in the definition of these indices. The dual decomposition of an OWA operator into the self-dual core and the anti-self-dual remainder allows us to propose a decomposition for all the rank-dependent poverty measures in terms of incidence, intensity and inequality. In fact, in the poverty field, it is well known that every poverty index should be sensitive to the incidence of poverty, the intensity of poverty and the inequality among the poor individuals. However, the inequality among the poor can be analyzed in terms of either incomes or gaps of the distribution of the poor. And, depending on the side we focus on, contradictory results can be obtained. Nevertheless, the properties inherited by the proposed decompositions from the OWA operators oblige the inequality components to measure equally the inequality of income and inequality of gap overcoming one of the main drawbacks in poverty and inequality measurement. Finally, we provide an empirical illustration showing the appeal of our decompositions for some European Countries in 2005 and 2011.

Majority Clusters-Density Ordered Weighting Averaging: A Family of New Aggregation Operators in Group Decision Making

In the process of aggregation, it is necessary, especially for group decision-making (GDM) problems, to consider distributed characteristic hidden in aggregates. In this case, clustering has been a common way for discovering the implicit distributed structures. This paper mainly investigates the characteristic of majority clusters, rather than majority elements and develops a new class of aggregation operators denominated majority clusters density-ordered weighting averaging (MC-DOWA) operators. Furthermore, we discuss properties of these operators and calculate the associated weights. Finally, a numerical example is provided to illustrate the application of the MC-DOWA operators, and the aggregations are compared with those of the other three aggregation operators: majority additive-OWA (MA-OWA), dependent OWA (DOWA) and cluster-based DOWA (Clus-DOWA) operators.

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.

Unbalanced interval-valued OWA operators

In this work, we introduce a new class of functions defined on the interval-valued setting. These functions extend classical OWA operators but allow for different weighting vectors to handle the lower bounds and the upper bounds of the considered intervals. As a consequence, the resulting functions need not be an interval-valued aggregation function, so we study, in the case of the lexicographical order, when these operators give an interval as output and are monotone. We also discuss an illustrative example on a decision making problem in order to show the usefulness of our developments.

TOPSIS method for intuitionistic fuzzy multiple-criteria decision making and its application to investment selection

Purpose – The purpose of this paper is to present a hybrid intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) method, called intuitionistic fuzzy ordered weighted averaging weighted averaging (OWAWA) distance TOPSIS (IFOWAWAD-TOPSIS) method for intuitionistic fuzzy multiple-criteria decision making (MCDM) problems. Design/methodology/approach – Based on the OWAWA operator, the authors develop the intuitionistic fuzzy OWAWA distance measure, then the IFOWAWAD-TOPSIS method is obtained by using the IFOWAWAD and traditional TOPSIS. Findings – The developed IFOWAWAD-TOPSIS method can overcome the drawback of traditional TOPSIS method that cannot consider both the subjective information of attributes and the attitudinal character of decision maker. Research limitations/implications – Clearly, this paper is devoted to the OWA operator, MCDM and intuitionistic fuzzy theory. Practical implications – The developed method is applicable in a wide range of situations such as decision-making, statistics, engineering and economics. A numerical example concerning investment selection is given to illustrate the practicability and usefulness of the proposed approach. Originality/value – This paper fulfils an identified need to study how to make a decision considering both the subjective information of attribute and the attitudinal character of decision maker in intuitionistic fuzzy environment.

A Behavioral Analysis of WOWA and SUOWA Operators

Weighted ordered weighted averaging WOWA and semiuninorm-based ordered weighted averaging SUOWA operators are two families of aggregation functions that simultaneously generalize weighted means and OWA operators. Both families can be obtained by using the Choquet integral with respect to normalized capacities. Therefore, they are continuous, monotonic, idempotent, compensative, and homogeneous of degree 1 functions. Although both families fulfill good properties, there are situations where their behavior is quite different. The aim of this paper is to analyze both families of functions regarding some simple cases of weighting vectors, the capacities from which they are building, the weights affecting the components of each vector, and the values they return.

Fusion functions based discrete Choquet-like integrals

In this paper, we generalize a formula for the discrete Choquet integral by replacing the standard product by a suitable fusion function. For the introduced fusion functions based discrete Choquet-like integrals we discuss and prove several properties and also show that our generalization leads to several new interesting functionals. We provide a complete characterization of the introduced functionals as aggregation functions. For n=2, several new aggregation functions are obtained, and if symmetric capacities are considered, our approach yields new generalizations of OWA operators. If n > 2, the introduced functionals are aggregation functions only if they are Choquet integrals with respect to some distorted capacity.

A note on properties of the continuous weighted OWA operator

A note on properties of the continuous weighted OWA operator

An MCDM approach towards handling outliers in web data: a case study using OWA operators

World Wide Web has emerged as one of the primary modes of information sharing and searching. Its reach has been extended to daily aspects of our life whether it is related to business or education. As the information is going online, and so is the complexity of finding the correct, precise and appropriate information. Many online companies rely heavily on analysis of web data to stay in business, to make strategic decisions, and for their existence. One of the problem in analyzing the web data is the web user. A typical web user exhibits highly uncertain pattern of web browsing and the same is captured in form of web server logs. Various data mining techniques like regression, are used to analyze such kind of data, but the inherent complex nature of web data introduces some outlier values while mining for information. Minimizing these outliers has always been a challenging task for data scientist and researchers. This paper uses an aggregation-based approach based on various ordered weighted averaging operators to reduce the outlier values in regression analysis. In this paper, a regression problem is being formulated followed by solving the problem with the help of concepts of multi-criteria decision making. Results, thus obtained are able to show that outliers can be reduced to a significant amount with the help of this approach.

An OWA-Based Model for Talent Enhancement in Cricket

Cricket being an extremely competitive game; players are always under pressure to perform and improve continuously. Talent enhancement in cricket is conventionally achieved through practice under coach's supervision and analysis using costly assistive technology. Although this approach is workable, but it is constrained due to nonavailability of quality coaches, equipment, and in many cases the limited domain knowledge of the coaching staff. This constraint is significant for a country like India where 55,000 matches and 1,210,000 players play cricket daily. The literature review did not reveal any algorithm/model/framework focused on the issue of talent enhancement. In this paper, we present an alternate/supporting approach based on comparison of the players' overall talent class viz-a-viz the corresponding performances of the player against the 28 aspects of talent from cricketing perspective. The Ordered Weighted Averaging Aggregation OWA operator was used to aggregate the opinion of experts for assessment of talent classes in cricket. The normative data obtained for a cricket enthusiast was then compared using normalized adequacy coefficient with aggregated opinions of experts. This resulted in identification of the talent class of the cricketer. Subsequently, the weaknesses were identified by comparing the outcomes of the identified parametric tests for this cricket enthusiast with the value corresponding to his/her talent class. The algorithm was validated using two-sided t test. A case showing implementation of algorithm is also explained.

Fuzzy Linguistic Induced Generalized OWA Operator and Its Application in Fuzzy Linguistic Decision Making

With respect to multiple attribute group decision making problems, in which the attribute values take the form of fuzzy linguistic scale variables, some decision analysis approaches are proposed. In this paper, we introduce the fuzzy linguistic induce generalized ordered weighted averaging operator and study some of its main properties by utilizing some operational laws of fuzzy linguistic scale variables. We end the paper with a numerical example of the new approach in a fuzzy linguistic decision making.