Geometric Averaging Operator Research Articles

An extended MULTIMOORA method based on OWGA operator and Choquet integral for risk prioritization identification of failure modes

Failure mode and effects analysis (FMEA) is one of the important methods for risk analysis, and has been used in various fields to improve the reliability of systems. However, in the fuzzy environment, the aggregation, weight calculation, risk evaluation and prioritization of evaluation information limit its wide application. Therefore, this paper proposes an extended multi-objective optimization by ratio analysis plus full multiplicative form (MULTIMOORA) method based on the ordered weighted geometric averaging (OWGA) operator and Choquet integral for FMEA. Firstly, trapezoidal fuzzy numbers (TrFNs) are used for describing the fuzzy ratings of failure modes. Secondly, considering the uncertainty preferences of decision-makers, the OWGA operator is adopted for aggregating the evaluation information given by multiple decision-makers. Thirdly, the TrFNs ranking method based on the relative preference relation is combined with Choquet integral to model the interactions among risk factors, thus capturing their importance weights. On this basis, an extended MULTIMOORA method is proposed to determine the risk priority of failure modes. Finally, two case studies are provided to illustrate the effectiveness and practicability of the proposed method.

Decision making with MABAC method under probabilistic single-valued neutrosophic hesitant fuzzy environment

Recently, there has been great interest on single valued neutrosophic hesitant fuzzy set theory. When compared single valued neutrosophic set, it is more convenient for real life situations. But even in this case, there is still missing data for some decision problems. Probabilistic single valued neutrosophic hesitant fuzzy sets (PSVNHFSs) are defined to solve this problem. Even though it contains more information, it needs some improvements. In this paper, the modified PSVNHFS is defined and some improvements in the theory of PSVNHFS are proposed. Also, we improve some algebraic properties of this set theory and define a distance operator for PSVNHFSs. Then we introduce two aggregation operators called probabilistic single valued neutrosophic hesitant fuzzy weighted arithmetic average (PSVNHFWA) operator and probabilistic single valued neutrosophic hesitant fuzzy weighted geometric average (PSVNHFWG) operator related to algebraic properties presented in this paper. Also, we extend the MABAC method under the probabilistic single valued neutrosophic hesitant fuzzy set theory. Finally, we give an illustrative example to demonstrate the stability and reliability of the proposed theory.

A new computational model based on Archimedean copula for probabilistic unbalanced linguistic term set and its application to multiple attribute group decision making

This paper proposes the concept of the probabilistic unbalanced linguistic term set which considers not only the probability of linguistic variables but also the non-uniform and non-symmetric distribution of linguistic labels. A new computational model on basis of Archimedean copula and corresponding co-copula is developed to deal with probabilistic unbalanced linguistic information. The most advantage of the model is that it can keep the closure of the operation. Some operational properties and particular cases are further investigated. We present the concepts of Archimedean copula weighted probabilistic unbalanced linguistic arithmetic average aggregation operator and Archimedean copula weighted probabilistic unbalanced linguistic geometric average aggregation operator, some properties are also discussed. Finally, the effectiveness and universality of the developed approach are illustrated by a hospital selection and comparison analysis. A sensitivity analysis is also performed to test the robustness of proposed methods.

New q-Rung Orthopair Fuzzy Bonferroni Mean Dombi Operators and Their Application in Multiple Attribute Decision Making

Some q-rung orthopair fuzzy Bonferroni mean Dombi aggregation operators have been developed based on the Bonferroni mean, Dombi T-norm and T-conorm in q-rung orthopair fuzzy environment. The q-rung orthopair fuzzy Bonferroni mean Dombi averaging (q-ROFBMDA) operator and the q-rung orthopair fuzzy geometric Bonferroni mean Dombi averaging (q-ROFGBMDA) operator are first developed. Then the q-rung orthopair fuzzy weighted Bonferroni mean Dombi averaging (q-ROFWBMDA) operator and the q-rung orthopair fuzzy weighted geometric Bonferroni mean Dombi averaging (q-ROFWGBMDA) operator have been developed. Based on the partitioned operation, the q-rung orthopair fuzzy partitioned Bonferroni mean Dombi averaging (q-ROFPBMDA) operator and the q-rung orthopair fuzzy partitioned geometric Bonferroni mean Dombi averaging (q-ROFPGBMDA) operator have been presented. Some desirable properties of the new aggregation operators have been studied. A new multiple attribute decision making method based on the q-ROFWBMDA (q-ROFWGBMDA) operator is proposed. Finally, a numerical example of new campus site selection has been presented to illustrate the new method.

Improved Possibility Degree Method for Intuitionistic Fuzzy Multi-Attribute Decision Making and Application in Aircraft Cockpit Display Ergonomic Evaluation

It is very important for the intuitionistic fuzzy decision making to rank the different intuitionistic fuzzy numbers (IFNs). Based on the full information of the membership degree and non-membership degree, an improved possibility degree method is defined for dealing with multi-attribute decision making (MADM) problems in this paper. Firstly, the limitations of the existing possibility degree are discussed, and then an improved one is defined to overcome these shortcomings. Subsequently, six properties of the proposed possibility degree, which are similar to that of the classic possibility degree, are presented and proved. Moreover, some numerical examples are provided to illustrate the superiority of the proposed method. And the calculation method of membership degree and non-membership degree from the statistical viewpoint is developed to construct the intuitionistic fuzzy evaluation matrix considering that the decision-makers are difficult to give exact values of the two variables directly. Furthermore, depending on the proposed possibility degree and the intuitionistic fuzzy generalized ordered weighted geometric average (IFGOWGA) operator, a new MADM approach is employed and used to solve the practical problem of aircraft cockpit display ergonomic evaluation under the intuitionistic fuzzy set environment. Finally, an evaluation example is examined to manifest the effectiveness and feasibility of the proposed decision-making method.

Group-decision making with induced ordered weighted logarithmic aggregation operators

This paper presents the induced generalized ordered weighted logarithmic aggregation (IGOWLA) operator, this operator is an extension of the generalized ordered weighted logarithmic aggregation (GOWLA) operator. It uses order-induced variables that modify the reordering process of the arguments included in the aggregation. The principal advantage of the introduced induced mechanism is the consideration of highly complex attitude from the decision makers. We study some families of the IGOWLA operator as measures for the characterization of the weighting vector. This paper presents the general formulation of the operator and some special cases, including the induced ordered weighted logarithmic geometric averaging (IOWLGA) operator and the induced ordered weighted logarithmic aggregation (IOWLA). Further generalizations using quasi-arithmetic mean are also proposed. Finally, an illustrative example of a group decision-making procedure using a multi-person analysis and the IGOWLA operator in the area of innovation management is analyzed.

A simplified neutrosophic multiplicative set‐based TODIM using water‐filling algorithm for the determination of weights

AbstractDue to the technological developments around the world, the amount of information that researchers work on increases continuously. This information density contains incomplete and uncertain data that cannot be fully expressed with crisp numbers. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are useful tools to manage such information, but these concepts use a symmetrical and uniform scale to express data, whereas real‐life problems contain nonsymmetrical and non‐uniform information. Intuitionistic multiplicative sets (IMSs) are effective tools for dealing with these real‐life problems. However, IMSs cannot handle real‐life problems completely because indeterminate information depends on membership and non‐membership information of IMSs, which is a restriction for decision makers and also for decision problems. To overcome this limitation, this paper generalizes the IMSs by using simplified neutrosophic set and introduces a novel approach that is called simplified neutrosophic multiplicative sets (SNMSs). Firstly, we define SNMS, show their set‐based operations, and then give a description of simplified neutrosophic multiplicative numbers (SNMNs). Based on SNMNs, we develop two simplified neutrosophic multiplicative aggregation operators on SNMNs that are called simplified neutrosophic multiplicative weighted arithmetic average operator and simplified neutrosophic multiplicative weighted geometric average operator. Furthermore, we define some simplified neutrosophic multiplicative distance measures. Finally, using a model based on water‐filling algorithm for determining criteria weights, we give a numerical example to demonstrate the effectiveness of the introduced concept with the proposed simplified neutrosophic multiplicative simplified neutrosophic multiplicative‐TODIM method.

A New Model for Stock Management in Order to Rationalize Costs: ABC-FUCOM-Interval Rough CoCoSo Model

Cost rationalization has become imperative in every economic system in order to create adequate foundations for its efficient and sustainable management. Competitiveness in the global market is extremely high and it is challenging to manage business and logistics systems, especially with regards to financial parameters. It is necessary to rationalize costs in all activities and processes. The presence of inventories is inevitability in every logistics system, and it tends to create adequate and symmetrical policies for their efficient and sustainable management. In order to be able to do this, it is necessary to determine which products represent the largest percentage share in the value of procurement, and which are the most represented quantitatively. For this purpose, ABC analysis, which classifies products into three categories, is applied taking into account different constraints. The aim of this paper is to form a new model that involves the integration of ABC analysis, the Full Consistency Method (FUCOM), and a novel Interval Rough Combined Compromise Solution (CoCoSo) for stock management in the storage system. A new IRN Dombi weighted geometric averaging (IRNDWGA) operator is developed to aggregate the initial decision matrix. After grouping the products into three categories A, B and C, it is necessary to identify appropriate suppliers for each category in order to rationalize procurement costs. Financial, logistical, and quality parameters are taken into account. The FUCOM method has been used to determine the significance of these parameters. A new Interval CoCoSo approach is developed to determine the optimal suppliers for each product group. The results obtained have been modeled throughout a multi-phase sensitivity analysis.

Multiple-attribute decision making problems based on SVTNH methods

The neutrosophic set (NS) is a leading tool in modeling of situations involving incomplete, indeterminate and inconsistent information. The single-valued neutrosophic sets (SVNs) is more useful tool than neutrosophic sets in some applications of engineering and scientific problems. In this paper, we study Hamacher operations and operations between single-valued trapezoidal neutrosophic numbers. Then we propose the single-valued trapezoidal neutrosophic Hamacher weighted arithmetic averaging (SVTNHWA) operator, single-valued trapezoidal neutrosophic Hamacher ordered weighted arithmetic averaging (SVTNHOWA) operator, single-valued trapezoidal neutrosophic Hamacher hybrid weighted averaging (SVTNHHWA) operator, single-valued trapezoidal neutrosophic Hamacher weighted geometric averaging (SVTNHWGA) operator and single-valued trapezoidal neutrosophic Hamacher ordered weighted geometric averaging (SVTNHOWGA) operator and single-valued trapezoidal neutrosophic Hamacher hybrid weighted geometric averaging (SVTNHHWGA) operator, and obtain some of their properties. Furthermore, we developed a multiple-attribute decision-making method in single-valued trapezoidal neutrosophic (SVTN) environment based on these operators. Finally, we proposed an application of MADM problem in assessment of potential of software system commercialization.

Multiple attribute group decision making based on weighted aggregation operators of triangular neutrosophic cubic fuzzy numbers

In this paper, we define the new concepts of a triangular neutrosophic cubic fuzzy number (TNCFN), the basic operational laws of TNCFNs, and the score function of TNCFNs. Then, we develop a triangular neutrosophic cubic fuzzy weighted arithmetic averaging (TNCFWAA) operator and a triangular neutrosophic cubic fuzzy weighted geometric averaging (TNCFWGA) operator to aggregate triangular neutrosophic cubic fuzzy number (TNCFN) information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the triangular neutrosophic cubic fuzzy weighted arithmetic averaging (TNCFWAA) operator and triangular neutrosophic cubic fuzzy weighted geometric averaging (TNCFWGA) operator and the score function of triangular neutrosophic cubic fuzzy number (TNCFN) is established under a triangular neutrosophic cubic fuzzy number (TNCFN) environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

A power quality evaluation method for distribution system with renewable energy

ABSTRACTPower quality evaluation data are heterogeneous and fluctuating, and there are large subjective factors in the evaluation process. To solve this problem, a power quality evaluation method based on incentive punishment factor and the ordered weighted aggregation (OWA) operators was proposed. The integrity and fairness of the evaluation information were guaranteed, through the homogenisation of the evaluation data. And using incentive and penalty factors to calculate the single index evaluation value without considering the time factor. By introducing the time weights and adopting the linear target programming model and ordered the weighted averaging operator to get the primary evaluation values of the indices in the inspection period. Then, the minimum variance method was used to get index weights, and the ordered weighted geometric averaging (OWGA) operator was applied to obtain the comprehensive evaluation value of the power quality. Finally, the power quality of a distribution system with photovoltaic generation under different load conditions is analysed as an example. The results showed that the method proposed in this paper distinguishes the power quality level under various load conditions significantly, which verify the feasibility and effectiveness of the model.

Pythagorean Dombi fuzzy aggregation operators with application in multicriteria decision‐making

A Pythagorean fuzzy set, an extension of intuitionistic fuzzy sets, is very helpful in representing vague information that occurs in real world scenarios. The Dombi operators with operational parameters, have excellent flexibility. Due to the flexible nature of these Dombi operational parameters, this research paper introduces some new aggregation operators under Pythagorean fuzzy environment, including Pythagorean Dombi fuzzy weighted arithmetic averaging (PDFWAA) operator, Pythagorean Dombi fuzzy weighted geometric averaging (PDFWGA) operator, Pythagorean Dombi fuzzy ordered weighted arithmetic averaging operator and Pythagorean Dombi fuzzy ordered weighted geometric averaging operator. Further, this paper presents several advantageous characteristics, including idempotency, monotonicity, boundedness, reducibility and commutativity of preceding operators. By utilizing PDFWAA and PDFWGA operators, this article describes a multicriteria decision-making (MCDM) technique for solving MCDM problems. Finally, a numerical example related to selection of a leading textile industry is presented to illustrate the applicability of our proposed technique.

Multi-criteria decision making approach based on PROMETHEE with probabilistic simplified neutrosophic sets

Probabilistic simplified neutrosophic set $$ \left( {PSNS} \right) $$ is an important tool to describe the vagueness existing in the real life. In this study, we define a PSNS and discuss some of theoretical set operations of $$ PSNSs $$. Also we propose the concepts of module on $$ PSNSs $$, as well as inner product and projection operator between two $$ PSNSs $$. In relation to this new set, we introduce a probabilistic simplified neutrosophic number $$ \left( {PSNN} \right) $$. A $$ PSNN $$ has three components which is called probabilistic-valued truth membership degree, probabilistic-valued indeterminacy membership degree and probabilistic-valued falsity membership degree, respectively. We give some of algebraic operational rules, a score function and an accuracy function on $$ PSNNs $$. Furthermore, we introduce two aggregation operators called the probabilistic simplified neutrosophic weighted arithmetic average operator and the probabilistic simplified weighted geometric average operator on $$ PSNNs $$. Furthermore, we determine weights of criteria with a method that is based on fuzzy measure and develop a method based on preference function to determine weight of each decision maker. We present an extended PROMETHEE method based on $$ PSNSs $$ for group decision problems. Finally, as an application of this theory, we give a practice on a multi-criteria group decision making problem based on $$ PSNNs $$ by using extended PROMETHEE method to ensure stability of the proposed method.

Extensions of Intuitionistic Fuzzy Geometric Interaction Operators and Their Application to Cognitive Microcredit Origination

The intuitionistic fuzzy set (IFS), a popular tool to present decision makers’ cognitive information, has received considerable attention from researchers. To extend the interaction operational laws in the computation of cognitive information, this paper focuses on investigating extensions of geometric interaction aggregation operators by means of the t-norm and the corresponding t-conorm under an intuitionistic fuzzy environment. We develop the extending intuitionistic fuzzy-weighted geometric interaction averaging (EIFWGIA) operator, the extending intuitionistic fuzzy-ordered weighted geometric interaction averaging (EIFOWGIA) operator, the intuitionistic fuzzy weighted geometric interaction quasi-arithmetic mean (IFWGIQAM), and the intuitionistic fuzzy-ordered weighted geometric interaction quasi-arithmetic mean (IFOWGIQAM). We investigate the properties of the proposed extensions and apply the extensions to the cognitive microcredit origination problem. For different generator functions h and ϕ, the proposed IFWGIQAM and IFOWGIQAM degenerate into existing intuitionistic fuzzy aggregation operators or extensions, some of which consider situations that in which no interactions exist between membership and non-membership functions, which can be used in more decision situations. The methods developed in this paper can be used to account for several decision situations. The numerical example demonstrates the validity of the proposed approaches by means of comparisons.

Human Immunodeficiency Virus (HIV) infection model based on triangular neutrosophic cubic hesitant fuzzy number

In this paper, we define the basic concept of triangular neutrosophic cubic hesitant fuzzy number and their properties. We develop a triangular neutrosophic cubic hesitant fuzzy ordered weighted arithmetic averaging (TNCHFOWAA) operator and a triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric averaging (TNCHFOWGA) operator to aggregate triangular neutrosophic cubic hesitant fuzzy number (TNCHFN) information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCHFOWAA operator and triangular neutrosophic cubic hesitant fuzzy ordered weighted geometric (TNCHFOWG) operator and the score function of TNCHFN is established under a TNCHFN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

New approach of triangular neutrosophic cubic linguistic hesitant fuzzy aggregation operators

In this paper, we define the new concepts of a triangular neutrosophic cubic linguistic hesitant fuzzy number (TNCLHFN), the basic operational relations of TNCHLFNs, and the score function of TNCLHFNs. Then, we develop a triangular neutrosophic cubic linguistic hesitant fuzzy weighted arithmetic averaging (TNCLHFWAA) operator and a triangular neutrosophic cubic linguistic hesitant fuzzy weighted geometric averaging (TNCLHFWGA) operator to aggregate TNCLHFN information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the TNCLHFWAA and TNCLHFWGA operators, and the score function of TNCLHFN is established under a TNCLHFN environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach. Triangular neutrosophic cubic linguistic hesitant fuzzy number with a wider scope of applications, and hence, the motivation for investigating into its applicability in different diseases in medical patients.

An extended MABAC method for multi-criteria group decision-making problems based on correlative inputs of intuitionistic fuzzy information

This study aims to introduce a series of novel distance measures of an intuitionistic fuzzy set and an extended Multi-attributive Border Approximation Area Comparison method to address multi-criteria group decision-making problems. To aggregate the intuitionistic fuzzy information, we propose two aggregation operators, namely, the intuitionistic fuzzy Dombi generalised $$ \lambda $$-Shapley Choquet arithmetical average operator and intuitionistic fuzzy Dombi generalised $$ \lambda $$-Shapley Choquet geometric average operator. These aggregation operators consider the importance of combinations and correlations among combinations of input arguments. Furthermore, an illustrative example of a human resource management problem is presented to verify the effectiveness of the proposed method, and sensitivity and comparison analyses are conducted to demonstrate the technique’s stability and advancements. Finally, conclusions are drawn.

Application of fuzzy ordered weighted geometric averaging (FOWGA) operator for project delivery system decision-making

Appropriate project delivery model is one of the key factors affecting a project’s success. Most decision-making methods of project delivery are based on vague qualitative indicators. However, a numerical scale is usually unable to effectively and accurately reflect the preferences of decision-makers. Scholars have found that applying the fuzzy set theory and using the fuzzy ordered weighted geometric averaging (FOWGA) operator for project delivery system (PDS) decision could reduce the judgment information losing to a certain extent and improve the objectivity and fairness of group decision-making. In this study, we further addressed the decision method and procedure for PDS decision by using the FOWGA operator and demonstrated the mode selection method as well. The results demonstrated that the method can overcome the current drawback of subjectivity of the project delivery decision method, better solve the decision-making information losing problem during assembling process and further reflect the priority of the PDS so as to improve the efficiency of the group decision.

A Robust Single-Valued Neutrosophic Soft Aggregation Operators in Multi-Criteria Decision Making

Molodtsov originated soft set theory that was provided a general mathematical framework for handling with uncertainties in which we meet the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as neutrosophic set theory. The main object of this paper is to lay a foundation for providing a new approach of single-valued neutrosophic soft tool which is considering many problems that contain uncertainties. In present study, a new aggregation operators of single-valued neutrosophic soft numbers have so far not yet been applied for ranking of the alternatives in decision-making problems. To this propose work, single-valued neutrosophic soft weighted arithmetic averaging (SVNSWA) operator, single-valued neutrosophic soft weighted geometric averaging (SVNSWGA) operator have been used to compare two single-valued neutrosophic soft numbers (SVNSNs) for aggregating different single-valued neutrosophic soft input arguments in neutrosophic soft environment. Then, its related properties have been investigated. Finally, a practical example for Medical diagnosis problems provided to test the feasibility and applicability of the proposed work.

A Novel Group Decision Making Method Under Uncertain Multiplicative Linguistic Environment for Information System Selection

An effective method is proposed to solve the group decision-making problems with uncertain multiplicative linguistic information. First, to compare two uncertain multiplicative linguistic variables, a possibility degree formula is introduced in accordance with the operation laws. Some desirable properties of possibility degree are provided. Then, the uncertain multiplicative linguistic hybrid weighted geometric averaging (ULHWG) operator is developed to aggregate uncertain multiplicative linguistic variables into an overall preference value. Thus, a comprehensive algorithm for linguistic group decision-making is proposed based on the deviation measure and the ULHWG operator. Finally, a numerical example is provided to illustrate the practicality and validity of the proposed method.