Geometric Averaging Operator Research Articles

Dam's risk identification under interval-valued intuitionistic fuzzy environment

This paper uses both fuzzy analytic hierarchy process (FAHP) and the cross entropy of interval-valued intuitionistic fuzzy sets on risk identification of dams. The problem of risk identification can be transformed into a multi-criteria decision-making problem under fuzzy environment. Based on the weight of criteria calculated by the FAHP method and the interval-valued intuitionistic fuzzy information of risk aggregated by geometric average operator, the weight of each alternative can be obtained. The proposed method is used to identify the main risk factors of an earth–rock dam and to rank potential failure modes of the dam. The proposed method takes into account the interval unknown degree (hesitancy degree) in dam safety assessment and it is more effective and accurate in real conditions of dam operation.

Intuitionistic Fuzzy Power Geometric Bonferroni Means and Their Application to Multiple Attribute Group Decision Making

The geometric Bonferroni mean (GBM) can capture the interrelationships between input arguments, which is an important generalization of Bonferroni mean (BM). In this paper, we combine geometric Bonferroni mean (GBM) with the power geometric average (PGA) operator under intuitionistic fuzzy environment and present the intuitionistic fuzzy geometric power Bonferroni mean (IFPGBM) and the weighted intuitionistic fuzzy power geometric Bonferroni mean (WIFPGBM). The desirable properties of these new extensions of Bonferroni mean and their special cases are investigated. We list the detailed steps of multiple attribute group decision making with the developed IFPGBM or WIFPGBM, and give a comparison of the new extensions of Bonferroni mean by this paper with the corresponding existing intuitionistic fuzzy Bonferroni means. Finally, examples are illustrated to show the validity and feasibility of the new approaches.

Some Geometric Operators for Aggregating Intuitionistic Linguistic Information

With respect to intuitionistic linguistic information aggregation problems, we first define a new score function and a new accuracy function of intuitionistic linguistic number (ILN) and present a simple method for the comparison between two ILNs. Then, based on the intuitionistic linguistic weighted geometric averaging (ILWGA) operator, we propose two new intuitionistic linguistic geometric operators, such as the intuitionistic linguistic ordered weighted geometric (ILOWG) operator and intuitionistic linguistic hybrid geometric (ILHG) operator, and establish various properties of these operators. Furthermore, we apply the ILHG and ILWGA operators to solve multi-criteria group decision making problems, in which the criterion values take the form of ILNs and the criterion weight information is known completely. Finally, an illustrative example is given to demonstrate the feasibility and effectiveness of the developed approach.

Prediction of Road Traffic Accidents Using a Combined Model Based on IOWGA Operator

Traffic accident prediction plays a important role in reducing the likelihood of traffic accidents and improving the management levels of traffic safety. A new combined prediction model based on the induced ordered weighted geometric average (IOWGA) operator was proposed. This new model combines the GM(1,1) model and the Verhulst model with changeable weight coefficients of each single model. A combined model based on the optimal weighted(OW) method is also presented for comparison. An example is given with the number of deaths by road traffic accidents in China from 2003 to 2008. The results indicate that the proposed combined model is better than the other three models.

Trapezoidal neutrosophic set and its application to multiple attribute decision-making

Based on the combination of trapezoidal fuzzy numbers and a single-valued neutrosophic set, this paper proposes a trapezoidal neutrosophic set, some operational rules, score and accuracy functions for trapezoidal neutrosophic numbers. Then, a trapezoidal neutrosophic number weighted arithmetic averaging (TNNWAA) operator and a trapezoidal neutrosophic number weighted geometric averaging (TNNWGA) operator are proposed to aggregate the trapezoidal neutrosophic information, and their properties are investigated. Furthermore, a multiple attribute decision-making method based on the TNNWAA and TNNWGA operators and the score and accuracy functions of a trapezoidal neutrosophic number is established to deal with the multiple attribute decision-making problems in which the evaluation values of alternatives on the attributes are represented by the form of trapezoidal neutrosophic numbers. Finally, an illustrative example about software selection is given to demonstrate the application and effectiveness of the developed method.

Multi-attribute group decision making using combined ranking value under interval type-2 fuzzy environment

In this paper, we investigate a new method to handle multiple attribute group decision making (MAGDM) problems based on combined ranking value under interval type-2 fuzzy environment, in which all the attribute values provided by experts take the form of interval type-2 fuzzy sets (IT2FSs). We first introduce some basic concepts and related operational laws on IT2FSs. Then, we put forward three kinds of ranking value formulas to calculate the ranking value of IT2FSs based on arithmetic average (AA) operator, geometric average (GA) operator and harmonic average (HA) operator, respectively, and discuss some of its desirable properties. Based on these properties, we define the concept of combined ranking value and also further develop a new interval type-2 fuzzy entropy with trigonometric sine function to measure the uncertainty of the IT2FSs. By using the three types ranking value formulas and interval type-2 fuzzy entropy we proposed, a new approach based on the principle of combinatorial optimization with ranking-entropy and the least squares for determining attribute weight is given. Furthermore, a decision making procedure based on combined ranking value is given to select the best alternative(s). Finally, a simple practical example concerns that urban rail transit evaluation is provided to illustrate the practicality and effectiveness of the proposed method, and a comparative analysis is performed.

Study of decision framework of wind farm project plan selection under intuitionistic fuzzy set and fuzzy measure environment

Project selection plays an important role in the entire life cycle of wind farm project and the multi-criteria decision making (MCDM) methods are very important in the whole wind farm project plan selection process. There are problems in the present MCDM methods decrease evaluation quality of the wind farm project plans: first, the information loss exists in the wind farm project plan evaluation process. Second, it is difficult to satisfy the independent assumption of the multi-criteria decision making methods used in the wind farm project plan evaluation in fact. Third, the compensatory problem of performance scores of the wind farm project plans is processed unreasonably. Hence the innovation points of this paper are as follows: first, the intuitionistic fuzzy numbers are used instead of fuzzy numbers or numerical values to reflect the experts’ intuitive preferences to decrease the probability of information loss; second, the fuzzy measure is used to rate the important degrees of criteria in order to avoid the independent assumption and to increase the reasonability; third, the partial compensatory problem of performance scores is well processed by using intuitionistic fuzzy Choquet (IFC) operator and generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator. These operators can deal with the compensatory performance scores and non-compensatory performance scores respectively. Finally, a case study demonstrates the effectiveness of decision framework.

Aggregation Operators on Triangular Intuitionistic Fuzzy Numbers and its Application to Multi-Criteria Decision Making Problems

Abstract The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Then, some geometric aggregation operators for aggregating triangular intuitionistic fuzzy numbers are developed, such as triangular intuitionistic fuzzy weighted geometric (TIFWG) operator, the triangular intuitionistic fuzzy ordered weighted geometric (TIFOWG) operator and the triangular intuitionistic fuzzy hybrid geometric (TIFHG) operator. Moreover, an application of the new approach to multi-criteria decision making method was proposed based on the geometric average operator of TIFNs, and the new ranking method for TIFNs is used to rank the alternatives. Finally, an example analysis is given to verify and demonstrate the practicality and effectiveness of the proposed method.

On Compatibility of Interval Multiplicative Preference Relations Based on the COWGA Operator

The aim of this paper is to develop a new compatibility, which is very suitable to deal with group decision making (GDM) problems involving interval multiplicative preference relations, based on the continuous ordered weighted geometric averaging (COWGA) operator. First, we define some concepts of the compatibility degree and the compatibility index for the two interval multiplicative preference relations based on the COWGA operator. Then, we study some desirable properties of the compatibility index and investigate the relationship between each expert's interval multiplicative preference relation and the synthetic interval multiplicative preference relation. The prominent characteristic of the compatibility index based on the COWGA operator is that it can deal with the compatibility of all the arguments in two interval arguments considering the risk attitude of decision maker rather than the compatibility of the two simple points in intervals. Second, in order to determine the experts' weights in the GDM with the interval multiplicative preference relations, we propose an optimal model based on the criterion of minimizing the compatibility index. Finally, we give a numerical example to develop the new approach to GDM with interval multiplicative preference relations.

An Approach to Multi-attribute Group Decision Making with Trapezoidal Interval Type-2 Fuzzy Sets and Application to Teaching Quality Assessment

AbstractTrapezoidal interval type-2 fuzzy sets (TIT2FSs) are a special kind of type-2 fuzzy sets. TIT2FSs are useful in dealing with fuzziness inherent in decision data and the decision-making process. For multi-attribute group decision-making problems in which the attribute values and attribute weights are TIT2FSs, a new decision-making approach is proposed. On the basis of the concept of barycenters, a new approach to ranking TIT2FSs is given. Four kinds of geometric aggregation operators for TIT2FSs are developed, including the TIT2FS weighted geometric average operator, TIT2FS ordered weighted geometric average operator, TIT2FS hybrid weighted geometric average operator, and extended TIT2FS hybrid weighted geometric average operator. The individual comprehensive values of alternatives are derived through the extended TIT2FS weighted geometric average operators. Using the TIT2FS hybrid weighted geometric average operator and the expert weights, the individual comprehensive values of alternatives are integrated into the collective ones, which are used to rank the alternatives. The practicability and effectiveness of the developed method are illustrated with a teaching quality assessment example.

Entrepreneurship and Decision- Making in Latin America

The principal purpose of this paper is to analyze different methods for decision making, with a focus on entrepreneurship in Latin America. Decision-making methods may be informed by aggregation operators that are based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. The paper presents a new generalized probabilistic weighted averaging (GPWA) operator that unifies WAs and probability in the same formulation, considering the degree of importance of each concept used in the analysis. The fundamental advantage of this approach is that it includes a wide range of particular cases including the probabilistic weighted averaging (PWA) operator, the probabilistic weighted geometric averaging (PWGA) operator and the probabilistic weighted quadratic averaging (PWQA) operator. Quasi-arithmetic means are used to obtain the Quasi-PWA operator and to generalize the approach, which is then applied to a set of hypothetical entrepreneurial investment decisions in a politically unified Latin American region.

An extended compromise ratio model with an application to reservoir flood control operation under an interval-valued intuitionistic fuzzy environment

This paper presents a novel multiple attribute group decision-making (MAGDM) model based on the compromise ratio method under an interval-valued intuitionistic fuzzy (IVIF) environment. The compromise ratio method under uncertainty is introduced by a group of experts based on the concept that the chosen alternative should be as close as possible to the IVIF-positive-ideal point and as far away from the IVIF-negative-ideal point as possible concurrently. First, an IVIF-weighted geometric averaging (IVIFWGA) operator is employed to aggregate all individual IVIF-decision matrices provided by a group of experts into a collective IVIF-decision matrix. Two new basic IVIF-operations are introduced to handle the evaluation process. Then, an extended collective index in an IVIF environment is proposed to discriminate among alternatives for the evaluation process in terms of subjective and objective information. Finally, to demonstrate the suitability and applicability of the proposed IVIF-MAGDM model, an application example of reservoir flood control operation is given from the recent literature.

On the properties of the generalized OWHA operators and their application to group decision making

Harmonic mean is suitable to aggregate negative indicators. In order to improve the flexibility of harmonic mean for modeling many situations, the ordered weighted harmonic averaging (OWHA) operator is extended to provide a new class of operators called the generalized OWHA (GOWHA) operators, and investigate some desirable properties of them. When different parameter of the GOWHA operator is employed, various conventional aggregation operators can be deduced, such as the ordered weighted averaging (OWA) operator and the ordered weighted geometric averaging (OWGA) operator. We further demonstrate that the OWHA operator and the GOWHA operator exhibit monotonicity with respect to the weighting vector. Furthermore, we introduce the generalized hybrid harmonic averaging (GHHA) operator, which can reflect the importance degrees of both the given arguments and the ordered position of the arguments. Finally, a new approach on the basis of the GHHA operator is presented in an example of an investment project with group decision making.

Generalized Ordered Weighted Proportional Averaging Operator and Its Application to Group Decision Making

We present a new aggregation operator called the generalized ordered weighted proportional averaging (GOWPA) operator based on an optimal model with penalty function, which extends the ordered weighted geometric averaging (OWGA) operator. We investigate some properties and different families of the GOWPA operator. We also generalize the GOWPA operator. The key advantage of the GOWPA operator is that it is an aggregation operator with theoretic basis on aggregation, which focuses on its structure and importance of arguments. Moreover, we propose an orness measure of the GOWPA operator and indicate some properties of this orness measure. Furthermore, we introduce the generalized least squares method (GLSM) to determine the GOWPA operator weights based on its orness measure. Finally, we present a numerical example to illustrate the new approach in an investment selection decision making problem.

Some aggregation operators of interval neutrosophic linguistic numbers for multiple attribute decision making

The paper proposes the concepts of an interval neutrosophic linguistic set (INLS) and an interval neutrosophic linguistic number (INLN) as a further generalization of the concepts of an intuitionistic linguistic set (ILS) and an intuitionistic linguistic fuzzy number (ILFN). Then, we introduce basic operational rules of INLNs and define the score function, accuracy function, and certainty function of an INLN. Furthermore, we propose an interval neutrosophic linguistic weighted arithmetic average (INLWAA) operator and an interval neutrosophic linguistic weighted geometric average (INLWGA) operator and investigate their properties, and then establish a decision-making method based on the INLWAA and INLWGA operators to handle multiple attribute decision-making problems with interval neutrosophic linguistic information. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

Some geometric aggregation operators based on log-normally distributed random variables

AbstractThe weighted geometric averaging (WGA) operator and the ordered weighted geometric (OWG) operator are two of most basic operators for aggregating information. But these two operators can only be used in situations where the given arguments are exact numerical values. In this paper, we first propose some new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG) operator, log-normal distribution ordered weighted geometric (LNDOWG) operator and log-normal distribution hybrid geometric (LNDHG) operator, which extend the WGA operator and the OWG operator to accommodate the stochastic uncertain environment in which the given arguments are log-normally distributed random variables, and establish various properties of these operators. Then, we apply the LNDWG operator and the LNDHG operator to develop an approach for solving multi-criteria group decision making (MCGDM) problems, in which the criterion values take the form of log-normally distributed random variabl...

A multicriteria decision-making method using aggregation operators for simplified neutrosophic sets

The paper introduces the concept of simplified neutrosophic sets SNSs, which are a subclass of neutrosophic sets, and defines the operational laws of SNSs. Then, we propose some aggregation operators, including a simplified neutrosophic weighted arithmetic average operator and a simplified neutrosophic weighted geometric average operator. Based on the two aggregation operators and cosine similarity measure for SNSs, a multicriteria decision-making method is established in which the evaluation values of alternatives with respective to criteria are represented by the form of SNSs. The ranking order of alternatives is performed through the cosine similarity measure between an alternative and the ideal alternative and the best ones can be determined as well. Finally, a numerical example shows the application of the proposed method.

Generalized intuitionistic fuzzy geometric interaction operators and their application to decision making

Considering that there may exist some interactions between membership function and non-membership function of different intuitionistic fuzzy sets, we present some new operational laws from the probability point of view and give a geometric interpretation of the new operations. Based on which, a new class of generalized intuitionistic fuzzy aggregation operators are developed, including the generalized intuitionistic fuzzy weighted geometric interaction averaging (GIFWGIA) operator, the generalized intuitionistic fuzzy ordered weighted geometric interaction averaging (GIFOWGIA) operator and the generalized intuitionistic fuzzy hybrid geometric interaction averaging (GIFHGIA) operator. The properties of these new generalized aggregation operators are investigated. Moreover, approaches to multiple attributes decision making are given based on the generalized aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of new approach. Finally, we give a systematic comparison between the work of this paper and that of other papers.

Intuitionistic fuzzy geometric interaction averaging operators and their application to multi-criteria decision making

This paper proposes some new geometric operations on intuitionistic fuzzy sets (IFSs) based on probability non-membership (PN) function operator, probability membership (PM) function operator and probability hetergeneous (PH) operator, which are constructed from the probability point of view. The geometric interpretations of these operations are given. Moreover, we develop some intuitionistic fuzzy geometric interaction averaging (IFGIA) operators. The properties of these aggregation operators are investigated. The key advantage of the IFGIA operators is that the interactions between non-membership function and membership function of different IFSs are considered. Finally, an approach to multiple attributes decision making is given based on the proposed aggregation operators under intuitionistic fuzzy environment, and an example is illustrated to show the validity and feasibility of the proposed approach.

Ordered Weighted Geometric Averaging Operator Multi-Attribute Decision-Making Model under the Preference Circumstances

The pouring concrete dam construction program decision-making, decision-makers preference program attributes should be considered in addition to consider the objective attributes of the options. In this paper, on the basis of traditional ordered weighted geometric average operator (OWGA), considering the preference attributes analysis, establish OWGA operator multiple attribute decision making model. The model is applied to the dam concrete construction program decisions of hydropower project to verify the feasibility and reasonableness of the model.