Geometric Averaging Operator Research Articles

Applications of Hesitant Interval Neutrosophic Linguistic Schweizer-Sklar Power Aggregation Operators to MADM

Hesitant interval neutrosophic linguistic sets (HINLSs) are one of the core generalization of various sets, such as neutrosophic set (NS), interval neutrosophic set (INS), and interval neutrosophic linguistic set (INLS). HINLS can represent the uncertainty, inconsistency, and reluctance of assessment specialists by expressing qualitative and quantitative information. The goal of this article is to introduce a novel MADM technique that can account for changes in the semantic environment as well as negative consequences of experts’ excessive evaluation values. First, several innovative operational rules based on Schweizer-Sklar (SS) t -norm and t -conorm and a novel comparison procedure for HINLS are established by integrating different linguistic scale functions. This allows for varied semantic settings to be handled. Then, various innovative HINL Schweizer-Sklar power aggregation operators (AOs) are suggested, containing hesitant interval neutrosophic SS power average (HINLSSPA) operator, weighted hesitant interval neutrosophic SS power average (WHINLSSPA) operator, hesitant interval neutrosophic SS power geometric average (HINLSSPGA) operator, weighted hesitant interval neutrosophic SS power geometric average (WHINLSSPGA) operator, some core properties, and various special cases of these AOs are examined. Additionally, based on the initiated AOs, a multiple attribute decision making (MADM) technique with HINL information is anticipated. Finally, a numerical example is illustrated to show the effectiveness and practicality of the anticipated MADM method. A comparison with existing approaches are also discussed.

Group Decision-Making Model of Renal Cancer Surgery Options Using Entropy Fuzzy Element Aczel-Alsina Weighted Aggregation Operators under the Environment of Fuzzy Multi-Sets

Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’ clinical experience and judgments, the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients. Fuzzy multi-sets (FMSs) have a number of properties, which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making (GDM) problems. To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma (RCC) (T1 stage kidney tumor), this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients. First, we propose a conversion method of transforming FMSs into entropy fuzzy sets (EFSs) based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element (EFE) for ranking EFEs. Second, we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging (EFEAAWAA) and EFE Aczel-Alsina weighted geometric averaging (EFEAAWGA) operators. Third, we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs. Finally, the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs. The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

The Ordered Weighted Average Human Development Index

The main aim is to propose a new method for estimating the Human Development Index using ordered weighted average. To develop this method, ordered weighted geometric average (OWGA), induced OWGA prioritized OWA (POWA) operator are studied. Using Human Development Index formulation in combination to aggregations operators presented above is proposed the prioritized induced ordered weighted geometric average (PIOWGA) operator. A mathematical application is carried out to estimate the Human Development Index and compare it with the traditional method and other existing methods. Finally, it is noted that decision makers have an influence on the order given in the ranking by its attitude and criterion, and method can capture the subjective information prioritized by them.

Weighted Aggregation Operators of Fuzzy Credibility Cubic Numbers and their Decision Making Strategy for Slope Design Schemes

Background: A Fuzzy Cubic Set (FCS) is composed of a Fuzzy Set (FS) (certain fuzzy numbers) and an Interval-Valued Fuzzy Set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world. Objective: This paper presents the notions of a Fuzzy Cubic Credibility Set (FCCS) and a Fuzzy Cubic Credibility Number (FCCN) as the new generalization of the FCS notion to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN Weighted Arithmetic Averaging (FCCNWAA) and FCCN Weighted Geometric Averaging (FCCNWGA) operators for Decision Making (DM) strategy. Method: A DM strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open-pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility, can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.

Assessing sustainable production under circular economy context using a novel rough-fuzzy MCDM model: a case of the forestry industry in the Eastern Black Sea region

Purpose Forests are negatively affected from rapid world population increase and industrialization that create intense pressures on natural resources and the possibility of an achieving circular economy. Forests can be considered as essential resources for providing sustainable society and meeting the requirements of future generations and circular economy. Therefore sustainable production tools as part of circular economy can be handled as one of the basic indicators for achieving circular economy. Accordingly the main purpose of this study is developing a novel rough – fuzzy multi-criteria decision-making model (MCDM) for evaluation sustainable production for forestry firms in Eastern Black Sea Region. Design/methodology/approach For determining 18 criteria weights a novel Rough PIPRECIA (PIvot Pairwise RElative Criteria Importance Assessment) method is developed. Eight decision-makers (DMs) participated in the research, and to obtain group rough decision matrix, rough Dombi weighted geometric averaging (RNDWGA) operator has been applied. For evaluation forestry firms fuzzy MARCOS (Measurement of alternatives and ranking according to COmpromise solution) method was utilized. Findings After application developed model the fourth alternative was found as the best. Sensitivity analysis and comparison were made to present the applicability of this method. Originality/value Development of novel integrated Rough PIPRECIA-Fuzzy MARCOS model with emphasis on developing new Rough PIPRECIA method.

Orthopair indeterminate information expression, aggregations and multiattribute decision making method with indeterminate ranges

A neutrosophic number (NN) (d = µ + vI) can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I. Regarding the hybrid concept of intuitionistic fuzzy set (IFS) and NN, this study presents an orthopair indeterminate set (OIS), an orthopair indeterminate element weighted arithmetic averaging (OIEWAA) operator and an orthopair indeterminate element weighted geometric averaging (OIEWGA) operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms. Thus, a multiattribute decision making (DM) approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting. Finally, the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes (alternatives) in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.

Representation and Aggregation of Multi-source Information of Modern Smart Cities Based on the Intuitionistic Polygonal Fuzzy Set

The aggregation of multi-source information can be realized by means of the ordered representation of polygonal fuzzy sets and their linear operations, especially the ordered representation plays an important role in multi-attribute decision analysis. An intuitionistic fuzzy set is not only a generalization of traditional fuzzy set, but also can overcome some defects of fuzzy phenomena described by binary logic. In this paper, we first propose the ordered representation and its arithmetic operations of n-intuitionistic polygonal fuzzy sets (n-IPFS) based on the idea of equidistant dissection, and give a method to solve the ordered representation of n-IPFS through an example. Secondly, a mathematical linear function describing multi-source information of modern smart city is given through an ordered representation of n-IPFS, a new normalization method and calculation formula are proposed for the intuitionistic polygonal decision matrix. Then, by using n-IPFS arithmetic operations the aggregation method of weighted average operator and geometric average operator of multi-source information is given. Finally, the effectiveness of the proposed method is verified by aggregating multi-source information, and thus an intuitionistic fuzzy set and polygonal fuzzy set are unified and applied to decision-making problem of multi-source information of modern smart cities.

Multicriteria Decision-Making Method and Application in the Setting of Trapezoidal Neutrosophic Z-Numbers

The information expression and modeling of decision-making are critical problems in the fuzzy decision theory and method. However, existing trapezoidal neutrosophic numbers (TrNNs) and neutrosophic Z-numbers (NZNs) and their multicriteria decision-making (MDM) methods reveal their insufficiencies, such as without considering the reliability measures in TrNN and continuous Z-numbers in NZN. To overcome the insufficiencies, it is necessary that one needs to propose trapezoidal neutrosophic Z-numbers (TrNZNs), their aggregation operations, and an MDM method for solving MDM problems with TrNZN information. Hence, this study first proposes a TrNZN set, some basic operations of TrNZNs, and the score and accuracy functions of TrNZN and their ranking laws. Then, the TrNZN weighted arithmetic averaging (TrNZNWAA) and TrNZN weighted geometric averaging (TrNZNWGA) operators are presented based on the operations of TrNZNs. Next, an MDM approach using the proposed aggregation operators and score and accuracy functions is established to carry out MDM problems under the environment of TrNZNs. In the end, the established MDM approach is applied to an MDM example of software selection for revealing its rationality and efficiency in the setting of TrNZNs. The main advantage of this study is that the established approach not only makes assessment information continuous and reliable but also strengthens the decision rationality and efficiency in the setting of TrNZNs.

Introducing a new type of HFSs and its application in solving MAGDM problems

Uncertainty has long been explored as an objective and inalienable reality, and then modeled via different theories such as probability theory, fuzzy sets (FSs) theory, vague sets, etc. Hesitant fuzzy sets (HFSs) as a generalization of FSs, because of their flexibility and capability, extended and applied in many practical problems very soon. However, the above theories cannot meet all the scientific needs of researchers. For example, in some decision-making problems we encounter predetermined definite data, which have inductive uncertainties. In other words, the numbers themselves are crisp in nature, but are associated with varying degrees of satisfaction or fairness from the perspective of each decision-maker/judge. To this end, in this article, hesitant fuzzy numbers as a generalization of hesitant fuzzy sets will be introduced. Some concepts such as the operation laws, the arithmetic operations, the score function, the variance of hesitant fuzzy numbers, and a way to compare hesitant fuzzy numbers will be proposed. Mean-based aggregation operators of hesitant fuzzy numbers, i.e. hesitant fuzzy weighted arithmetic averaging (HWAA), hesitant fuzzy weighted geometric averaging (HWGA), hesitant fuzzy ordered weighted arithmetic averaging (HOWAA), and hesitant fuzzy ordered weighted geometric averaging (HOWGA) operators have been discussed in this paper, too. These new concepts will be used to model, and solve an uncertain multi-attribute group decision making (MAGDM) problem. The proposed method will be illustrated by a numerical example and the validity of the obtained solution will be checked by test criteria.

Application of Intuitionistic Fuzzy Evaluation Method in Aircraft Cockpit Display Ergonomics

The ergonomic level of cockpit display design can be improved by establishing an objective and effective method for evaluating the ergonomics of the cockpit display. Given the fuzz problem in ergonomic evaluation, a new intuitionistic fuzzy evaluation method is proposed based on the Intuitionistic Fuzzy Ordered Weighted Geometric Average (IFOWGA) operator and the possible degree function in this work. Firstly, the intuitionistic fuzzy evaluation matrix considering the hesitation degree of experts' determination is first constructed as the basis of intuitionistic fuzzy evaluation. Secondly, using the IFOWGA operator the intuitionistic fuzzy evaluation values are obtained through aggregating the evaluation matrix. And these values are ranked to get the level of ergonomic evaluation by possible degree ranking function. Finally, an evaluation example based on the cockpit display of a certain aircraft is given to verify the effectiveness of the proposed approach. Six alternatives of the evaluation result are obtained by the aggregation of the IFOWGA operator. Applied the possible degree function, the ergonomic evaluation grade of the aircraft cockpit display is the second level by ranking the alternative sand the variation of intuitionistic fuzzy value is already small when the number of experts is more than 16. It can be shown from the results that the ergonomic level of cockpit display can be objectively and scientifically evaluated by the proposed quantitative method, and it can provide a theoretical basis and practical methods for improving the ergonomic level of cockpit display design.

Coal Refinery Process Absorbability Index Assessment against Foot Print of Air Pollution by Usage of Robust Optimization Algorithms: A Novel Green Environment Initiative

Coals are employed as fiery substance, and every day, millions of ton coal are consumed by coal users around the world. It is investigated that the millions of coal’s transportation/logistic till the coal user plants via road route and also inside the coal user plants (known as twice factors) not only enhance the air pollution but also cause the global warming. It is earlier known that coals emit the toxic pollutants and offensive gases such as sulfur dioxide, SO2; nitrogen oxides, NOX; hydrogen chloride arsenic; carbon monoxide, CO; methane; CH4; and CO2 on reacting with environmental O2 due to said twice factors, i.e., during the transportation from coal refinery spot to entry gate of coal user plants (another spot) and in process logistic/movement inside the coal user plants (loading to conveyor to coal fire tubes “attached with coal crushers”). Therefore, the coal refinery technique/process is found as the best practice to control air pollution under concerns of twice factors. The reliable and trustworthy coal refining technology improves the quality of coal by eradicating or eliminating the coating or layers of toxic particles from coal’s surface, which speedily crumble or decompose in reacting with environmental O2 under twice factors. As results, coal refining technology adds the green supply chain value into proposed twice factors and also save the world from breeding of ills and viruses. It is understood that the best coal refinery technique/process helps to overcome and reduce air pollution by responding discussed twice factors (accepted as research challenge and motivation of research). In the presented research work, the authors developed and proposed a dynamic multidimension Coal Refinery Process Absorbability Index (CRPAI) structure (consisted of coal refinery core dimension and subdimensions correspond to CRPA alternative techniques/processes) appended with Robust Optimization Algorithm (ROA) to be explored for opting the best CRP from available options. But due to inherent ambiguity, vagueness, and inconsistency involve in both dimensions of proposed structure, the assessment of expert’s panel is gathered in the terms of linguistic variable “appropriateness ratings” against the subdimensions of CRPAI structure corresponding to preferred CRP options. Next, assigned appropriateness ratings against the subdimensions are substituted by GIVFN. To arrive to core dimensions from subdimensions of CRPAI structure, a GITFN-OWGO (Ordered Weighted Geometric Operator) is investigated and modified as a Ordered Weighted Geometric Average Operator (OWGAO) to be applied for estimating the weights of subdimensions (core novelty of work). Finally, a ROA (consisted of MULTI-MOORA with dominance theory) is applied on the output of OWGAO for opting the viable and best CRP option. The positive effect of the dynamic multidimension CRPAI structure is that it helps the coal refinery companies to assess measure and evaluate the best and feasible coal refinery process under concern of twice factors using expert information. The research can be used to control the air pollution by responding aforesaid twice factors by single practice (the best coal refinery process/technique assessment and evaluation).

Decision Method of Probabilistic Hesitant Fuzzy Information Based on Hamacher Aggregation Operators and MULTIMOORA

Aiming at solving the problem of probability hesitation fuzzy multi-attribute decision making, a new decision-making method of probability hesitation fuzzy multi-attribute is proposed in this paper, based on Hamacher operations and MULTIMOORA method. Firstly, probability hesitation fuzzy Hamacher operations are defined, including sum, product, scalar multiplication and exponentiation, and their properties are studied. On this basis, probability hesitation fuzzy Hamacher weighted average operator and probability hesitation fuzzy Hamacher weighted geometric average operator are proposed, and their properties are also studied. Secondly, alternative from multiple perspectives are chosen and compared by using the MULTIMOORA method. Finally, the effectiveness and feasibility of the decision-making method are verified by an example.

Some aggregation operators of neutrosophic Z-numbers and their multicriteria decision making method

As the generalization of the classical fuzzy number, the concept of Z-number introduced by Zadeh indicates more ability to depict the human knowledge and judgments of both restraint and reliability as an order pair of fuzzy numbers. In indeterminacy and inconsistent environment, a neutrosophic set is described by the truth, falsity, and indeterminacy degrees, but they lack measures related to reliability. To describe the hybrid information of combining the truth, falsity and indeterminacy degrees with their corresponding reliability degrees, this paper first proposes the concept of a neutrosophic Z-number (NZN) set, which is a new framework of neutrosophic values combined with the neutrosophic measures of reliability, as the generalization of the Z-number and the neutrosophic set. Then, we define the operations of neutrosophic Z-numbers (NZNs) and a score function for ranking NZNs. Next, we present NZN weighted arithmetic averaging (NZNWAA) and NZN weighted geometric averaging (NZNWGA) operators to aggregate NZN information and investigate their properties. Regarding the NZNWAA and NZNWGA operators and the score function, a multicriteria decision making (MDM) approach is developed in the NZN environment. Finally, an illustrative example about the selection problem of business partners is given to demonstrate the applicability and effectiveness of the developed MDM approach in NZN setting.

Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision‐making

AbstractA complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators.

Innovative Method to Evaluate Halal Assurance System (HAS 23000) Audit Results using Single Value Neutrosophic Number

The Halal food industry in Indonesia has became an alternative and trend in the global market. The quality management system plays a role in maintaining company consistency in implementing a quality management system which continue to develop in the food industry such as the Halal Assurance System (HAS 23000) LPPOM MUI. Internal audit is a part of the verification tools carries out internally by the company to meet the eleven criteria such as procedures, work instructions and documentation has been implemented with consistency and integrity. However, there are many problems in assessing consistency and integrity, among others, expertise auditor factor and also the auditor’s assessment as a human being tends to be doubtful related to standard interpretation, using a general impression in his assessment, incorrectly determining the classification/grading of findings, so the audit results has not produced a quantitative assessment. The research aims to use of the Neutrosophic Quality Audit (NQA) model. The proposed model uses Single Value Neutrosophic Numbers (SVNN). Simplified Neutrosophic Weighted Geometric Average Operator (SNWGAO) and cosine similarity degree. The result an innovative model will be reliable solution in improving the halal assurance system audit in the food industry. An illustrative example is provided to validate the proposed model.

Complex Pythagorean Dombi fuzzy graphs for decision making

A complex Pythagorean fuzzy set (CPFS) is the generalization of Pythagorean fuzzy set (PFS) in which the range of degrees is extended from [0, 1] to complex plane with unit disk. The averaging operators play a significant role to transform the information into a single value. The flexibility of Dombi operators with operational parameters is outstanding, and the Dombi operators are very efficient in decision-making problems. In this research article, we present a new graph called, complex Pythagorean Dombi fuzzy graph (CPDFG) as the Dombi operators are not yet applied on CPFSs. We employ graph terminology on CPFSs using Dombi operators. We define regular, totally regular, strongly regular and biregular graphs with appropriate elaboration, and their pivotal properties are discussed. Moreover, edge regularity of CPDFG is also explained with significant characteristics. We introduce two operators, namely complex Pythagorean Dombi fuzzy arithmetic averaging (CPDFAA) and complex Pythagorean Dombi fuzzy geometric averaging (CPDFGA) operators, which are capable to aggregate the complex Pythagorean fuzzy information. We utilize CPDFAA and CPDFGA operators in solving a decision-making numerical example, which is related to the selection of suitable place to build a bus terminal in a city. In order to examine the superiority of our propose operators, we provide a comparative analysis with the existing operators.

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.