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

2011 ◽  
Vol 17 (2) ◽  
pp. 335-351 ◽  
Author(s):  
José M. Merigó ◽  
Guiwu Wei
Keyword(s):  
Decision Making ◽  
Complete Information ◽  
Aggregation Operator ◽  
Weighted Averaging ◽  
Uncertain Information ◽  
Interval Numbers ◽  
Monetary Policies ◽  
Owa Operators ◽  
Probabilistic Information ◽  
Political Management

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.

scholarly journals UNCERTAIN GROUP DECISION-MAKING WITH INDUCED AGGREGATION OPERATORS AND EUCLIDEAN DISTANCE

2013 ◽  
Vol 19 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Weihua Su ◽  
Shouzhen Zeng ◽  
Xiaojia Ye
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Euclidean Distance ◽  
Group Decision ◽  
Weighted Averaging ◽  
Uncertain Information ◽  
Uncertain Environments ◽  
Interval Numbers ◽  
Ordered Weighted Averaging ◽  
Induced Aggregation

In this paper, we present the induced uncertain Euclidean ordered weighted averaging distance (IUEOWAD) operator. It is an extension of the OWA operator that uses the main characteristics of the induced OWA (IOWA), the Euclidean distance and uncertain information represented by interval numbers. The main advantage of this operator is that it is able to consider complex attitudinal characters of the decision-maker by using order-inducing variables in the aggregation of the Euclidean distance. Moreover, it is able to deal with uncertain environments 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 maximum distance, the uncertain minimum distance, the uncertain normalized Euclidean distance (UNED), the uncertain weighted Euclidean distance (UWED) and the uncertain Euclidean ordered weighted averaging distance (UEOWAD) operator. We also apply this aggregation operator to a group decision-making problem regarding the selection new artillery weapons under uncertainty.

scholarly journals METHODS FOR PROBABILISTIC DECISION MAKING WITH LINGUISTIC INFORMATION

2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operators ◽  
Uncertain Information ◽  
Owa Operator ◽  
Linguistic Information ◽  
Probabilistic Information ◽  
Ordered Weighted Average ◽  
Linguistic Labels ◽  
Selection Of

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

scholarly journals Induced intuitionistic fuzzy ordered weighted averaging: Weighted average operator and its application to business decision-making

2014 ◽  
Vol 11 (2) ◽  
pp. 839-857 ◽  
Author(s):  
Zeng Shouzhen ◽  
Wang Qifeng ◽  
José Merigó ◽  
Pan Tiejun
Keyword(s):  
Decision Making ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Weighted Averaging ◽  
Business Decision ◽  
Ordered Weighted Averaging ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Weighted Average ◽  
Decision Making Problem ◽  
Selection Of

We present the induced intuitionistic fuzzy ordered weighted averaging-weighted average (I-IFOWAWA) operator. It is a new aggregation operator that uses the intuitionistic fuzzy weighted average (IFWA) and the induced intuitionistic fuzzy ordered weighted averaging (I-IFOWA) operator in the same formulation. We study some of its main properties and we have seen that it has a lot of particular cases such as the IFWA and the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator. We also study its applicability in a decision-making problem concerning strategic selection of investments. We see that depending on the particular type of I-IFOWAWA operator used, the results may lead to different decisions.

scholarly journals Pythagorean Fuzzy Soft Einstein Ordered Weighted Average Operator in Sustainable Supplier Selection Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Rana Muhammad Zulqarnain ◽  
Imran Siddique ◽  
Shahzad Ahmad ◽  
Aiyared Iampan ◽  
Goran Jovanov ◽  
...  
Keyword(s):  
Decision Making ◽  
Membership Function ◽  
Weighted Average ◽  
Aggregation Operator ◽  
Soft Set ◽  
Weighted Averaging ◽  
Accurate Estimation ◽  
Sustainable Supply Chain ◽  
Fuzzy Soft Set ◽  
Sustainable Supplier Selection

Pythagorean fuzzy soft set (PFSS) is the most influential and operative extension of the Pythagorean fuzzy set (PFS), which contracts with the parametrized standards of the substitutes. It is also a generalized form of the intuitionistic fuzzy soft set (IFSS) and delivers a well and accurate estimation in the decision-making (DM) procedure. The primary purpose is to prolong and propose ideas related to Einstein’s ordered weighted aggregation operator from fuzzy to PFSS, comforting the condition that the sum of the degrees of membership function and nonmembership function is less than one and the sum of the squares of the degree of membership function and nonmembership function is less than one. We present a novel Pythagorean fuzzy soft Einstein ordered weighted averaging (PFSEOWA) operator based on operational laws for Pythagorean fuzzy soft numbers. Furthermore, some essential properties such as idempotency, boundedness, and homogeneity for the proposed operator have been presented in detail. The choice of a sustainable supplier is also examined as an essential part of sustainable supply chain management (SSCM) and is considered a crucial multiattribute group decision-making (MAGDM) issue. In some MAGDM problems, the relationship between alternatives and uncertain environments will be the main reason for deficient consequences. We have presented a novel aggregation operator for PFSS information to choose sustainable suppliers to cope with those complex issues. The Pythagorean fuzzy soft number (PFSN) helps to represent the obscure information in such real-world perspectives. The priority relationship of PFSS details is beneficial in coping with SSCM. The proposed method’s effectiveness is proved by comparing advantages, effectiveness, and flexibility among the existing studies.

Some Interval-Valued Pythagorean Fuzzy Einstein Weighted Averaging Aggregation Operators and Their Application to Group Decision Making

2018 ◽  
Vol 29 (1) ◽  
pp. 393-408 ◽  
Author(s):  
Khaista Rahman ◽  
Saleem Abdullah ◽  
Muhammad Sajjad Ali Khan
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Weighted Averaging ◽  
Fuzzy Information ◽  
Multiple Attribute ◽  
Interval Valued

Abstract In this paper, we introduce the notion of Einstein aggregation operators, such as the interval-valued Pythagorean fuzzy Einstein weighted averaging aggregation operator and the interval-valued Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. We also discuss some desirable properties, such as idempotency, boundedness, commutativity, and monotonicity. The main advantage of using the proposed operators is that these operators give a more complete view of the problem to the decision makers. These operators provide more accurate and precise results as compared the existing method. Finally, we apply these operators to deal with multiple-attribute group decision making under interval-valued Pythagorean fuzzy information. For this, we construct an algorithm for multiple-attribute group decision making. Lastly, we also construct a numerical example for multiple-attribute group decision making.

EXTENDED INDUCED ORDERED WEIGHTED AVERAGING DISTANCE OPERATORS AND THEIR APPLICATION TO GROUP DECISION-MAKING

2013 ◽  
Vol 12 (04) ◽  
pp. 789-811 ◽  
Author(s):  
SHOUZHEN ZENG ◽  
WEI LI ◽  
JOSÉ M. MERIGÓ
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Fuzzy Numbers ◽  
Group Decision ◽  
Weighted Averaging ◽  
Interval Numbers ◽  
Ordered Weighted Averaging ◽  
Special Cases ◽  
Decision Making Problem ◽  
Available Information

The induced ordered weighted averaging distance (IOWAD) approach is very suitable in situations in which the available information is represented with exact numerical values. In this paper, we develop some extended IOWAD operators: the linguistic induced ordered weighted averaging distance (LIOWAD) operator, the uncertain induced ordered weighted averaging distance (UIOWAD) operator and the fuzzy induced ordered weighted averaging distance (FIOWAD) operator. Their main objective is to assess uncertain situations in which the available information is given in the form of linguistic variables, interval numbers and fuzzy numbers. Some special cases of these three new extensions are studied. Finally, we develop an application of the new operators in a group decision-making problem under an uncertain environment and illustrate it with a numerical example.

Interval TOPSIS with a novel interval number comprehensive weight for threat evaluation on uncertain information

2021 ◽  
pp. 1-17
Author(s):  
Chen Xiang ◽  
Wang Xing ◽  
Zhang Hubiao ◽  
Xu Yuheng ◽  
Chen You ◽  
...  
Keyword(s):  
Decision Making ◽  
Situation Awareness ◽  
Interval Number ◽  
Uncertain Information ◽  
Interval Numbers ◽  
Subjective Weight ◽  
Order Preference ◽  
The Mean ◽  
Deviation Method ◽  
Threat Evaluation

Threat evaluation (TE) is essential in battlefield situation awareness and military decision-making. The current processing methods for uncertain information are not effective enough for their excessive subjectivity and difficulty to obtain detailed information about enemy weapons. In order to optimize TE on uncertain information, an approach based on interval Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the interval SD-G1 (SD standard deviation) method is proposed in this article. By interval SD-G1 method, interval number comprehensive weights can be calculated by combining subjective and objective weights. Specifically, the subjective weight is calculated by interval G1 method, which is an extension of G1 method into interval numbers. And the objective weight is calculated by interval SD method, which is an extension of SD method with the mean and SD of the interval array defined in this paper. Sample evaluation results show that with the interval SD-G1 method, weights of target threat attributes can be better calculated, and the approach combining interval TOPSIS and interval SD-G1 can lead to more reasonable results. Additionally, the mean and SD of interval arrays can provide a reference for other fields such as interval analysis and decision-making.

OWA aggregation with dual preferences for basic uncertain information

2021 ◽  
pp. 1-10
Author(s):  
LeSheng Jin ◽  
Ronald R. Yager ◽  
Jana Špirková ◽  
Radko Mesiar ◽  
Daniel Paternain ◽  
...  
Keyword(s):  
Decision Makers ◽  
Input Vector ◽  
Weighted Averaging ◽  
Preference Aggregation ◽  
Uncertain Information ◽  
Interval Vector ◽  
Owa Operators ◽  
Ordered Weighted Averaging ◽  
Wide Range ◽  
Original Information

Basic Uncertain Information (BUI) as a newly introduced concept generalized a wide range of uncertain information. The well-known Ordered Weighted Averaging (OWA) operators can flexibly and effectively model bipolar preferences of decision makers over given real valued input vector. However, there are no extant methods for OWA operators to be carried out over given BUI vectors. Against this background, this study firstly discusses the interval transformation for BUI and elaborately explains the reasonability within it. Then, we propose the corresponding preference aggregations for BUI in two different decisional scenarios, the aggregation for BUI vector without original information influencing and the aggregation for BUI vector with original information influencing after interval transformation. For each decisional scenario, we also discuss two different orderings of preference aggregation, namely, interval-vector and vector-interval orderings, respectively. Hence, we will propose four different aggregation procedures of preference aggregation for BUI vector. Some illustrative examples are provided immediately after the corresponding aggregation procedures.

An Interval Type-2 Fuzzy Number Based Approach for Multi-Criteria Group Decision-Making Problems

2015 ◽  
Vol 23 (04) ◽  
pp. 565-588 ◽  
Author(s):  
Jian-Qiang Wang ◽  
Su-Min Yu ◽  
Jing Wang ◽  
Qing-Hui Chen ◽  
Hong-Yu Zhang ◽  
...  
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Aggregation Operator ◽  
Weighted Averaging ◽  
Ranking Methods ◽  
Arithmetic Operations ◽  
New Approach ◽  
Interval Type

In this paper, a new approach is presented for solving multi-criteria group decision-making (MCGDM) problems, which is based on new arithmetic operations and the ranking rules of trapezoidal interval type-2 fuzzy numbers (IT2FNs). Firstly, the shortcomings of some existing arithmetic operations of trapezoidal IT2FNs are discussed along with their ranking methods, before some new arithmetic operations and ranking rules are proposed. Secondly, some new aggregation operators including the arithmetic averaging aggregation operator, the ordered weighted averaging aggregation operator and the hybrid weighted averaging aggregation operator for trapezoidal IT2FNs are also developed. Thirdly, a new approach for MCGDM problems is developed based on the proposed operators and ranking rules. Finally, an example is provided to illustrate the feasibility and validity of this new approach, and a comparison analysis referring to the same example is also presented.

A LINGUISTIC AGGREGATION OPERATOR INCLUDING WEIGHTS FOR LINGUISTIC VALUES AND EXPERTS IN GROUP DECISION MAKING

2013 ◽  
Vol 21 (06) ◽  
pp. 927-943 ◽  
Author(s):  
ZHENG PEI ◽  
LI ZOU ◽  
LIANGZHONG YI
Keyword(s):  
Decision Making ◽  
Aggregation Operator ◽  
Point Of View ◽  
Weighted Averaging ◽  
Ordered Weighted Averaging ◽  
Averaging Operator ◽  
Aggregation Processes ◽  
Decision Making Problem ◽  
Ordered Weighted Averaging Operator ◽  
Linguistic Decision Making

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.

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