Fuzzy Multi-criteria Decision-making Problems Research Articles

Picture Fuzzy Interactional Bonferroni Mean Operators via Strict Triangular Norms and Applications to Multicriteria Decision Making

Based on the closed operational laws in picture fuzzy numbers and strict triangular norms, we extend the Bonferroni mean (BM) operator under the picture fuzzy environment to propose the picture fuzzy interactional Bonferroni mean (PFIBM), picture fuzzy interactional weighted Bonferroni mean (PFIWBM), and picture fuzzy interactional normalized weighted Bonferroni mean (PFINWBM) operators. We prove the monotonicity, idempotency, boundedness, and commutativity for the PFIBM and PFINWBM operators. We also establish a novel multi-criteria decision making (MCDM) method under the picture fuzzy environment by applying the PFINWBM operator. Furthermore, we apply our MCDM method to the enterprise resource planning (ERP) systems selection. The comparative results for our MCDM method induced by six classes of well-known triangular norms ensure that the best selection is always the same ERP system. Therefore, our MCDM method is effective for dealing with the picture fuzzy MCDM problems.

Complex dual hesitant fuzzy TODIM method and their application in Russia–Ukraine war’s impact on global economy

The primary objective of this research is to examine how the Russia–Ukraine war impacted the global economy. To achieve this goal, we propose operational laws, a score and accuracy function, and a divergence measure for complex dual hesitant fuzzy sets. Furthermore, we investigate the challenges associated with multi-criteria decision-making (MCR) using aggregation operators and the TODIM method with complex dual hesitant fuzzy (CDHF) information. Drawing inspiration from arithmetic aggregation operations, we introduce several aggregation operators for complex dual hesitant fuzzy information, including the complex dual hesitant fuzzy weighted average (CDHFWA) operator, complex dual hesitant fuzzy ordered weighted average (CDHFOWA) operator, and complex dual hesitant fuzzy hybrid average (CDHFHA) operator. We thoroughly analyze the unique characteristics of these proposed operators and use them in conjunction with the TODIM method to develop practical approaches for solving complex dual hesitant fuzzy multi-criteria decision-making problems. To validate our approach and demonstrate its applicability, we provide a practical example of how the Russia–Ukraine war affected the global economy. Our study confirms the effectiveness of our approach and highlights how it can be used to solve real-world problems.

Application of Intuitionistic Z-Numbers in Supplier Selection

Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems. A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives. The proposed model is then implemented in a supplier selection problem. The obtained ranking is compared to the existing models based on Z-numbers. The results show that the ranking order is slightly different from the existing models. Sensitivity analysis is performed to validate the obtained ranking. The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80% to 100% consistency despite the drastic change of criteria weights. Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’ opinions in solving decision-making problems.

A interval valued intuitionistic fuzzy multi criteria decision making

The limitations and disadvantages of the available intuitionistic fuzzy set scoring functions are investigated. Two improved methods for handling multi-criteria fuzzy decision-making problems are provided. They are based on the two theories of intuitionistic fuzzy set and cross entropy, with the adoption of cross entropy of the degree of membership from the degree of non-membership handling the effect of hesitancy degree. Score function method and weighted score function method are their names. This study presents and investigates a novel strategy for ranking interval-valued intuitionistic fuzzy sets. Examples using numbers are used to demonstrate the technique.

Membership Score of an Interval-Valued Pythagorean Fuzzy Numbers and Its Applications

The main aim of the paper is to define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers which can overcome the drawbacks of existing familiar ranking methods. In this paper, firstly, we show the limitations of various ranking functions in ordering/ comparing any two arbitrary interval-valued Pythagorean fuzzy numbers in detail. Secondly, we define a new Membership score function on the class of interval-valued Pythagorean fuzzy numbers and study their properties. Then we compare our proposed method with many other different existing methods for showing the efficacy of the proposed method. Finally, we show the applicability of the proposed Membership score function in solving interval-valued Pythagorean fuzzy multi-criteria decision-making problems using a numerical example.

RETRACTED ARTICLE: An innovative framework to forecast the best inventory management system module by hesitant fuzzy VQA-TOPSIS technique for textile industry

The textile industry has major attributes to evaluate which is reeling under manifold problems. The utmost issue is the erratic nature of supply and demand. Textile industry has scheduling problems because of its multi-production business like weaving, dyeing, wrap making, and cloth cutting due to the combination of make-to-stock and make-to-order production. These specific characters make the production strategy and planning, and control a difficult task. Another complexity is the distribution of products where certain collections are limited by production time, season, market, and quantities during sales. To meet the complication, a management strategy needs to be employed. Hence, the rationale of the article is to develop and examine the best inventory management system for the textile industry in terms of basic inventory control, barcoding, accounting integration, demand forecasting, lot tracking, and bundled kits. The scope of the inventory system covers measuring the feature change and planning for future uncertain inventory levels. A multi-objective and criteria decision-making (MOACDM) method is implemented by hesitant fuzzy vector quantified attribute-TOPSIS (FHVQAT) to evaluate the best inventory management system. The decision-making matrix is formed, normalized, and multiplied concerning criterion weights. The multi-criteria decision-making (MCDM) method is analyzed, the positive-ideal (PIS) and negative-ideal solutions (NIS) are found, and the distance of each alternative is calculated for obtaining the correct solution. Finally, the good alternatives are positioned dependent on their relative closeness to the perfect arrangement. As a result, we found out the proposed approach is useful and practical to examine the best inventory management system and other fuzzy MCDM problems. The novelty of the hesitant fuzzy VQA-TOPSIS method can be highly useful in large-scale decision-making issues as regularly found within the inventory control system.

Interval-Valued Fuzzy Multi-Criteria Decision-Making with Dependent Evaluation Criteria for Evaluating Service Performance of International Container Ports

Due to COVID-19 barriers, the needs of international container ports have become more important than in the past. Therefore, it is very critical and essential for the scientific developments of port-logistics. To gain the scientific developments of port logistics, effective and efficient evaluation methods for decision-making are indispensable, especially for assessing service performance of international container ports based on dependent evaluation criteria (DEC). Among numerous decision-making methods, technique for order preference by similarity to ideal solution (TOPSIS) was often expanded under fuzzy environments into fuzzy multi-criteria decision-making (FMCDM) to preserve imprecise messages. The FMCDM was able to be associated with quality function deployment (QFD) into a hybrid method to solve problems with DEC. To gain more messages, QFD and TOPSIS are combined and then expanded under interval-valued fuzzy environment (IVFE) to solve a FMCDM problem with DEC. Practically, evaluating service performance of international container ports in Taiwan and the surrounding sea areas is considered a problem with DEC because the related evaluation criteria are partially connected. By the hybrid method of combining QFD with TOPSIS under IVFE, international container ports with DEC are effectively and efficiently evaluated for service performance, and more insights are gained than the past for establishing essential fundamentals in recent scientific developments of port logistics on account of breaking down COVID-19 barriers.

A Novel Integrating Data Envelopment Analysis and Spherical Fuzzy MCDM Approach for Sustainable Supplier Selection in Steel Industry

Supply chain sustainability, which takes environmental, economic, and social factors into account, was recently recognized as a critical component of the supply chain (SC) management evaluation process and known as a multi-criteria decision-making problem (MCDM) that is heavily influenced by the decision-makers. While some criteria can be analyzed numerically, a large number of qualitative criteria require expert review in linguistic terms. This study proposes an integration of Data Envelopment Analysis (DEA), spherical fuzzy analytic hierarchy process (SF-AHP), and spherical fuzzy weighted aggregated sum product assessment (SF-WASPAS) to identify a sustainable supplier for the steel manufacturing industry in Vietnam. In this study, both quantitative and qualitative factors are considered through a comprehensive literature review and expert interviews. The first step employs DEA to validate high-efficiency suppliers based on a variety of quantifiable criteria. The second step evaluates these suppliers further on qualitative criteria, such as economic, environmental, and social factors. The SF-AHP was applied to obtain the criteria’s significance, whereas the SF-WASPAS was adopted to identify sustainable suppliers. The sensitivity analysis and comparative results demonstrate that the decision framework is feasible and robust. The findings of this study can assist steel industry executives in resolving the macrolevel supplier selection problem. Moreover, the proposed method can assist managers in selecting and evaluating suppliers more successfully in other industries.

Interval-Valued Fuzzy Multi-Criteria Decision-Making by Combining Analytic Hierarchy Process with Utility Representation Function

To encompass uncertainty and vagueness of information, the analytic hierarchy process (AHP) was often extended into fuzzy multi-criteria decision-making (FMCDM) under an uncertain environment. However, the extension of AHP was rarely constructed on interval-valued fuzzy numbers. Recently, interval-valued fuzzy numbers were utilized for decision-making to obtain more messages than others. For AHP extended under a fuzzy environment into fuzzy AHP, fuzzy computations are critical to derive priorities of pairwise comparison matrices. Although AHP’s approximate computations including the normalization of row arithmetic averages may be adopted to the fuzzy environment, the fuzzy extension of AHP is still complicated for division and multiplication of fuzzy numbers, especially interval-valued fuzzy numbers. To resolve complicated ties, a utility representation function of interval-valued fuzzy numbers in fuzzy AHP is used for yielding vectors consisting of priority representations of fuzzy pairwise comparison matrices on evaluation criteria based on objective, alternatives based on evaluation criteria, and more hierarchies. Then, sum product of multiplying the priority representation vectors is derived to form the utility representations of alternative performance indices, and alternative performance indices are represented by their corresponding utility representations. Therefore, FMCDM problems are easily solved by fuzzy AHP, i.e., combining AHP with the utility representation function under an interval-valued fuzzy environment.

Multicriteria decision making approach using an efficient novel similarity measure for generalized trapezoidal fuzzy numbers.

Multicriteria Decision Making (MCDM) has a huge role to play while ruling out one suitable alternative among a pool of alternatives governed by predefined multiple criteria. Some of the factors like imprecision, lack of information/data, etc., which are present in traditional MCDM processes have showcased their lack of efficiency and hence eventually it has paved the ways for the development of Fuzzy multicriteria decision making (FMCDM). In FMCDM processes, the decision makers can model most of the real-life phenomena by fuzzy information-based preferences. The availability of a wide literature on similarity measure (SM) emphasizes the vital role of SM of generalized fuzzy numbers (GFNs) to conduct accurate and precise decision making in FMCDM problems. Despite having few advantages, most of the existing approaches possessed a certain degree of counter intuitiveness and discrepancies. Thus, we have attempted to propose a novel SM for generalized trapezoidal fuzzy numbers (GTrFNs) which could deliberately overcome the impediments associated with the earlier existing approaches. Moreover, a meticulous comparative study with the existing approaches is also presented. This paper provides us with an improved method to obtain the similarity values between GTrFNs and the proposed SM consists of calculating the prominent features of fuzzy numbers such as expected value and variance. We use fourteen different sets of GTrFNs, to compare the fruition of the present approach with the existing SM approaches. Furthermore, to show the utility and applicability of our proposed measure, we illustrate few practical scenarios such as the launching of an electronic gadget by a company, a problem of medical diagnosis and finally, a proper anti-virus mask selection in light of the recent COVID-19 pandemic. The obtained results with our proposed SM, for the mentioned FMCDM problems, are analytically correct and they depict the efficiency and novelty of the present article.

Hexagonal fuzzy approximation of fuzzy numbers and its applications in MCDM

Numerous research papers and several engineering applications have proved that the fuzzy set theory is an intelligent effective tool to represent complex uncertain information. In fuzzy multi-criteria decision-making (fuzzy MCDM) methods, intelligent information system and fuzzy control-theoretic models, complex qualitative information are extracted from expert’s knowledge as linguistic variables and are modeled by linear/non-linear fuzzy numbers. In numerical computations and experiments, the information/data are fitted by nonlinear functions for better accuracy which may be little hard for further processing to apply in real-life problems. Hence, the study of non-linear fuzzy numbers through triangular and trapezoidal fuzzy numbers is very natural and various researchers have attempted to transform non-linear fuzzy numbers into piecewise linear functions of interval/triangular/trapezoidal in nature by different methods in the past years. But it is noted that the triangular/trapezoidal approximation of nonlinear fuzzy numbers has more loss of information. Therefore, there is a natural need for a better piecewise linear approximation of a given nonlinear fuzzy number without losing much information for better intelligent information modeling. On coincidence, a new notion of Generalized Hexagonal Fuzzy Number has been introduced and its applications on Multi-Criteria Decision-Making problem (MCDM) and Generalized Hexagonal Fully Fuzzy Linear System (GHXFFLS) of equations have been studied by Lakshmana et al. in 2020. Therefore, in this paper, approximation of nonlinear fuzzy numbers into the hexagonal fuzzy numbers which includes trapezoidal, triangular and interval fuzzy numbers as special cases of Hexagonal fuzzy numbers with less loss/gain of information than other existing methods is attempted. Since any fuzzy information is satisfied fully by its modal value/core of that concept, any approximation of that concept is expected to be preserved with same modal value/core. Therefore, in this paper, a stepwise procedure for approximating a non-linear fuzzy number into a new Hexagonal Fuzzy Number that preserves the core of the given fuzzy number is proposed using constrained nonlinear programming model and is illustrated numerically by considering a parabolic fuzzy number. Furthermore, the proposed method is compared for its efficiency on accuracy in terms of loss of information. Finally, some properties of the new hexagonal fuzzy approximation are studied and the applicability of the proposed method is illustrated through the Group MCDM problem using an index matrix (IM).

Multi-criteria decision-making using a complete ranking of generalized trapezoidal fuzzy numbers

The decision-making under several uncertainties is a major concern to choose the best alternative among the several separate alternatives. This paper deals with the uncertainty of using a complete ranking classification of generalized trapezoidal fuzzy numbers (GTrFNs). In the view of that several measures such as mode, spread, midpoint the score, radius, left and right fuzziness score and linguistic expression are considered to compute the ranking order of GTrFN. Using the proposed complete ranking of GTrFN, this paper presents a method for solving fuzzy multi-criteria decision-making problems. The comparative analysis of existing methods with our proposed method is also described.

DIGITAL SUPPLIER SELECTION FOR A GARMENT BUSINESS USING INTERVAL TYPE-2 FUZZY TOPSIS

Recent advances in digital technology and manufacturing have changed the industry dramatically. Fundamentally, Industry 4.0 has begun to affect many areas, aiming at improving production and engineering processes, improving the quality of products and services, optimizing the relationship between customers and organizations, bringing new business opportunities and providing economic benefits. One of those areas is the supply chain management, which greatly affects business productivity. Industry 4.0 has provided a highly efficient digital supply chain that has established a smart connection between supply, production, logistics and customers. This has promoted the digitization of suppliers resulting in an increase in the performance of parent companies, which, therefore, wish to identify and use the suppliers that best use digital technologies. However, it is an uncertain decision problem which has many criteria in order to determine these suppliers. Therefore, this problem can be solved by multi-criteria decision-making methods that can best model uncertainties. In this study, it is aimed to select the best one among the suppliers which are digitalized by using the industry 4.0 technologies from the suppliers of a parent firm operating in the garment industry. In order to solve the selection problem, the interval type-2 fuzzy TOPSIS method, which includes a interval of type-2 fuzzy sets and which can model the uncertainties very well in solving fuzzy multi-criteria decision making problems, was used. At the end of the study, alternatives were listed according to closeness indexes and the best digital supplier selection was made according to the results of sensitivity analysis and necessary evaluations were made. As a result, the selection model used in this paper, which is the first study in the literature on the selection of digital suppliers and which is not included in the selection of traditional suppliers, can contribute to researchers and practitioners by using them for other industries.

Trapezoidal Interval Type-2 Fuzzy TOPSIS Using Alpha-Cuts

Fuzzy multi-criteria decision-making (FMCDM) provides solutions to the problems involving multiple criteria for decision-makers under uncertain environments. The Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is one of the most popular methods to address FMCDM problems. In this paper, we propose an extension of the TOPSIS method with trapezoidal interval type-2 fuzzy sets (IT2 FSs) using the concept of α-cut. We first propose a new method to calculate the distance between two trapezoidal IT2 FSs with the tool of α-cut and ordered weighted averaging (OWA) operator. Next, based on the distance method, we extend the TOPSIS method to the context of trapezoidal IT2 FSs and utilize it to solve FMCDM problems. Finally, an illustrative example is used to demonstrate the feasibility of the proposed method, and some comparisons with other existing works are presented to show the highlights of the proposed method. The proposed method provides a flexible solution for the FMCDM problems by taking the decision-makers’ attitudes into consideration.

An advanced dice similarity measure of generalized fuzzy numbers and its application in multicriteria decision making

Multicriteria decision making (MCDM) is an important process to select best alternative among a set of alternatives based on preassigned multiple criteria. Presence of uncertainty due to lack of information/data, imprecision, vagueness etc. classical MCDM process becomes more complex and inappropriate. To overcome such types of situations, different types of fuzzy sets are explored and consequently fuzzy multicriteria decision making (FMCDM) was developed. In FMCDM problems, similarity measure of generalized fuzzy numbers plays crucial role in making appropriate decision by choosing best alternative. A handful number of work done on similarity measures are confronted in literature. Even though some advantages of these existing works are encountered, most of the works have impediments. In this regard, an attempt has been made to devise a similarity measure (SM) of GFNs with same or unequal height. It is observed that the proposed SM has the capability to overcome the deficiencies of the available earlier approaches and outplays in all the environments. To showcase the novelty and efficiency of the present SM comparative studies have been performed. Moreover, FMCDM problem has been solved under this setting and found that results obtained by this approach confronts human intuitions and analytical output.

Combining technique for order preference by similarity to ideal solution with relative preference relation for interval-valued fuzzy multi-criteria decision-making

In the past, technique for order preference by similarity to ideal solution (TOPSIS) was one of multi-criteria decision-making (MCDM) methods and often extended into a fuzzy multi-criteria decision-making (FMCDM) one for encompassing uncertainty and vagueness messages. Obviously, TOPSIS extended under fuzzy environment is useful to solve FMCDM problems, but the extension only constructed on general fuzzy numbers (i.e., triangular or trapezoidal fuzzy ones), not interval-valued fuzzy ones. In real world, the recent decision-making process is getting complicated and thus more information now must be grasped than ever. For presenting varied and added data, general fuzzy numbers may not be adequate, whereas interval-valued fuzzy numbers are suitable. Based on above, TOPSIS should be extended under interval-valued fuzzy environment. In this paper, we associate TOPSIS with a relative preference relation under interval-valued fuzzy environment into interval-valued FMCDM for dealing with complicated decision-making problems to obtain more information. The proposed relative preference relation as similar as Wang’s relative preference relation is also improved from Lee’s fuzzy preference relation on general fuzzy numbers. An important difference is the proposed relative preference relation used on interval-valued fuzzy numbers, but Wang’s relative preference relation is utilized on triangular fuzzy numbers. Through the combination of TOPSIS and relative preference relation under interval-valued fuzzy environment, interval-valued FMCDM can be feasibly and rationally finished.

Intuitionistic Fuzzy Possibility Degree Measure for Ordering of IVIFNs with Its Application to MCDM

In this article, the concept of an intuitionistic fuzzy possibility degree (IFPD) for ordering several interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The IFPD ranks IVIFNs by distinguishing the comparable and non-comparable components of the joint intervals of membership and non-membership degrees. The incomparable cases of nested joint intervals can also rank respective IVIFNs through the proposed IFPD approach. An intuitionistic fuzzy possibility preference relation based on the proposed IFPD measure for IVIFNs is defined as a more effective tool for modelling uncertainty than existing intuitionistic preference relations. Further, an approach for solving multicriteria interval-valued intuitionistic fuzzy decision-making problems based on IFPD measure of IVIFNs is advanced also provides a possibility degree as supplementary information to the ranking of alternatives. The validity and effectiveness of the advanced approach are demonstrated through two illustrative examples.

A Novel Hybrid Fuzzy Grey TOPSIS Method: Supplier Evaluation of a Collaborative Manufacturing Enterprise

Recently, there is of significant interest in developing multi-criteria decision making (MCDM) techniques with large applications for real-life problems. Making a reasonable and accurate decision on MCDM problems can help develop enterprises better. The existing MCDM methods, such as the grey comprehensive evaluation (GCE) method and the technique for order preference by similarity to an ideal solution (TOPSIS), have their one-sidedness and shortcomings. They neither consider the difference of shape and the distance of the evaluation sequence of alternatives simultaneously nor deal with the interaction that universally exists among criteria. Furthermore, some enterprises cannot consult the best professional expert, which leads to inappropriate decisions. These reasons motivate us to contribute a novel hybrid MCDM technique called the grey fuzzy TOPSIS (FGT). It applies fuzzy measures and fuzzy integral to express and integrate the interaction among criteria, respectively. Fuzzy numbers are employed to help the experts to make more reasonable and accurate evaluations. The GCE method and the TOPSIS are combined to improve their one-sidedness. A case study of supplier evaluation of a collaborative manufacturing enterprise verifies the effectiveness of the hybrid method. The evaluation result of different methods shows that the proposed approach overcomes the shortcomings of GCE and TOPSIS. The proposed hybrid decision-making model provides a more accurate and reliable method for evaluating the fuzzy system MCDM problems with interaction criteria.

Hesitant Fuzzy Linguistic Archimedean Aggregation Operators in Decision Making with the Dempster–Shafer Belief Structure

We propose a novel method for hesitant fuzzy linguistic decision making by utilizing Dempster–Shafer (D–S) theory of evidence. First, we propose some novel operations of hesitant fuzzy linguistic term sets (HFLTSs) on the basis of closed operations on linguistic 2-tuples and distribution linguistic average aggregation (DLAA) operators. These novel operations not only avoid information loss and operational results exceeding the boundary of linguistic term sets, but also make the aggregation results interpretable. Then, we define the hesitant fuzzy linguistic Archimedean weighted arithmetic mean (HFLAWAM) and hesitant fuzzy linguistic Archimedean weighted geometric mean (HFLAWGM) operators of HFLTSs. These two proposed operators are able to overcome the shortcomings of the existing approaches to multicriteria decision making (MCDM) with HFLTSs. Then, to take into account the novel operations of HFLTSs and the MCDM under uncertainty, we propose the belief structure-HFLAWAM (BS-HFLAWAM) and belief structure-HFLAWGM (BS-HFLAWGM) operators of HFLTSs. After that, we create an approach to handle the hesitant fuzzy linguistic MCDM problems in light of proposed operators. Finally, we apply the created approach to a MCDM problem regarding political management of a country.

A Method for Partner Selection of Supply Chain Using Interval-Valued Fuzzy Sets — Fuzzy Choquet Integral and Improved Dempster–Shafer Theory

Supply chain partner selection (SCPS) is an important issue for firms to remain highly competitive. SCPS is generally formulated as a fuzzy multi-criteria decision-making problem, of which the most crucial step is how to cope with the fuzzy correlations of multi-criteria and individual differences of experts. To gain more exact results, we adopt interval-valued intuitionistic fuzzy sets to express the fuzziness of multi-criteria. Fuzzy Choquet integral model is developed to explain correlations of multi-criteria and calculate the evaluation results of each expert. An improved Dempster–Shafer theory is utilized to reconcile differences and synthesize each expert decision results. Additionally, an example is presented to illustrate the potential application of the proposed method.