Showing papers on "Fuzzy number published in 2021"

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

Abstract: Reasonable and effective assessment of express service quality can help express company discover its own shortcomings and overcome them, which is crucial significant to enhance its service quality. When considering the decision assessment of express company, the key issue that emerge powerful ambiguity. Pythagorean fuzzy set as an efficient math tool can capture the indeterminacy successfully. The major focus of this manuscript is to explore various interactive Hamacher power aggregation operators for Pythagorean fuzzy numbers. Firstly, we defined novel interactive Hamacher operation, on this basis we presented some Pythagorean fuzzy interactive Hamacher power aggregation operators such as Pythagorean fuzzy interactive Hamacher power average, weighted average (PFIHPWA), ordered weighted average, Pythagorean fuzzy interactive Hamacher power geometric, weighted geometric (PFIHPWG) and ordered geometric operators,respectively. Meanwhile, we verified their general properties and specific cases as well. The salient feature of proposed operators is that they can not only reduce the impact of negative data and consider the interactions between membership and nonmembership degrees, but also provide more general results through a parameter. Secondly, we defined a Pythagorean fuzzy entropy measure, and then establish a method to determine the attribute weights. Further, based on the conceived PFIHPWA and PFIHPWG operators we explored a novel approach to manage multiple attribute decision making problems. At last, the proposed techniques are carried out in a real application concerning on the assessment of express service quality to display the applicability and effectiveness, as well as the influence of changed parameters on the results. In addition, its advantages are displayed by a systematic comparison with relevant approaches.

A novel Pythagorean fuzzy AHP and fuzzy TOPSIS methodology for green supplier selection in the Industry 4.0 era

Abstract: Advances in information and communication technology have created innovator technologies such as cloud computing, Internet of Things, big data analysis and artificial intelligence. These technologies have penetrated production systems and converted them smart. However, this transformation did not only affect production systems, but also differentiated supplier selection processes. In the supplier selection process, the usage of new technologies along with traditional and green criteria extensively has been investigated in recent years. This paper aims to develop a new group decision-making approach based on Industry 4.0 components for selecting the best green supplier by integrating AHP and TOPSIS methods under the Pythagorean fuzzy environment. In the proposed approach, judgments of different experts are expressed by linguistic terms based on Pythagorean fuzzy numbers. The interval-valued Pythagorean Fuzzy AHP method is utilized to determine the criteria weights. The Pythagorean Fuzzy TOPSIS method based on the distances of suppliers is applied to obtain the ranking of the suppliers and determine the most suitable one. Finally, a real case study on an agricultural tools and machinery company is presented to indicate the effectiveness and accuracy of the proposed selection approach.

Career selection of students using hybridized distance measure based on picture fuzzy set and rough set theory

Abstract: Since the future of the society depends upon the role of students and their services construct the prosperous and advanced society, so suitable career selection for the students' is considered to be an important problem to explore. As per psychology, if a student has the required capability, and positive attitudes towards a subject in terms of interest, attitude, memory, knowledge, environment, and career, then the student will achieve more in that subject. To consider this kind of uncertain issues, picture fuzzy set and rough set are found to be appropriate due to their inherent characteristics to deal with incomplete and imprecise information. In this study, picture fuzzy set and rough set-based approaches are proposed to help the student to choose an appropriate subject and consequently provide a good service or contribution to the society particularly in that domain. The main purpose of the article is to analyse student's features in terms of career, memory, interest, knowledge, environment and attitude and then predict the appropriate stream for making the career comfortable so that the student can conveniently explore much in that area. To select students' career, a hybridized distance measure under picture fuzzy environment is proposed where the evaluating information regarding students, subjects and student's features are given in picture fuzzy numbers. In this paper, two types of hybridization approaches are proposed which are the hybridization of Hausdorff and Hamming distance measures and hybridization of Hausdorff and Euclidean distance measures. Next, we apply rough set theory to determine whether a particular subject is appropriate for a student even if there is controversy to select a stream. Lower and higher approximation with boundary region of rough set theory is used to manage inconsistency situations. Finally, two case studies are demonstrated to validate the applicability of the proposed idea.

Risk evaluation in failure modes and effects analysis: hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information

Abstract: This article proposes two novel modified techniques, namely Pythagorean fuzzy hybrid Order of Preference by Similarity to an Ideal Solution (PFH-TOPSIS) method and Pythagorean fuzzy hybrid ELimination and Choice Translating REality I (PFH-ELECTRE I) method, in order to measure risk rankings in failure modes and effects analysis (FMEA). These methods are designed to overcome the flaws and shortcomings of traditional crisp risk priority numbers and fuzzy FMEA techniques in risk rankings. The proposed methods consider subjective as well as objective weight values of all factors in risk rankings of identified failures. The FMEA experts team are allowed to submit their information by linguistic terms using Pythagorean fuzzy numbers. Both techniques use a Pythagorean fuzzy weighted averaging operator to aggregate their independent evaluations into group assessments. Subsequent steps are different. The PFH-TOPSIS approach computes the distances of failure modes from the Pythagorean fuzzy positive ideal solution and Pythagorean fuzzy negative ideal solution. To evaluate failure modes, the PFH-ELECTRE I approach produces Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. We illustrate the structure of both techniques with the help of flowcharts. The effectiveness of the methods that we develop is described by a numerical example, namely a case study of 1.8-in. color super-twisted nematic (CSTN). To validate their effectiveness and accuracy, we provide a comprehensive comparative analysis with existing techniques of risk evaluation, including intuitionistic fuzzy hybrid TOPSIS, intuitionistic fuzzy TOPSIS, IWF-TOPSIS, and fuzzy TOPSIS methods.

Picture fuzzy interactional partitioned Heronian mean aggregation operators: an application to MADM process

Abstract: The picture fuzzy sets (PFSs) state or model the voting information accurately without information loss. However, their existing operational laws usually generate unreasonable computing results, especially when the agreement degree (AD) or neutrality degree (ND) or opposition degree (OD) is zero. To tackle this issue, we propose the interactional operational laws (IOLs) to compute picture fuzzy numbers (PFNs), which can capture the interaction between the ADs and NDs in two PFNs, as well as the interaction between the ADs and ODs in two PFNs. Based on the proposed novel IOLs, partitioned Heronian mean (PHM) operator, and partitioned geometric Heronian mean (PGHM) operator, some picture fuzzy interactional PHM (PFIPHM), weighted PFIPHM (PFIWPHM), geometric PFIPHM (PFIPGHM), and weighted PFIPGHM (PFIWPGHM) operators are proposed in this paper. Afterwards, we investigate the properties of these operators. Using the PFIWPHM and PFIWPGHM operators, a novel multiple attribute decision-making (MADM) method with PFNs is elaborated. Finally, a study example that involves the service quality ranking of nursing facilities is provided to show the decision procedure of the proposed MADM method and we also give the comparative analysis between the proposed operators and the existing aggregation operators developed for PFNs.

Geometric picture fuzzy numbers and three-dimensional copulas with the non-linear programming approach

Abstract: This study presents a possible relationship between two main objects, which are three-dimensional copulas (3D-Cs) and geometric picture fuzzy numbers (GPFNs). This opens up a potential field for future studies for these two objects that three-dimensional copulas can become useful tools for handling uncertainty information in the form of a picture fuzzy set (PFS). Specifically, we define a GPFN as a base element of the PFS and a defined domain of three-dimensional copulas that contains a set of GPFNs, then we show some examples of three-dimensional copulas identified on this domain. In this framework, we present the theorems related to these two objects. At the same time, we provide some examples for three-dimensional semi-copulas, three-dimensional quasi-copulas, and three-dimensional empirical copulas defined on D, which is a defined domain of a three-dimensional copula and contains a set of GPFNs D g * . In addition, we also introduce a new approach to non-linear programming problems.

An optimization study based on Dijkstra algorithm for a network with trapezoidal picture fuzzy numbers

Abstract: Path finding models attempt to provide efficient approaches for finding shortest paths in networks. A well-known shortest path algorithm is the Dijkstra algorithm. This paper redesigns it in order to tackle situations in which the parameters of the networks may be uncertain. To be precise, we allow that the parameters take the form of special picture fuzzy numbers. We use this concept so that it can flexibly fit the vague character of subjective decisions. The main contributions of this article are fourfold: $$\mathrm{(i)}$$ The trapezoidal picture fuzzy number along with its graphical representation and operational laws is defined. $$\mathrm{(ii)}$$ The comparison of trapezoidal picture fuzzy numbers on the basis of their expected values is proposed in terms of their score and accuracy functions. $$\mathrm{(iii)}$$ Based on these elements, we put forward an adapted form of the Dijkstra algorithm that works out a picture fuzzy shortest path problem, where the costs associated with the arcs are captured by trapezoidal picture fuzzy numbers. Also, a pseudocode for the application of our solution is provided. $$\mathrm{(iv)}$$ The proposed algorithm is numerically evaluated on a transmission network to prove its practicality and efficiency. Finally, a comparative analysis of our proposed method with the fuzzy Dijkstra algorithm is presented to support its cogency.

A novel ant colony algorithm for solving shortest path problems with fuzzy arc weights

Abstract: The shortest path (SP) problem constitutes one of the most prominent topics in graph theory and has practical applications in many research areas such as transportation, network communications, emergency services, and fire stations services, to name just a few. In most real-world applications, the arc weights of the corresponding SP problems are represented by fuzzy numbers. The current paper presents a fuzzy-based Ant Colony Optimization (ACO) algorithm for solving shortest path problems with different types of fuzzy weights. The weights of the fuzzy paths involving different kinds of fuzzy arcs are approximated using the α -cut method. In addition, a signed distance function is used to compare the fuzzy weights of paths. The proposed algorithm is implemented on three increasingly complex numerical examples and the results obtained compared with those derived from a genetic algorithm (GA), a particle swarm optimization (PSO) algorithm and an artificial bee colony (ABC) algorithm. The results confirm that the fuzzy-based enhanced ACO algorithm could converge in about 50% less time than the alternative metaheuristic algorithms.

Pythagorean fuzzy AHP-TOPSIS integrated approach for transportation management through a new distance measure

Abstract: This study represents an integrated approach consisting of AHP (analytical hierarchy process) and TOPSIS (technique for order preference by similarity to ideal solution) in Pythagorean fuzzy environment to solve multicriteria decision-making (MCDM) problems with completely unknown weights of criteria. Pythagorean fuzzy numbers are used to capture uncertainties associated with decision makers’ ambiguous judgment for the selection of transportation companies in an MCDM context which can also be considered as an important area of supply chain management. In the proposed approach, a new distance measure based on cross-evaluation of Pythagorean fuzzy sets is introduced to overcome the disadvantages of existing distance measures. Unlike existing MCDM approaches, in which either subjective or objective weights of criteria are used, in this method AHP is modified using Pythagorean fuzzy information to calculate subjective weights of criteria, as well as Pythagorean fuzzy entropy weight model is applied to compute objective weights of criteria. Finally, both the weights of criteria are simultaneously taken into consideration to obtain final ranking of the alternatives. To demonstrate the application potentiality of the proposed method, a numerical example is considered with Pythagorean fuzzy input in the context of selecting the best transportation company which is one of the most important parts of transportation management. Further, a comparative analysis is executed with other existing techniques to establish the efficacy of the proposed methodology.

Optimal selection of sustainable battery supplier for battery swapping station based on Triangular fuzzy entropy -MULTIMOORA method

Abstract: As one of the important infrastructures for promoting electric vehicles (EVs), the battery swapping station (BSS) has been widely popularized at present due to its convenience and time saving. According to the service mode of BSS, we can find that the batteries of EVs are the core component and their prices account for approximately half of the total operation expenses of the BSS, which directly affect its operation and benefits. Therefore, this paper proposes a sustainable battery supplier selection framework for BSS based on MCDM (Multi-criteria decision making) technique. Firstly, two new criteria are put forward based on the consideration of different requirements between BSS and new energy vehicle manufacture. Then, the Triangular fuzzy numbers (TFNs) are utilized to deal with uncertainty and ambiguity in decision-making process. Afterwards, under the consideration of the relationship between criteria and logic importance, the Triangular fuzzy entropy weight method is applied to determine the criteria weights. Subsequently, the MULTIMOORA approach under the Triangular fuzzy environment is applied to rank alternatives. Finally, a case in Beijing, China with sensitivity analysis and comparative analysis are executed to prove the feasibility of the proposed approach. This paper provides a critical tool for investors to select the most appropriate battery supplier of BSS.

Group decision-making analysis based on linguistic q-rung orthopair fuzzy generalized point weighted aggregation operators

Abstract: The q-rung orthopair fuzzy sets (q-ROFSs), originally proposed by Yager, can express uncertain data to give decision-makers more space. The q-ROFS is a useful tool for describing imprecision, ambiguity, and inaccuracy, and the point operator is a useful aggregation operator which can manage the uncertainty and thus obtain intensive information within the decision-making process. In the latest realization, the linguistic q-rung orthopair fuzzy number (Lq-ROFN) is suggested where the linguistic variables are expressed as membership and non-membership of the Lq-ROFN. In this article, we propose the q-rung orthopair fuzzy linguistic family of point aggregation operators for linguistic q-rung orthopair fuzzy sets (Lq-ROFSs). Firstly, with the arithmetic and geometric operators, we introduce a new class of point-weighted aggregation operators to aggregate linguistic q-rung orthopair fuzzy information such as linguistic q-rung orthopair fuzzy point weighted averaging (Lq-ROFPWA) operators, linguistic q-rung orthopair fuzzy point weighted geometric (Lq-ROFPWG) operators, linguistic q-rung orthopair fuzzy generalized point weighted averaging (Lq-ROFGPWA) operators and linguistic q-rung orthopair fuzzy generalized point weighted geometric (Lq-ROFGPWG) operators. Then, we discuss some special cases and study the properties of these proposed operators. Based on Lq-ROFPWA and Lq-ROFPWG operators, a novel multi attribute group decision-making (MAGDM) methodology is designed to process the linguistic q-rung orthopair fuzzy information. Finally, we provide an example to demonstrate the applicability of the MAGDM. Consequently, the outstanding superiority of the developed methodology is assisted in a variety of ways by parameter exploration and thorough comparative analysis.

Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications

Abstract: The paper aims at introducing novel distance measures for the intuitionistic fuzzy set (IFS) to discuss the decision-making problems. The current work exploits four different notions of centers, namely centroid, orthocenter, circumcenter and incenter of the triangle. First, we mold knowledge embedded in IFSs into isosceles TFN (triangular fuzzy number). Hence, based on these TFNs, we design four-novel distance/similarity measures for IFSs using the structures of the four aforementioned centers and inspect their properties. To avoid the loss of information during the conversion of IFSs into isosceles TFNs, we included the degree of hesitation (t) between the pairs of the membership function in the process. The compensations and authentication of the proposed measures are established with diverse counter-intuitive patterns and decision-making obstacles. Further, a clustering algorithm is also given to match the objects based on confidence levels. The performed analysis shows that the proposed measures give distinguishable and compatible results as contrasted to existing ones.

A new approach for generation of generalized basic probability assignment in the evidence theory

Abstract: The process of information fusion needs to deal with a large number of uncertain information with multi-source, heterogeneity, inaccuracy, unreliability, and incompleteness. In practical engineering applications, Dempster–Shafer evidence theory is widely used in multi-source information fusion owing to its effectiveness in data fusion. Information sources have an important impact on multi-source information fusion in an environment with the characteristics of complex, unstable, uncertain, and incomplete. To address multi-source information fusion problem, this paper considers the situation of uncertain information modeling from the closed-world to the open-world assumption and studies the generation of basic probability assignment with incomplete information. A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy number representation model. Then, by calculating the length of the intersection points between the sample and the triangular fuzzy number model, a GBPA set with an assignment for the empty set can be determined. The proposed method can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing. Finally, a series of comprehensive experiments basing on the UCI data sets is used to verify the rationality and superiority of the proposed method.

Modified Vogel’s approximation method for transportation problem under uncertain environment

Abstract: The fuzzy transportation problem is a very popular, well-known optimization problem in the area of fuzzy set and system. In most of the cases, researchers use type 1 fuzzy set as the cost of the transportation problem. Type 1 fuzzy number is unable to handle the uncertainty due to the description of human perception. Interval type 2 fuzzy set is an extended version of type 1 fuzzy set which can handle this ambiguity. In this paper, the interval type 2 fuzzy set is used in a fuzzy transportation problem to represent the transportation cost, demand, and supply. We define this transportation problem as interval type 2 fuzzy transportation problems. The utility of this type of fuzzy set as costs in transportation problem and its application in different real-world scenarios are described in this paper. Here, we have modified the classical Vogel’s approximation method for solved this fuzzy transportation problem. To the best of our information, there exists no algorithm based on Vogel’s approximation method in the literature for fuzzy transportation problem with interval type 2 fuzzy set as transportation cost, demand, and supply. We have used two Numerical examples to describe the efficiency of the proposed algorithm.

T-spherical fuzzy TODIM method for multi-criteria group decision-making problem with incomplete weight information

Abstract: In this paper, we investigate the multi-criteria group decision-making (MCGDM) problems with incomplete weight information under T-spherical fuzzy environment. Firstly, motivated by the idea of the intuitionistic fuzzy interaction method, we propose some operation laws of T-spherical fuzzy numbers (T-SFNs), as well as some T-spherical fuzzy interaction aggregation operators, such as the T-spherical fuzzy weighted averaging interaction (T-SFWAI) operator, the T-spherical fuzzy weighted geometric interaction (T-SFWGI) operator, the T-spherical fuzzy ordered weighted interaction aggregation operators and the generalized T-spherical fuzzy interaction aggregation operators. Then, some desirable properties of the proposed T-SFWAI and T-SFWGI operators and some special cases of the generalized T-spherical fuzzy interaction aggregation operators are discussed in detail. Secondly, for the situations where the information about the weights of criteria is partly known or completely unknown, we establish two optimization models to determine the weights of criteria based on the maximizing deviation method and Lagrange function method, respectively. Thirdly, the traditional TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) approach is extended to solve MCGDM problem under the T-spherical fuzzy environment by defining the distance between T-SFNs, score function and accuracy function of T-spherical fuzzy number. Finally, a numerical example is given to illustrate the application of the extended TODIM approach, and further the sensitivity analysis and comparison analysis are carried out to demonstrate the influence of parameter on the final result and the effectiveness of the extended method.

A fuzzy system of operation safety assessment using multi-model linkage and multi-stage collaboration for in-wheel motor

Abstract: To simultaneously monitor some electrical or mechanical faults of an in-wheel motor and intelligently evaluate the operation safety, a fuzzy system of operation safety assessment (OSA) is proposed. This method firstly uses many symptom parameters (SPs) such as root mean square, crest factor, temperature rise and current covariance to express the features of the electrical and mechanical faults from different perspectives such as vibration, noise, temperature, current and voltage, possibility theory is employed to translate the probability density function of each SP into the possibility function, and sample data are gradually updated to optimize the possibility function for obtaining the SPs’ membership functions that are evaluation models. Secondly, the probabilities of the current operation state that is safety, attention or danger are obtained from each evaluation model in a stage. Picture fuzzy set (PFS) is used to define a basic picture fuzzy number (PFN), then many PFNs from multiple models and multiple stages are used to establish an OSA's decision matrix. Thirdly, Mahalanobis distance is reintegrated into PFS's theory for objectively judging the real-time evaluation information, and best-worst method is used to estimate subjectively the initial evaluation experience, then the multi-model linkage mechanism is designed. Finally, TODIM is modified to define the relative safety ratio, and prospect theory is employed to structure the global index for formulating the multi-stage collaboration approach, then a fuzzy OSA's system is established. The effectiveness of the proposed method was verified by experimental analysis for the operation safety of in-wheel motor with electrical and mechanical faults.

Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem

Abstract: In this article, we envisage the hexagonal number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. Hexagonal fuzzy number is used as an authoritative logic to ease understanding of vagueness information. This article portrays an impression of different representation, ranking, defuzzification and application of hexagonal fuzzy number. Additionally, disjunctive types of linear and nonlinear hexagonal fuzzy numbers both with symmetry and asymmetry are addressed here along with its graphical representation. Further, a new ranking method is established and two different kinds of approaches to computing the defuzzification of hexagonal fuzzy number are fabricated in this research arena. Finally, one production inventory management problem has been analyzed and solved in the hexagonal fuzzy environment along with the numerical sensitivity analysis tables. This real-life problem plays a crucial role to demonstrate the effectiveness of this method compared to the usual results in crisps environment. This noble thought will help us to solve a plethora of daily-life problems in uncertainty arena.

A holistic FMEA approach by fuzzy-based Bayesian network and best–worst method

Abstract: Failure mode and effect analysis (FMEA) is a risk analysis tool widely used in the manufacturing industry. However, traditional FMEA has limitations such as the inability to deal with uncertain failure data including subjective evaluations of experts, the absence of weight values of risk parameters, and not considering the conditionality between failure events. In this paper, we propose a holistic FMEA to overcome these limitations. The proposed approach uses the fuzzy best–worst (FBWM) method in weighting three risk parameters of FMEA, which are severity (S), occurrence (O), and detection (D), and to find the preference values of the failure modes according to parameters S and D. On the other side, it uses the fuzzy Bayesian network (FBN) to determine occurrence probabilities of the failure modes. Experts use a procedure using linguistic variables whose corresponding values are expressed in trapezoidal fuzzy numbers, and determine the preference values of the failure modes according to parameter O in the constructed BN. Thus, the FBN including expert judgments and fuzzy set theory addresses uncertainty in failure data and includes a robust probabilistic risk analysis logic to capture the dependence between failure events. As a demonstration of the approach, a case study was conducted in an industrial kitchen equipment manufacturing facility. The results of the approach have also been compared with existed methods demonstrating its robustness.

Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making

Abstract: Decision-making problems are more often tainted with uncertainty. Fuzzy numbers play utmost important role to band uncertainty, more especially intuitionistic fuzzy number (IFN) which is the extension of fuzzy number (FN). Different types of IFNs such as normal and generalized trapezoidal, triangular and symmetric hexagonal IFNs are explored. However, based on nature of the data, semi-elliptic type of IFN may exists in real world decision-making problems. In this paper, a maiden attempt has been made to study normal semi elliptic intuitionistic fuzzy number (NSEIFN). Our emphasis has been on arithmetic operations of NSEIFNs and comparing with the other existing IFNs. Also rank of NSEIFNs has been proposed based on mean and value. Apart from that inverse, exponential, logarithm, square root and nth root of NSEIFNs are derived. Finally, the proposed ranking method is applied to the decision making problem where criteria and rating of alternatives are represented in terms of NSEIFN. It is observed that the proposed model produces better results and overcome the drawbacks of existing approaches.

A robust extension of VIKOR method for bipolar fuzzy sets using connection numbers of SPA theory based metric spaces

Abstract: The purpose of this study is to introduce an innovative multi-attribute group decision making (MAGDM) based on bipolar fuzzy set (BFS) by unifying“ VIseKriterijumska Optimizacija I Kompromisno Rasenje (VIKOR)” method. The VIKOR method is considered to be a useful MAGDM method, specifically in conditions where an expert is unable to determine his choice correctly at the initiation of designing a system. The method of VIKOR is suitable for problems containing conflicting attributes, with an assumption that compromising is admissible for conflict decision, the expert wishes a solution very near to the best, and the different alternatives or choices are processed according to all developed attributes. The theory of set pair analysis is a state-of-the-art uncertainty theory which consists of three factors, including “identity degree”, “discrepancy degree”, and “contrary degree” of connection numbers (CNs) and coincidence with many existing theories dealing with vagueness in the given information. Consequently, inspired by this, in the present study, we make an effort to improve the theory of data measurement by introducing some metric spaces using CNs of BFSs. In this research paper, we extend VIKOR method in the context of CNs based metrics, which are obtained form bipolar fuzzy numbers (BFNs). Firstly, we develop CNs of BFNs as well as metric spaces based on CNs. We also discuss some interesting properties of proposed metric spaces. Secondly, we develop VIKOR method using CNs based metrics to handle an MAGDM problem under bipolar fuzzy type information. The predominance of proposed metric spaces is also studied by the means of examples. Furthermore, we demonstrate the efficiency of the extended VIKOR method by solving a numerical example, sensitivity analysis and a detailed comparison with some existing approaches.

Multi-attribute decision-making with q -rung picture fuzzy information

Abstract: q-rung picture fuzzy sets can handle complex fuzzy and impression information by changing a parameter q based on the different hesitation degree and yield a flexible framework that captures imprecise information involving different views (typically but not exclusively: yes, abstention, no, and rejection). The Einstein operators perform well for the aggregation of data in various other frameworks of uncertain information. By combining these concepts, in this article we expand the field of application of the Einstein operators to the q-rung picture fuzzy environment. Thus, we develop novel concepts of q-rung picture fuzzy aggregation operators under Einstein operators and discuss their application in multi-attribute decision-making. First, we propose Einstein operational laws for q-rung picture fuzzy numbers. We then introduce the q-rung picture fuzzy Einstein weighted averaging, q-rung picture fuzzy Einstein ordered weighted averaging, generalized q-rung picture fuzzy Einstein weighted averaging and generalized q-rung picture fuzzy Einstein ordered weighted averaging operators. We develop an algorithm to solve complex decision-making problems using these operators. Finally, to show the practicality and effectiveness of the proposed method, we discuss two multi-attribute decision-making problems (1) selection of a suitable business location (2) selection of a supplier. To demonstrate the superiority and advantage of our proposed method, a comparison with existing methods is presented.

Back-ordered inventory model with inflation in a cloudy-fuzzy environment

Abstract: In this paper, an Economic Production Quantity model for deteriorating items with time-dependent demand and shortages including partially back-ordered is developed under a cloudy-fuzzy environment. At first, we develop a crisp model by considering linearly time-dependent demand with constant deterioration rate, constant inflation rate and shortages under partially back-ordered, then we fuzzify the model to archive a decision under the cloudy-fuzzy (extension of fuzziness) demand rate, inflation rate, deterioration rate and the partially back-ordered rate which are followed by their practical applications. In this model, we assume ambiances where cloudy normalized triangular fuzzy number is used to handle the uncertainty in information which is coming from the data. The main purpose of our study is to defuzzify the total inventory cost by applying Ranking Index method of fuzzy numbers as well as cloudy-fuzzy numbers and minimize the total inventory cost of crisp, fuzzy, and cloudy-fuzzy model. Finally, a comparative analysis among crisp, fuzzy and cloudy-fuzzy total cost is carried out in this paper. Numerical example, sensitivity analysis, and managerial insights are elaborated to justify the usefulness of the new approach. A comparative inquiry of the numerical result with a new existing paper is also carried out. This paper ends with a conclusion along with advantages and limitations of our solution approach, and an outlook towards possible future studies.