Multi-attribute Decision-making Problems Research Articles

Associated Probabilities in Interactive MADM under Discrimination q-Rung Picture Linguistic Environment

In some multi-attribute decision-making (MADM) models studying attributes’ interactive phenomena is very important for the minimizing decision risks. Usually, the Choquet integral type aggregations are considered in such problems. However, the Choquet integral aggregations do not consider all attributes’ interactions; therefore, in many cases, when these interactions are revealed in less degree, they do not perceive these interactions and their utility in MADM problems is less useful. For the decision of this problem, we create the Choquet integral-based new aggregation operators’ family which considers all pair interactions between attributes. The problem under the discrimination q-rung picture linguistic and q-rung orthopair fuzzy environments is considered. Construction of a 2-order additive fuzzy measure (TOAFM) involves pair interaction indices and importance values of attributes of a MADM model. Based on the attributes’ pair interactions for the identification of associated probabilities of a 2-order additive fuzzy measure, the Shapley entropy maximum principle is used. The associated probabilities q-rung picture linguistic weighted averaging (APs-q-RPLWA) and the associated probabilities q-rung picture linguistic weighted geometric (APs-q-RPLWG) aggregation operators are constructed with respect to TOAFM. For an uncertainty pole of experts’ evaluations on attributes regarding the possible alternatives, the associated probabilities of a fuzzy measure are used. The second pole of experts’ evaluations as arguments of the aggregation operators by discrimination q-rung picture linguistic values is presented. Discrimination q-rung picture linguistic evaluations specify the attribute’s dominant, neutral and non-dominant impacts on the selection of concrete alternative from all alternatives. Constructed operators consider the all relatedness between attributes in any consonant attribute structure. Main properties on the rightness of extensions are showed: APs-q-RPLWA and APs-q-RPLWG operators match with q-rung picture linguistic Choquet integral averaging and geometric operators for the lower and upper capacities of order two. The conjugation among the constructed operators is also considered. Connections between the new operators and the compositions of dual triangular norms (Tp,Spq) and (Tmin,Smax) are also constructed. Constructed operators are used in evaluation of a selection reliability index (SRI) of candidate service centers in the facility location selection problem, when small degree interactions are observed between attributes. In example MADM, the difference in optimal solutions is observed between the Choquet integral aggregation operators and their new extensions. The difference, however, is due to the need to use indices of all interactions between attributes.

Q-Rung orthopair fuzzy TOPSIS method and the application to information service quality evaluation in online health community

Since the information quality in the online health community is very important for users to obtain valuable health information, information quality evaluation is a necessary research that involves a multi-attribute decision-making (MADM) problem. However, few researches have been done to address both the construction of evaluation criteria and the expression and processing of fuzzy information, especially in online health community. This paper proposes a novel evaluation framework of information service quality combined principal component analysis (PCA) method with the TOPSIS method under q-rung orthopair fuzzy set (q-ROFS) environment. An accurate evaluation criteria system is optimized by the PCA method, and the q-ROF TOPSIS method is proposed to process larger space of fuzzy evaluation information and overcome information loss and information distortion, in which a new distance measure between q-ROFSs is defined and an entropy weight model is initiated to determine the unknown weight of attribute. Moreover, a numerical example is performed to prove the practicability and superiority of the method through comparative analysis, which gives clear results of information quality evaluation of four online health communities. This research ends with fuzzy decision-making theory and application, and provides references for standardizing and improving the information quality of online health communities.

Construction and generation of distance and similarity measures for intuitionistic fuzzy sets and various applications

The distance measure between intuitionistic fuzzy sets (IFSs) is a concept of very contemporary interest among the researchers in the field of decision-makings, such as pattern recognition, medical diagnosis, and multiattribute decision-making (MADM) problems. Consequently, diverse distance measures are developed and used in determining the similarity and dissimilarity between IFSs. In the existing methods, the distance measures are calculated based on the geometry of the IFSs. However, the IFSs hold information about the elements in a set. As such, some of the existing distance measures are misleading and unreasonable. Hence, in this paper, a nonlinear distance formula is devised to follow the problem definition. Further, by explicitly proving the distance properties, it is being established that the distance formula is a distance measure. Further, theories for the construction of distance measures are developed. The convex combination of two distance measures is also a distance measure is being proved explicitly. Furthermore, based on the proposed distance measures, similarity measures have been developed. Aside from that, an intriguing idea has been introduced, namely, that an infinite number of distance measures can be constructed from a given pair of distance measures. Additionally, the proposed distance and similarity measures are applied to a variety of problems, including medical diagnosis, pattern recognition, and a MADM problem in COVID-19 face mask selection, where the legitimacy and applicability of the proposed advanced distance measure is demonstrated.

A Public-Participation-Based Mixed Multiattribute Decision-Making Approach for Major Public Affairs

The decision-making activities of major public affairs are closely related to the public, so the decision results of such affairs must be supported by the public. The public must participate in decision-making activities to ensure their effectiveness, which further increases the complexity. In addition, attribute information and public opinion usually present different forms of expression in this type of problem, making decision-making more difficult. Therefore, a suitable decision approach must be chosen to deal with this type of decision problem. This paper addresses the decision-making characteristics of major public affairs and proposes a public-participation-based decision-making approach for mixed multiattribute decision-making problems in major public affairs. The proposed approach can work with entirely unknown attribute weights and decision-making values represented in multiple formats. First, the statistical distribution of public opinions is determined based on the expectation of the attributes, resulting in decision-making reference points for various attributes. The different forms of attributes and reference points are unified. Then, the values of the attributes and reference points are standardized. Afterward, the attribute prospect value for each alternative is calculated using the attribute value and corresponding reference points. The attribute weight intervals are determined based on the importance information of the attributes provided by the public. An optimization model is established to determine the attribute weights to maximize the alternative attribute deviation. Next, the comprehensive prospect value of each alternative is obtained to determine the ranking of the alternatives. Finally, a case analysis is conducted with a method comparison and sensitivity analysis, and the feasibility and effectiveness of the proposed approach are verified. In the proposed method, the reference points for each attribute are set according to the distribution characteristics and ambiguity of public expectations, guaranteeing that public expectations can be effectively reflected in the attribute reference points. In the process of attribute weighting, based on the information for the attribute importance given by the public, the range of attribute weights is determined. Then, we obtain the exact value of the attribute weights using an optimization model to maximize the alternative attribute deviation. The final result of the attribute weights ensures the full expression of public opinion and can improve the differentiation of decision results, which is convenient for ranking alternatives. During evaluation of the alternatives based on prospect theory, the expression forms of attributes and reference points are unified. Subsequently, the values of them are normalized, which satisfy the decision-making requirement of major public affairs.

Distance measure for Pythagorean fuzzy sets with varied applications.

Distance measure is one of the research hotspot in Pythagorean fuzzy environment due to its quantitative ability of distinguishing Pythagorean fuzzy sets (PFSs). Various distance functions for PFSs are introduced in the literature and have their own pros and cons. The common thread of incompetency for these existing distance functions is their inability to distinguish highly uncertain PFSs distinctly. To tackle this point, we introduce a novel distance measure for PFSs. An added advantage of the measure is its simple mathematical form. Moreover, superiority and reasonability of the prescribed definition are demonstrated through proper numerical examples. Boundedness and nonlinear behaviour of the distance measure is established and verified via suitable illustrations. In the current scenario, selecting an antivirus face-mask as a preventive measure in the COVID-19 pandemic and choosing the best school in private sector for children are some of the burning issues of a modern society. These issues are addressed here as multi-attribute decision-making problems and feasible solutions are obtained using the introduced definition. Applicability of the distance measure is further extended in the areas of pattern recognition and medical diagnosis.

Multi-attribute three-way decisions based on ideal solutions under interval-valued intuitionistic fuzzy environment

Multi-attribute three-way decision (MA3WD) has been a novel tool to solve multi-attribute decision-making (MADM) problems by considering the transforming relationship between loss functions and decision matrix. However many practical decision-making problems face the information with uncertainty and complexity, which makes it impossible to obtain relative loss functions in MA3WD. By introducing the thinking of ideal solutions (IS), this study extends MA3WD to interval-valued intuitionistic fuzzy environment, giving a more flexible and general model to handle with uncertain MADM problems. In this paper, we firstly propose an interval-valued intuitionistic fuzzy three-way decision (IVIF3WD) model by obtaining relative loss functions derived from evaluation values, and introduce ideal solutions to construct an ideal-solution based three-way decision model with single interval-valued intuitionistic fuzzy attribute. Then in consideration of all the attributes, two multi-attribute IVIF3WD models are proposed in the perspectives of individual ideal solutions and global ideal solutions respectively. Finally, two cases of investment with different fuzzy information are utilized to illustrate the application and superiority of proposed models.

A decision-theoretic fuzzy rough set in hesitant fuzzy information systems and its application in multi-attribute decision-making

Decision-theoretic rough sets (DTRSs) as a classic model of three-way decisions have been widely applied in the field of risk decision-making. Considering situations where experts hesitate among several evaluation values, hesitant fuzzy sets, as a new generalization of fuzzy sets, can describe uncertain information flexibly in the decision-making process. In this paper, we propose a decision-theoretic fuzzy rough set (DTFRS) model in hesitant fuzzy information systems and discuss its application in multi-attribute decision-making (MADM). More specifically, we first define a novel fuzzy binary relation between two objects by using the hesitant fuzzy distance function. Then, we study the calculations of the fuzzy similarity class and the conditional probability. At the same time, based on the connection between the loss functions and the attribute values, we develop a data-driven calculation method of the relative loss functions. With these discussions, we construct a DTFRS model in hesitant fuzzy information systems and explore the related decision-making mechanism. Furthermore, a three-way decision method based on the proposed DTFRS model is established to handle MADM problems in the context of a hesitant fuzzy environment. The established method not only takes the decision risk into consideration, but also instructs us how to choose the action for each alternative and gives its corresponding semantic explanation. An illustrative example of the stock investment problem is presented to verify the efficacy of our method. Finally, we take a sensitivity analysis and a comparison analysis to show the established method’s performance and characteristics.

Multiattribute decision making based on new score function of interval-valued intuitionistic fuzzy values and normalized score matrices

In this paper, we propose a novel multiattribute decision making (MADM) method on the basis of the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs) and normalized score matrices. Firstly, it calculates the score value of each IVIFV in the decision matrix (DM) based on the proposed score function of IVIFVs to construct the score matrix. Then, it constructs the normalized score matrix based on the obtained score matrix. Then, it computes the optimal weight of the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute. Then, based on the obtained normalized score matrix and the obtained optimal weight of the IVIF weight of each attribute, it constructs the weighted normalized DM. Then, based on the obtained weighted normalized DM, it calculates the weighted score value of each alternative. Finally, it ranks the alternatives based on the weighted score values of the alternatives. The larger the weighted score value of an alternative, the better the preference order (PO) of the alternative. The proposed MADM method overcomes the drawbacks of the existing MADM methods. The proposed MADM method provides a very useful way to us for dealing with MADM problems in IVIF environments.

A three-way decision method based on fuzzy rough set models under incomplete environments

The paper primarily explores the applicability of three-way decision (TWD) to multi-attribute decision-making (MADM), and establishes a new three-way multi-attribute decision-making (TW-MADM) method under an incomplete environment. For the sake of making rational decisions for MADM problems with fuzzy values, fuzzy rough set models are first utilized to investigate a new TWD model. By taking into account the hesitation degree of each evaluation value, a data-driven method to determine the relative loss functions is presented. Moreover, a new conditional probability calculation method is put forth via the information granularity of each object. In light of the above statement, a novel TWD model with three strategies is proposed. Afterwards, the arithmetic mean method is adopted for patching the lost data to effectively address incomplete MADM problems. Given the uncertainty of the patched data and real data, a new TW-MADM method as well as a corresponding MADM algorithm is designed. By several comparative analysis and experimental analysis, the feasibility, effectiveness, superiority and stability of the method are demonstrated. In addition, the results show that the presented method with optimistic strategies is more viable and stable than the method with compromise and pessimistic strategies.

Critic-entropy based fuzzy decision making models: a systematic analysis

This research article presents a comprehensive analysis of weighting methods used in fuzzy multi attribute decision making (MADM) methods. These methods involve various criteria in order to evaluate alternatives and determining the weights of criteria is a significant problem that arises very often in many MADM problems. In this research paper, CRTITIC and Entropy weighting methods have been used for finding criteria’s weights like in many research works. Using these unsupervised methods of assigning criteria weights, seven fuzzy MADM methods are examined in the context of ranking the best company to invest in. From the results of these methods, ranking order of alternatives is obtained and are analysed for reliability.

Adaptation of a compromise programming approach for evaluating the localized impacts of water allocation

ABSTRACT Evaluating localized impacts of water allocation scenarios (WASs) is an important multi-attribute water decision problem. The impacts of WASs are not the same across a basin, and may have their own spatial variations. Conventional multi-attribute decision-making (MADM) is not capable of capturing and implementing the spatial variations. Using these methods often results in simplification or even oversimplification. Herein a new framework is developed involving a compromise programming approach (CP), fuzzy analytical hierarchy process (FAHP) and distributed indicators. The framework is applied to the Aras basin, Iran. Adaptation of the proposed framework leads to an evaluation of WASs based on their integrated localized impacts and spatial trade-offs. Results show that using lumped indicators rather than distributed indicators imposes significant uncertainties in the evaluation process. Applying CP, distributed indicators and fuzzy weights simultaneously extended the interval with stable ranking and allowed the determination of regional overall priorities and optimal spatial water allocation.

Interval Valued T-Spherical Fuzzy Information Aggregation Based on Dombi t-Norm and Dombi t-Conorm for Multi-Attribute Decision Making Problems

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. Expressing the information under uncertainty using closed subintervals of [0, 1] is beneficial and effective instead of using crisp numbers from [0, 1]. The goal of this paper is to enhance the notion of Dombi aggregation operators (DAOs) by introducing the DAOs in the interval-valued T-spherical fuzzy (IVTSF) environment where the uncertain and ambiguous information is described with the help of membership grade (MG), abstinence grade (AG), non-membership grade (NMG), and refusal grade (RG) using closed sub-intervals of [0, 1]. One of the key benefits of the proposed work is that in the environment of information loss is reduced to a negligible limit. We proposed concepts of IVTSF Dombi weighted averaging (IVTSFDWA) and IVTSF Dombi weighted geometric (IVTSFDWG) operators. The diversity of the IVTSF DAOs is proved and the influences of the parameters, associated with DAOs, on the ranking results are observed in a MADM problem where it is discussed how a decision can be made when there is asymmetric information about alternatives.

The voting linear assignment method for determining priority and weights in solving MADM problems

Linear Assignment (LAM) is one of the Multi-Attribute Decision Making (MADM) methods that uses integer programming models in the solution process. In this method, only the final priority of the alternatives is determined and the distance between the alternatives is not clear. The purpose of this paper is to modify this method so that instead of the final priority of the alternatives, the final weight of the alternatives is presented. This is done using a linear programming model of Data Envelopment Analysis (DEA). In this paper, we propose a hybrid MADM-DEA method called Linear Assignment Voting (VLAM). The new method is explained with a numerical example. The method will then be implemented on a problem in the real world to demonstrate the application of the method. In this case study, VLAM demonstrates the prioritization of models proposed by experts for the purchase of excavators in a road construction company. Also, based on the results of this method, the weight of the first, second and third priorities are 0.39, 0.35 and 0.26, respectively. These results increase the decision maker's power in making the final decision and choice.

Generalized MULTIMOORA method and Dombi prioritized weighted aggregation operators based on T‐spherical fuzzy sets and their applications

In this manuscript, the technique of the generalized MULTIMOORA method is investigated by using the concept of a T-spherical fuzzy set (T-SFS), which is the modified idea of a picture fuzzy set to handle awkward and vague information in daily life problems. T-SFS covers the degree of truth, abstinence, and falsity with a rule that the sum of the qth-powers of all degrees is restricted to the unit interval. Moreover, for examining the interrelationships among any number of T-SFSs, we construct the idea of T-spherical fuzzy Dombi prioritized weighted arithmetic (T-SFDPWA) aggregation operators, T-spherical fuzzy Dombi prioritized arithmetic, T-spherical fuzzy Dombi prioritized geometric, and T-spherical fuzzy Dombi prioritized weighted geometric (T-SFDPWG) aggregation operators are given. Then, the basic properties of T-SFDPWA and T-SFDPWG aggregation operators are investigated and discussed in some of their cases. The investigated operators based on T-SFS are utilized in the environment of multiattribute decision-making problems to find the consistency and proficiency of the developed operators. In last, we illustrated some numerical examples based on explored operators is to examine the reliability and validity of the investigated operators with the help of comparative analysis and graphical representations with some existing ideas to show the presented approaches are extensive powerful.

Multi-attribute Cognitive Decision Making via Convex Combination of Weighted Vector Similarity Measures for Single-Valued Neutrosophic Sets.

Similarity measure (SM) proves to be a necessary tool in cognitive decision making processes. A single-valued neutrosophic set (SVNS) is just a particular instance of neutrosophic sets (NSs), which is capable of handling uncertainty and impreciseness/vagueness with a better degree of accuracy. The present article proposes two new weighted vector SMs for SVNSs, by taking the convex combination of vector SMs of Jaccard and Dice and Jaccard and cosine vector SMs. The applications of the proposed measures are validated by solving few multi-attribute decision-making (MADM) problems under neutrosophic environment. Moreover, to prevent the spread of COVID-19 outbreak, we also demonstrate the problem of selecting proper antivirus face mask with the help of our newly constructed measures. The best deserving alternative is calculated based on the highest SM values between the set of alternatives with an ideal alternative. Meticulous comparative analysis is presented to show the effectiveness of the proposed measures with the already established ones in the literature. Finally, illustrative examples are demonstrated to show the reliability, feasibility, and applicability of the proposed decision-making method. The comparison of the results manifests a fair agreement of the outcomes for the best alternative, proving that our proposed measures are effective. Moreover, the presented SMs are assured to have multifarious applications in the field of pattern recognition, image clustering, medical diagnosis, complex decision-making problems, etc. In addition, the newly constructed measures have the potential of being applied to problems of group decision making where the human cognition-based thought processes play a major role.

A Novel Three-Way Decision Model Based on Utility Theory in Incomplete Fuzzy Decision Systems

The existing three-way decision (TWD)-making methods cannot effectively handle incomplete multiattribute decision-making (MADM) problems in real life; it is necessary to explore an effective three-way MADM model in incomplete fuzzy decision systems (IFDSs). First, we consider the preference of decision makers for each alternative and introduce the concept of predecisions, thus an IFDS is obtained. Then, the weighted conditional probabilities are calculated with the aid of the defined similarity relation. Subsequently, we introduce the notion of relative utility functions and then present an approach to determine the relative utility function values. Afterward, we construct a TWD model in IFDSs and apply it to the modeling of incomplete MADM (IMADM) problems. Our study not only enriches TWD and MADM theories but also provides a new perspective for realistic IMADM problems. At last, the results of comparative and experimental analyses demonstrate the validity, stability, and superiority of our proposed model.

Multiple-Attribute Decision-Making Method Based on Normalized Geometric Aggregation Operators of Single-Valued Neutrosophic Hesitant Fuzzy Information

As a generalization of both single-valued neutrosophic element and hesitant fuzzy element, single-valued neutrosophic hesitant fuzzy element (SVNHFE) is an efficient tool for describing uncertain and imprecise information. Thus, it is of great significance to deal with single-valued neutrosophic hesitant fuzzy information for many practical problems. In this paper, we study the aggregation of SVNHFEs based on some normalized operations from geometric viewpoint. Firstly, two normalized operations are defined for processing SVNHFEs. Then, a series of normalized aggregation operators which fulfill some basic conditions of a valid aggregation operator are proposed. Additionally, a decision-making method is developed for resolving multiattribute decision-making problems based on the proposed operators. Finally, a numerical example is provided to illustrate the feasibility and effectiveness of the method.

A 2-dimensional uncertain linguistic MABAC method for multiattribute group decision-making problems

The 2-dimensional uncertain linguistic variable (2DULV) can depict decision-makers’ subjective assessments on the reliability of given evaluation results, which is a valid and practical tool to express decision information. In this study, we develop an improved MABAC method with 2DULVs to handle multiattribute group decision-making (MAGDM) problems where the weight information of attributes is unknown. First, some related theories of 2DULVs and the basic procedure of the MABAC method are briefly reviewed. Then, the maximum comprehensive evaluation value method is extended to 2DULVs to obtain combination weights of attributes, in which the subjective weights are determined according to the best–worst method (BWM) and the objective weights are calculated by the maximum deviation method. Besides, the generalized weighted average operator for 2DULVs (2DULGWA) is utilized to aggregate the evaluation information given by all experts. Finally, an improved MABAC for 2DULVs (2DUL-MABAC) is proposed, and an example is carried out to explain the validity of the proposed approach.

Multiattribute Decision-Making Method with Intuitionistic Fuzzy Archimedean Bonferroni Means

The Bonferroni mean (BM) can portray the inter-relationships among the arguments, which is based on algebraic norm. Archimedean norm is the generalization of algebraic norm. In this work, the intuitionistic fuzzy (IF) BMs on the basis of the Archimedean norm are investigated, including the Archimedean norm-based IF arithmetic BM (AN-IFABM) and the Archimedean norm-based IF geometric BM (AN-IFGBM). Then, we discuss their typical properties and several particular cases of the AN-IFABM and AN-IFGBM in detail. Moreover, we design the Archimedean norm-based IF weighted arithmetic BM (AN-IFWABM) and the Archimedean norm-based IF weighted geometric BM (AN-IFWGBM) to consider the importance of each argument and their interconnections. Applying the proposed extensions, an approach is designed to cope with the multiattribute decision-making (MADM) problems. Finally, an efficiency evaluation problem of some public companies in China is analyzed by the proposed approach to demonstrate its applicability and validity.

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

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.