Uncertainty In Decision-making Problems Research Articles

Mathematical analysis of parameters belonging to the universe in the soft set theory with new distance measures

Introduction: The soft set theory has drawn the attention of many researchers, particularly for dealing with uncertainty in decision-making problems. Despite its remarkable advantages, the soft set theory has only been used to tackle decision-making problems that aim to choose the best option. However, there exist different forms of decision-making problems that involve different forms of uncertainty. Methods: In this study, we present various algorithms based on the soft set theory in order to handle the cases where one has different uncertainty forms in decision-making problems. Some new concepts such as object code, personal object code, parameter significance weight and new distance measures have been introduced to the literature for the construction of these algorithms. Furthermore, we show the application results of those algorithms and provide several examples. Results and Conclusions: As a result, a comparison among the application results of the algorithms implies that the best objects might not always yield the most efficient outcomes.

Projection-based TOPSIS method to MAGDM in dual probabilistic linguistic information environment

The dual probabilistic linguistic term sets (DPLTSs) are more effective than PLTSs in solving the problem of multi-attribute group decision-making (MAGDM). In this paper, an improved TOPSIS method is developed combining the TOPSIS method and projection measure of DPLTS to supplement the existing research. Firstly, considering the mathematical characteristics of DPLTS, this paper defines the concepts of the module, cosine function, and projection of DPLTS, and then proves the mathematical properties of the cosine function. Secondly, considering the uncertainty of decision-making problems, the weight-solving models are established respectively under the condition that the weight information is completely unknown and partially known. Furthermore, a novel DPLPrj-TOPSIS approach is established based on the projection measure proposed. It involves integrating experts’ DPLTS evaluations, normalizing different DPLTSs, calculating alternatives’ relative closeness and score, etc. Secondly, the proposed method’s feasibility is demonstrated through a case study that entails selecting network promotion plans for food manufacturers. Finally, the proposed method’s effectiveness and validity are verified by comparing and analyzing it with the traditional TOPSIS method based on a distance measure and other existing decision methods.

An overview of granular computing in decision-making: Extensions, applications, and challenges

The management of uncertainty in decision-making problems remains a very challenging and timely research issue despite many proposals. An interesting topic in this area in recent years has been Granular Computing. In this paper, we present a coherent framework for various models of information granules, using hierarchies of information for dealing with knowledge acquired and processed at different levels of abstraction. Granular Computing, a paradigm for handling higher types of uncertainty in decision analysis, is considered a new conceptual and algorithmic asset of decision-making studies and, in particular, data-driven decision-making. Most relevant studies have focused on categories of information granules, namely intervals, fuzzy sets, rough sets, and shadowed sets. To better understand this promising area, this study provides a comprehensive overview of Granular Computing for decision-making through literature analysis, enhancing a variety of extensions, applications, and challenges.

A consensus model under framework of prospect theory with acceptable adjustment and endo-confidence

Consensus is an important issue in group decision making to make a reliable and scientific decision, and it has become a hot topic recently. Due to the complexity and uncertainty of decision-making problems, several aspects of alternatives should be considered in decision-making process. Also, the bounded rational characteristics of decision makers (DMs) may significantly affect the decision results. This paper proposes a multi-criteria consensus model based on prospect theory (PT) to consider the unsymmetrical risk attitudes of DM for gain or loss and on endo-confidence (confidence which is derived by DMs’ evaluation information) levels of DMs to determine their weights. First, the reference point in PT is selected and how to measure the prospect consensus degree is presented. Then, the way to identify the expert who need to modify his/her evaluation is given and two programming models are proposed to obtain the updated evaluation. Subsequently, both the overall difference and the endo-confidence level of the DM are used to determine the weights of DMs. Finally, an illustrative example and the comparative analysis are used to demonstrate the feasibility of the proposed model.

Fermatean hesitant fuzzy rough aggregation operators and their applications in multiple criteria group decision-making

The precise selection of suppliers to fulfill production requirements is a fundamental component of all manufacturing and process industries. Due to the increasing consumption levels, green supplier selection (GSS) has been one of the most important issues for environmental preservation and sustainable growth. The present work aims to develop a technique based on Fermatean hesitant fuzzy rough set (FHFRS), a robust fusion of Fermatean fuzzy set, hesitant fuzzy set, and rough set for GSS in the process industry. On the basis of the operational rules of FHFRS, a list of innovative Fermatean hesitant fuzzy rough weighted averaging operators has been established. Further, several intriguing features of the proposed operators are highlighted. To cope with the ambiguity and incompleteness of real-world decision-making (DM) challenges, a DM algorithm has been developed. To illustrate the applicability of the methodology, a numerical example for the chemical processing industry is presented to determine the optimum supplier. The empirical findings suggest that the model has a significant application of scalability for GSS in the process industry. Finally, the improved FHFR-VIKOR and TOPSIS approaches are employed to validate the proposed technique. The results demonstrate that the suggested DM approach is practicable, accessible, and beneficial for addressing uncertainty in DM problems.

Neutrosophic Soft n-Topological Spaces: A Framework for Decision-Making Problems

This article introduces the concept of neutrosophic soft n-topological spaces and their application in decision-making problems. Neutrosophic soft sets are used to define the open sets in these spaces, which allow for greater flexibility and uncertainty in the decision-making process. The concept of neutrosophic soft n-homeomorphism is also introduced, which describes the topological equivalence between two neutrosophic soft n-topological spaces. The article provides examples of how neutrosophic soft n-topological spaces can be used in decision-making problems, such as medical diagnosis and stock market analysis. The theory and applications presented in this article provide a valuable tool for dealing with uncertainty in decision-making problems.

A new multi-objective optimization ratio analysis plus full multiplication form method for the selection of an appropriate mining method based on 2-tuple spherical fuzzy linguistic sets.

The selection of an appropriate mining method is considered as an important tool in the mining design process. The adoption of a mining method can be regarded as a complex multi-attribute group decision-making (MAGDM) problem as it may contain uncertainty and vagueness. The main goal of this paper is to propose an extended multi-objective optimization ratio analysis plus full multiplication form (MULTIMOORA) method that is based on a 2-tuple spherical fuzzy linguistic set (2TSFLS). The MULTIMOORA method under 2TSFL conditinos has been developled as a novel approach to deal with uncertainty in decision-making problems. The proposed work shows that 2TSFLSs contain collaborated features of spherical fuzzy sets (SFSs) and 2-tuple linguistic term sets (2TLTSs) and, hence, can be considered as a rapid and efficient tool to represent the experts' judgments. Thus, the broader structure of SFSs, the ability of 2TLTSs to represent linguistic assessments, and the efficiency of the MULTIMOORA approach have motivated us to present this work. To attain our desired results, we built a normalized Hamming distance measure and score function for 2TSFLSs. We demonstrate the applicability and realism of the proposed method with the help of a numerical example, that is, the selection of a suitable mining method for the Kaiyang phosphate mine. Then, the results of the proposed work are compared with the results of existing methods to better reflect the strength and effectiveness of the proposed work. Finally, we conclude that the proposed MULTIMOORA method within a 2TSFLS framework is quite efficient and comprehensive to deal with the arising MAGDM problems.

Rough q-Rung Orthopair Fuzzy Sets and Their Applications in Decision-Making

Yager recently introduced the q-rung orthopair fuzzy set to accommodate uncertainty in decision-making problems. A binary relation over dual universes has a vital role in mathematics and information sciences. During this work, we defined upper approximations and lower approximations of q-rung orthopair fuzzy sets using crisp binary relations with regard to the aftersets and foresets. We used an accuracy measure of a q-rung orthopair fuzzy set to search out the accuracy of a q-rung orthopair fuzzy set, and we defined two types of q-rung orthopair fuzzy topologies induced by reflexive relations. The novel concept of a rough q-rung orthopair fuzzy set over dual universes is more flexible when debating the symmetry between two or more objects that are better than the prevailing notion of a rough Pythagorean fuzzy set, as well as rough intuitionistic fuzzy sets. Furthermore, using the score function of q-rung orthopair fuzzy sets, a practical approach was introduced to research the symmetry of the optimal decision and, therefore, the ranking of feasible alternatives. Multiple criteria decision making (MCDM) methods for q-rung orthopair fuzzy sets cannot solve problems when an individual is faced with the symmetry of a two-sided matching MCDM problem. This new approach solves the matter more accurately. The devised approach is new within the literature. In this method, the main focus is on ranking and selecting the alternative from a collection of feasible alternatives, reckoning for the symmetry of the two-sided matching of alternatives, and providing a solution based on the ranking of alternatives for an issue containing conflicting criteria, to assist the decision-maker in a final decision.

Optimized score function and its application in group multiattribute decision making based on fuzzy neutrosophic sets

Some extensions of fuzzy sets such as interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type n-fuzzy sets, and neutrosophic sets provided powerful and practical tools for dealing with uncertainty in decision-making problems. Neutrosophic set is defined with three-dimensional membership functions to describe the degrees of truth, indeterminacy, and falsity. Neutrosophic set theory is a useful instrument to handle incomplete, inconsistent, and indeterminate information. In this paper, we first propose a modified score function for ranking single-valued neutrosophic numbers. Then, we suggest a TOPSIS method based on the proposed function for decision-making under group recommendation. The method is applied to deal with the hotel location selection problem, where the decision values of the attributes for alternatives and the weights of the attributes are given by decision-makers based on single-valued neutrosophic sets. Finally, numerical experiments are done. They show that the given method is more efficient as well as more reasonable tool for decision-making in contrast to the other existing methods.

Linear Diophantine Fuzzy Relations and Their Algebraic Properties with Decision Making

Binary relations are most important in various fields of pure and applied sciences. The concept of linear Diophantine fuzzy sets (LDFSs) proposed by Riaz and Hashmi is a novel mathematical approach to model vagueness and uncertainty in decision-making problems. In LDFS theory, the use of reference or control parameters corresponding to membership and non-membership grades makes it most accommodating towards modeling uncertainties in real-life problems. The main purpose of this paper is to establish a robust fusion of binary relations and LDFSs, and to introduce the concept of linear Diophantine fuzzy relation (LDF-relation) by making the use of reference parameters corresponding to the membership and non-membership fuzzy relations. The novel concept of LDF-relation is more flexible to discuss the symmetry between two or more objects that is superior to the prevailing notion of intuitionistic fuzzy relation (IF-relation). Certain basic operations are defined to investigate some significant results which are very useful in solving real-life problems. Based on these operations and their related results, it is analyzed that the collection of all LDF-relations gives rise to some algebraic structures such as semi-group, semi-ring and hemi-ring. Furthermore, the notion of score function of LDF-relations is introduced to analyze the symmetry of the optimal decision and ranking of feasible alternatives. Additionally, a new algorithm for modeling uncertainty in decision-making problems is proposed based on LDFSs and LDF-relations. A practical application of proposed decision-making approach is illustrated by a numerical example. Proposed LDF-relations, their operations, and related results may serve as a foundation for computational intelligence and modeling uncertainties in decision-making problems.

A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19.

The emergency situation of COVID-19 is a very important problem for emergency decision support systems. Control of the spread of COVID-19 in emergency situations across the world is a challenge and therefore the aim of this study is to propose a q-linear Diophantine fuzzy decision-making model for the control and diagnose COVID19. Basically, the paper includes three main parts for the achievement of appropriate and accurate measures to address the situation of emergency decision-making. First, we propose a novel generalization of Pythagorean fuzzy set, q-rung orthopair fuzzy set and linear Diophantine fuzzy set, called q-linear Diophantine fuzzy set (q-LDFS) and also discussed their important properties. In addition, aggregation operators play an effective role in aggregating uncertainty in decision-making problems. Therefore, algebraic norms based on certain operating laws for q-LDFSs are established. In the second part of the paper, we propose series of averaging and geometric aggregation operators based on defined operating laws under q-LDFS. The final part of the paper consists of two ranking algorithms based on proposed aggregation operators to address the emergency situation of COVID-19 under q-linear Diophantine fuzzy information. In addition, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

CEQD: A Complex Mass Function to Predict Interference Effects.

Uncertainty is inevitable in the decision-making process of real applications. Quantum mechanics has become an interesting and popular topic in predicting and explaining human decision-making behaviors, especially regarding interference effects caused by uncertainty in the process of decision making, due to the limitations of Bayesian reasoning. In addition, complex evidence theory (CET), as a generalized Dempster-Shafer evidence theory, has been proposed to represent and handle uncertainty in the framework of the complex plane, and it is an effective tool in uncertainty reasoning. Particularly, the complex mass function, also known as a complex basic belief assignment in CET, is complex-value modeled, which is superior to the classical mass function in expressing uncertain information. CET is considered to have certain inherent connections with quantum mechanics since both are complex-value modeled and can be applied in handling uncertainty in decision-making problems. In this article, therefore, by bridging CET and quantum mechanics, we propose a new complex evidential quantum dynamical (CEQD) model to predict interference effects on human decision-making behaviors. In addition, uniform and weighted complex Pignistic belief transformation functions are proposed, which can be used effectively in the CEQD model to help explain interference effects. The experimental results and comparisons demonstrate the effectiveness of the proposed method. In summary, the proposed CEQD method provides a new perspective to study and explain the interference effects involved in human decision-making behaviors, which is significant for decision theory.

Efficient MCDM Model for Evaluating the Performance of Commercial Banks: A Case Study

Evaluation of commercial banks (CBs) performance has been a significant issue in the financial world and deemed as a multi-criteria decision making (MCDM) model. Numerous research assesses CB performance according to different metrics and standers. As a result of uncertainty in decision-making problems and large economic variations in Egypt, this research proposes a plithogenic based model to evaluate Egyptian commercial banks’ performance based on a set of criteria. The proposed model evaluates the top ten Egyptian commercial banks based on three main metrics including financial, customer satisfaction, and qualitative evaluation, and 19 sub-criteria. The proportional importance of the selected criteria is evaluated by the Analytic Hierarchy Process (AHP). Furthermore, the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Vlse Kriterijumska Optimizacija Kompro-misno Resenje (VIKOR), and COmplex PRoportional ASsessment (COPRAS) are adopted to rank the top ten Egyptian banks based on their performance, comparatively. The main role of this research is to apply the proposed integrated MCDM framework under the plithogenic environment to measure the performance of the CBs under uncertainty. All results show that CIB has the best performance while Faisal Islamic Bank and Bank Audi have the least performance among the top 10 CBs in Egypt.

A New Computational Method Based on Probabilistic Linguistic Z-Number With Unbalanced Semantics and Its Application to Multi-Criteria Group Decision Making

Z-number that proposed by Zadeh is an effective tool to describe the information with uncertainty in decision-making problems. However, most of the researches on Z-numbers employed linguistic cardinalities with uniformly distributed scales. In fact, unbalance situation is much common in terms of the psychology of experts. In this paper, we propose a new computational method based on Probabilistic Linguistic Z-number with Unbalanced semantics(UPLZ), which can represent the linguistic evaluations of experts precisely combined with individual risk appetite. A new score function of UPLZs is provided based on hesitant degree and linguistic scale function to reduce the computational complexity. Afterward, a linear programming is constructed to determine weights of criteria by considering cross entropy maximization. The robust decision result can be obtained by applying MULTIMOORA method since it is specific with peculiarities of three subordinate models. Finally, a case study concerning medicine selection for the patients with mild symptoms of the COVID-19 is provided to illustrate the feasibility and effectiveness of the proposed method. The advantages of it are highlighted by sensitivity analysis and comparative analysis with two outstanding multi-criteria decision-making methods.

Decision support framework for the risk ranking of agroforestry biomass power generation projects with picture fuzzy information

With the rapid growth of the global population and economy, energy consumption and demad are increasing sharply. As an essential renewable energy, biomass energy can promote the reform of energy production and consumption. Considering the characteristics of long investment cycle and large investment scale of agroforestry biomass power generation (AFBPG) projects, this study establishes a decision support framework for risk ranking of AFBPG project under picture fuzzy environment. The proposed framework considers not only the fuzziness and uncertainty of decision-making problems but also the decision-makers’ (DMs) psychological behavior. First, given the integrity of information representation, DMs provide risk assessment information expressed with picture fuzzy numbers, and then gives the distance of the picture fuzzy set (PFS) to maximize the PFS information. Second, the entropy weight method is used to compute the objective weight. Third, the VIKOR (Vlse Kriterijumska Optimizacija I Kompromisno Resenje) – TODIM (an acronym in Portuguese for an interactive multi-criteria decision making) method is suggested for ranking risk factors, which reflects the behavioral psychology of DMs. Moreover, the proposed evaluation model is successfully applied in a practical case. The results show that the model is valid for ranking risk factors under picture fuzzy environment. Last but not least, comparison and sensitivity analysis are implemented to verify the effectiveness and applicability of the proposed method and some suggestions for practical application are put forward.

Linguistic Approaches to Interval Complex Neutrosophic Sets in Decision Making

One of the most efficient tools for modeling uncertainty in decision-making problems is the neutrosophic set (NS) and its extensions, such as complex NS (CNS), interval NS (INS), and interval complex NS (ICNS). Linguistic variables have been long recognized as a useful tool in decision-making problems for solving the problem of crisp neutrosophic membership degree. In this paper, we aim to introduce new concepts: single-valued linguistic complex neutrosophic set (SVLCNS-2) and interval linguistic complex neutrosophic set (ILCNS-2) that are more applicable and adjustable to real-world implementation than those of their previous counterparts. Some set-theoretic operations and the operational rules of SVLCNS-2 and ILCNS-2 are designed. Then, gather classifications of the candidate versus criteria, gather the significance weights, gather the weighted rankings of candidates versus criteria and a score function to arrange the candidates are determined. New TOPSIS decision-making procedures in SVLCNS-2 and ICNS-2 are presented and applied to lecturer selection in the case study of the University of Economics and Business, Vietnam National University. The applications demonstrate the usefulness and efficiency of the proposal.

FUZZY EXTENSION OF THE CODAS METHOD FOR MULTI-CRITERIA MARKET SEGMENT EVALUATION

One of the important activities of a company that can increase its competitiveness is market segment evaluation and selection (mse/mss). We can usually consider mse/mss as a multi-criteria decision-making (mcdm) problem, and so we need to use an mcdm method to handle it. Uncertainty is one of the important factors that can affect the process of decision-making. Fuzzy mcdm approached have been designed to deal with the uncertainty of decision-making problems. In this study, a fuzzy extension of the codas (combinative distance-based assessment) method is proposed to solve multi-criteria group decision-making problems. We use linguistic variables and trapezoidal fuzzy numbers to extend the codas method. The proposed fuzzy codas method is applied to an example of market segment evaluation and selection problem under uncertainty. To validate the results, a comparison is performed between the fuzzy codas and two other mcdm methods (fuzzy edas and fuzzy topsis). A sensitivity analysis is also carried out to demonstrate the stability of the results of the fuzz codas. For this aim, ten sets of criteria weights are randomly generated and the example is solved using each set separately. The results of the comparison and the sensitivity analysis show that the proposed fuzzy codas method gives valid and stable results.