Uncertain OWA Research Articles

A family of IOWA operators with reliability measurement under interval-valued group decision-making environment

Aggregation operators play an essential role in the aggregation of various individual input arguments in group decision-making (GDM). In this paper, we have proposed a family of IOWA operators with reliability measurement to aggregate uncertain decision information represented by interval numbers in GDM problems. In particular, we introduce the reliability-induced uncertain OWA (R-IUOWA) operator and the clusters’ reliability-induced uncertain OWA (CR-IUOWA) operator. This type of operators uses the reliability measurement representing the opinion consensus of individuals as the associated order-inducing variable and considers the decision-makers’ preference in the calculation of the position weights. Thus, the aggregation results have a higher consensus level. The R-IUOWA and CR-IUOWA operators have three primary properties such as commutativity, idempotency and boundness. The generalized formulas and some special cases of the two operators are outlined. Finally, the proposed operators are applied to a GDM problem regarding the selection of an investment company. The validity of the two operators is illustrated by comparing the aggregation results with that of other operators.

An Extension of OWAD Operator and Its Application to Uncertain Multiple-Attribute Group Decision-Making

ABSTRACTWe present the uncertain OWA distance (UOWAD) operator. It is an extension of the OWA distance (OWAD) operator for uncertain situations in which the available information is given in the form of interval numbers. We study some of their main properties and different particular cases. We further generalize the UOWAD operator by using quasi-arithmetic means, obtaining the quasi-arithmetic UOWAD (Quasi-UOWAD) operator. We also present its application to multiple-attribute group decision-making (MAGDM) problems with interval numbers. Finally, an illustrative numerical example is used to verify the developed approaches.

Uncertain Induced Heavy Aggregation Distance Operator and its Application to Decision Making

We introduce a new decision-making approach for dealing with uncertain information and apply it to decision making. We have developed the uncertain induced heavy ordered weighted averaging distance (UIHOWAD) operator. It is a new aggregation operator that generalizes a wide range of uncertain aggregation operators such as the uncertain minimum distance, the uncertain weighted Hamming distance (UWHD), the uncertain OWA distance (UOWAD) operator, and the uncertain heavy OWA distance (UHOWAD) operator. We studied some of its main properties and different particular cases. We also present its applicability in a decision-making problem concerning the selection of investments.

The uncertain probabilistic OWA distance operator and its application in group decision making

In this paper, we present the uncertain probabilistic ordered weighted averaging distance (UPOWAD) operator. Its main advantage is that it uses distance measures in a unified framework between the probability and the OWA operator that considers the degree of importance of each concept in the aggregation. Moreover, it is able to deal with uncertain environments represented in the form of interval numbers. We study some of its main properties and particular cases such as the uncertain probabilistic distance (UPD) and the uncertain OWA distance (UOWAD) operator. We end the paper by presenting an application to a group decision making problem regarding the selection of robots.

PROBABILISTIC AGGREGATION OPERATORS AND THEIR APPLICATION IN UNCERTAIN MULTI-PERSON DECISION-MAKING / TIKIMYBINIAI SUMAVIMO OPERATORIAI IR JŲ TAIKYMAS PRIIMANT GRUPINIUS SPRENDIMUS NEAPIBRĖŽTOJE APLINKOJE

We present the uncertain probabilistic ordered weighted averaging (UPOWA) operator. It is an aggregation operator that uses probabilities and OWA operators in the same formulation considering the degree of importance of each concept in the analysis. Moreover, it also uses uncertain information assessed with interval numbers in the aggregation process. The main advantage of this aggregation operator is that it is able to use the attitudinal character of the decision maker and the available probabilistic information in an environment where the information is very imprecise and can be assessed with interval numbers. We study some of its main properties and particular cases such as the uncertain probabilistic aggregation (UPA) and the uncertain OWA (UOWA) operator. We also develop an application of the new approach in a multi-person decision-making problem in political management regarding the selection of monetary policies. Thus, we obtain the multiperson UPOWA (MP-UPOWA) operator. We see that this model gives more complete information of the decision problem because it is able to deal with decision making problems under uncertainty and under risk in the same formulation. Santrauka Autoriai pristato tikimybinį svertinio vidurkio operatorių, taikytiną neapibrežtumo sąlygomis. Tai tikimybėmis pagrįstas sumavimo operatorius, kuris kartu su svertinio vidurkio operatoriais gali įvertinti alternatyvų svarbumo laipsnį. Be to, jis gali operuoti neapibrežta informacija, išreikšta skaičiais intervaluose. Pagrindinis šio operatoriaus privalumas yra tas, kad jį galima taikyti uždaviniams, kuriuose informacija yra netiksli. Išnagrinėtos kai kurios minėto operatoriaus savybės. Sukurtas metodas pritaikytas monetarinei politikai parinkti, situacijai, kai sprendimus priima žmoniu grupė. Modelis suteikia išsamesnę informaciją apie problemą, nes gali įvertinti neapibrežtumus ir riziką.

THE UNCERTAIN GENERALIZED OWA OPERATOR AND ITS APPLICATION TO FINANCIAL DECISION MAKING

We introduce the uncertain generalized OWA (UGOWA) operator. This operator is an extension of the OWA operator that uses generalized means and uncertain information represented as interval numbers. By using UGOWA, it is possible to obtain a wide range of uncertain aggregation operators such as the uncertain average (UA), the uncertain weighted average (UWA), the uncertain OWA (UOWA) operator, the uncertain ordered weighted geometric (UOWG) operator, the uncertain ordered weighted quadratic averaging (UOWQA) operator, the uncertain generalized mean (UGM), and many specialized operators. We study some of its main properties, and we further generalize the UGOWA operator using quasi-arithmetic means. The result is the Quasi-UOWA operator. We end the paper by presenting an application to a decision-making problem regarding the selection of financial strategies.

The uncertain induced quasi-arithmetic OWA operator

We present the uncertain induced quasi-arithmetic OWA (Quasi-UIOWA) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the quasi-arithmetic OWA (Quasi-OWA) and the uncertain OWA (UOWA) operator. Thus, this generalization uses quasi-arithmetic means, order inducing variables in the reordering process and uncertain information represented by interval numbers. A key feature of the Quasi-UIOWA operator is that it generalizes a wide range of aggregation operators such as the uncertain quasi-arithmetic mean, the uncertain weighted quasi-arithmetic mean, the UOWA, the uncertain weighted generalized mean, the uncertain induced generalized OWA (UIGOWA), the Quasi-UOWA, the uncertain IOWA, the uncertain induced ordered weighted geometric (UIOWG), and the uncertain induced ordered weighted quadratic averaging (UIOWQA) operator. We study some of the main properties of this approach including how to obtain a wide range of particular cases. We further generalize the Quasi-UIOWA operator by using discrete Choquet integrals. We end the article with an application of the new approach in a decision making problem about investment selection. © 2010 Wiley Periodicals, Inc.

Type-1 OWA operators for aggregating uncertain information with uncertain weights induced by type-2 linguistic quantifiers

The OWA operator proposed by Yager has been widely used to aggregate experts’ opinions or preferences in human decision making. Yager's traditional OWA operator focuses exclusively on the aggregation of crisp numbers. However, experts usually tend to express their opinions or preferences in a very natural way via linguistic terms. These linguistic terms can be modelled or expressed by (type-1) fuzzy sets. In this paper, we define a new type of OWA operator, the type-1 OWA operator that works as an uncertain OWA operator to aggregate type-1 fuzzy sets with type-1 fuzzy weights, which can be used to aggregate the linguistic opinions or preferences in human decision making with linguistic weights. The procedure for performing type-1 OWA operations is analysed. In order to identify the linguistic weights associated to the type-1 OWA operator, type-2 linguistic quantifiers are proposed. The problem of how to derive linguistic weights used in type-1 OWA aggregation given such type of quantifier is solved. Examples are provided to illustrate the proposed concepts.

Dependent uncertain ordered weighted aggregation operators

Xu and Da [Z.S. Xu, Q.L. Da, The uncertain OWA operator, International Journal of Intelligent Systems, 17 (2002) 569–575] introduced the uncertain ordered weighted averaging (UOWA) operator to aggregate the input arguments taking the form of intervals rather than exact numbers. In this paper, we develop some dependent uncertain ordered weighted aggregation operators, including dependent uncertain ordered weighted averaging (DUOWA) operators and dependent uncertain ordered weighted geometric (DUOWG) operators, in which the associated weights only depend on the aggregated interval arguments and can relieve the influence of unfair interval arguments on the aggregated results by assigning low weights to those “false” and “biased” ones.