Incomplete Weight Information Research Articles

A novel BWM-entropy-COPRAS group decision framework with spherical fuzzy information for digital supply chain partner selection

The transformation and upgrading of traditional supply chain models through digital technology receive widespread attention from the fields of circular economy, manufacturing, and sustainable development. Enterprises need to choose a digital supply chain partner (DSCP) during the process of digital transformation in uncertain and sustainable environments. Thus, the research constructs an innovative decision methodology for selecting the optimal DSCP to achieve digital transformation. The proposed methodology is propounded based upon the entropy measure, generalized Dombi operators, integrated weight-determination model, and complex proportional assessment (COPRAS) method under spherical fuzzy circumstances. Specifically, a novel entropy measure is proposed for measuring the fuzziness of spherical fuzzy (SF) sets, while generalized Dombi operators are presented for fusing SF information. The related worthwhile properties of these operators are discussed. Further, an integrated criteria weight-determination model is presented by incorporating objective weights obtained from the SF entropy-based method and subjective weights from the SF best worst method. Afterward, an improvement of the COPRAS method is proposed based on the presented generalized Dombi operators with SF information. Lastly, the practicability and validity of the proposed methodology are verified by an empirical study that selects an appropriate DSCP for a new energy vehicle enterprise to finish the goal of digital transformation. The sensitivity and comparative analysis are carried out to illustrate the stability, reliability, and superiority of the propounded methodology from multiple perspectives. The results and conclusions indicate that the propounded method affords a synthetic and systematic uncertain decision-making framework for identifying the optimal DSCP with incomplete weight information.

A novel uncertain information modeling method based on cosine similarity and cross entropy under spherical uncertain linguistic fuzzy set

Multi-attribute group decision-making (MAGDM) is one of the research hotspots in human cognitive and decision-making theory. However, there are still challenges to the existing MAGDM methods in modeling uncertain linguistics of decision-makers’ (DMs’) cognitive information and objectively obtaining weights. Therefore, this paper aims to develop a new MAGDM method considering incomplete known weight information under spherical uncertain linguistic sets (SULSs) to model uncertain information in MAGDM problems. The method mainly includes the following aspects. Firstly, a new concept, which enables an intuitive evaluation of neutral membership and hesitancy degrees at the linguistic evaluation, has been is first developed for capturing the more uncertain information. Secondly, the cosine similarity measure (CSM) and cross-entropy measure (CEM) are widely used to measure ambiguous information because of their robustness of measurement results. The CSM and CEM are extended to SULSs to calculate the DMs’ and attributes weights quantitively, respectively. Thirdly, in terms of effective integration of fuzzy information to obtain more accurate decision results, the Hamy mean (HM) and dual Hamy mean (DHM) operators are valued due to their consideration of the interrelationships between inputs. Two extension operators, named spherical fuzzy uncertain linguistic weight HM and DHM, are proposed to integrate spherical fuzzy uncertain linguistic information in the third stage. In the experiment, a decision case is presented to illustrate the applicability of the proposed method, and results show the effectiveness, flexibility and advantages of the proposed method are demonstrated by numerical examples and comparative analysis.

Grey relational analysis-driven optimization of neutrosophic MAGDM for cloud SaaS credibility evaluation

In the basic cloud service delivery model, since SaaS (Software as a Service) is located at the application layer, if a relatively complete cloud service credibility comprehensive evaluation framework can be established from the perspective of SaaS cloud service consumers and combined with their trust context, it can not only effectively solve the trust problem between cloud service consumers (CSC) and cloud service provider (CSP), but also has very important practical significance for the popularization and promotion of SaaS service applications. The credibility evaluation of SaaS services in cloud computing environment is often considered as a multi-attribute group decision making (MAGDM) problem. In this paper, the grey relational analysis (GRA) method is extended to the single-valued neutrosophic sets (SVNSs) setting to deal with MAGDM with incomplete weight information. First, the SVNSs are reviewed. In addition, the single-valued neutrosophic number GRA (SVNN-GRA) is established for MAGDM with incomplete weight information, and the computational steps for all designs are listed. Finally, the credibility evaluation of SaaS services in cloud computing environment is given to demonstrate the SVNN-GRA model and some comparative analysis is done to demonstrate the SVNN-GRA.

Multi-criteria group decision-making method in disposal of municipal solid waste based on cubic Pythagorean fuzzy EDAS approach with incomplete weight information

Municipal solid waste management (MSWM) has always been a typical issue in India. The rapid population growth, impetuous adoption of modern lifestyle, and fast urbanization resulted in India’s swift generation of complicated municipal solid waste (MSW). Consequently, municipalities of different cities in India face various difficulties in MSW collection, treatment and disposal methodology. Inefficient or poorly managed MSW causes numerous troubles, including air pollution, soil fouling, contamination in drinking water and health hazard, and it also impacts socio-economic deterioration. MSWM technique selection is based on several criteria, which are generally imprecise, uncertain, and vague. This paper uses the cubic Pythagorean fuzzy number to comprise the fuzzy characteristics of the criteria value concerning the five alternatives (Thermochemical methods in MSW treatment and disposal). The best MSW treatment and disposal method is selected amongst the five alternatives under the novel multi-criteria group decision-making (MCGDM) approach, the cubic Pythagorean fuzzy EDAS (Evaluation based on Distance from Average Solution) in the Indian context. The weight information of the criteria has yet to be wholly known. A non-linear optimization scheme is proposed to determine the criteria weights that are partially known to maximize the generalized total distance measure between alternatives corresponding to all criteria. The present method is explained with a case study. Finally, a comparative analysis is drawn between the present and some existing methods, showing that the present method is consistent and robust enough to apply in practice.

Consensus-based failure mode and effect analysis in group decision-making with incomplete weights of risk factors: Case study of stereotactic body radiation therapy for lung cancer

Failure mode and effect analysis (FMEA) is a widely used management technique to identify potential failure modes in products, processes, systems, and services to assign limited resources for implementing improvement efforts. For the FMEA with a number of experts, the experts may take different influences on the decision-making process due to the difference between individual rationality and cognition and the influence of social relations. Besides, incomplete weights of risk factors are vital to capturing the fuzziness of experts’ evaluation. Therefore, this paper proposes a consensus-based FMEA method to explore that how cooperative relationship network of experts, the consensus process, and incomplete weight information of risk factors in FMEA influence the decision-making process. First, a consensus reaching process considering cooperative relationships between experts, the self-confidence of experts, and minimum adjustment of expert opinion is proposed to derive a collective evaluation of group. Afterward, the stochastic multicriteria acceptability analysis method is integrated with the gained and lost dominance score method to deal with incomplete weights of risk factors in the FMEA. The proposed method is employed in a case study about ranking the failure modes of stereotactic body radiation therapy for lung cancer patients. The robustness and feasibility of the proposed method are validated by comparative analysis.

Pythagorean fuzzy multi-attribute decision making approach with incomplete weight information

Pythagorean fuzzy (PF) set is widely employed in multi-attribute decision making (MADM) process as it provides excellent convenience in describing the inference information of decision makers. In this paper, we develop a new PF MADM framework with incomplete weight information. Firstly, a linear programming model based on PF decision matrix and PF judgment matrix is introduced to determine the weights of attribute. Secondly, a new additive consistency checking index based on the order σ discriminant PF information is proposed. Then, we present the PF Yager weighted averaging aggregation operator to aggregate the PF decision information based on Yager triangular norms, which has the desirable property of being monotonic with respect to the total order. Finally, a comprehensive MADM framework is constructed by integrating the above elements, and a case of purchasing air conditioner is given to illustrate the applicability of the proposed approach.

On spherical fuzzy distance measure and TAOV method for decision-making problems with incomplete weight information

A spherical fuzzy set is one of the reliable tools to handle the uncertainties in the data with the help of the three membership degrees: Positive, neutral, and negative. Under this environment, the paper aims to present a novel decision-making algorithm named as MCDM-TAOV with some novel distance measures using matrix norms. In the literature, several kinds of distance measures occur, but they fail to meet certain axioms of the measure. To overwhelm this, the proposed measure satisfies all axiomatic requirements and overcomes the hindrances in the existing distance measures. Several counter-intuitive examples are provided to justify the superiority of the proposed measures. Furthermore, we addressed the total area based on orthogonal vector (TAOV) methodology to solve the MCDM (“multi-criteria decision-making”) problems. A distance-based criteria weight determination method is presented to compute the unknown criteria weight. The approach has been demonstrated by assessing the third-party reverse logistics provider (3PRLP) problem. The practical applicability, comparative analysis and advantages of the study with other decision-making methods are furnished to depict the efficiency of the moulded process.

Grey relational analysis method for typhoon vulnerability assessment of civil engineering structures based on the 2-tuple linguistic neutrosophic number.

As one of the severe natural disasters, typhoon hazard brings tremendous tragedy to human beings. The foreland in the southeast of China is one of the most typhoon prone areas in the world. There are amount of damage of civil engineering structures induced by typhoon every year. Especially for the spacious villages, the low-rise buildings are vulnerable to typhoon so that many of them are destroyed regionally. The typhoon vulnerability assessment of civil engineering structures is a classical multiple attribute group decision making (MAGDM) issues. In this paper, the 2-tuple linguistic neutrosophic number grey relational analysis (2TLNN-GRA) method is built based on the grey relational analysis (GRA) and 2-tuple linguistic neutrosophic sets (2TLNSs) with incomplete weight information. For deriving the weight information of the attribute, an optimization model is built on the basis of the GRA, by which the attribute weights can be decided. Then, the optimal alternative is chosen through calculating largest relative relational degree from the 2-tuple linguistic neutrosophic number positive ideal solution (2TLNNPIS) which considers both the largest grey relational coefficient (GRC) from the 2TLNNPIS and the smallest GRC form 2-tuple linguistic neutrosophic number negative ideal solution (2TLNN NIS). Then, combine the traditional fuzzy GRA model with 2TLNNSs information, the 2TLNN-GRA method is established and the computing steps for MAGDM are built. Finally, a numerical example for typhoon vulnerability assessment of civil engineering structures has been given and some comparisons is used to illustrate advantages of 2TLNN-GRA method.

Extension of GRA method for multiattribute group decision making problem under linguistic Pythagorean fuzzy setting with incomplete weight information

Extension of GRA method for multiattribute group decision making problem under linguistic Pythagorean fuzzy setting with incomplete weight information

Supplier selection with different risk preferences and attribute sets: An innovative study based on generalized linguistic term sets

Selecting the optimal supplier is crucial to the management of the company’s supply chain, which has received widespread attention from academia and business circles. Generally, a variety of suppliers and multiple attributes are usually involved in this selection proceeding which can be comparatively regarded as a linguistic multiple attribute group decision making (MAGDM) problem. However, common linguistic MAGDM problems may not take the following characteristics into consideration. Due to the limited knowledge, distinctive interests, and different semantic value expectations of decision makers (DMs), it is necessary for them to consider their diverse risk preferences and use multi-granular linguistic term sets (LTSs) to assess suppliers on individual attribute sets independently. Meanwhile, the complex decision environment may have influences on the integrity of the attribute weight information, such that it is always incompletely known. To deal with the afore-mentioned situations, this paper presents a procedure based on risk preferences and several attribute sets with incomplete weight information for choosing the desirable supplier. Firstly, a new multi-granular fuzzy linguistic transformation model is constructed to normalize linguistic domains of multi-granular generalized linguistic term sets (GLTSs). Multi-granular GLTSs are introduced to describe semantic values of multi-granular LTSs given by DMs with risk preferences. Secondly, according to the maximizing deviation method with incomplete attribute weight information, an optimization model is also established to determine attribute weight vectors of individual attribute sets. Thirdly, a novel method that comprises of the aforesaid models is presented to handle supplier selection problems with risk preferences and several attribute sets. Finally, an illustrative example on supplier selection and comparative analyses are provided to clarify the validity and feasibility of our proposed method. Significantly, the initiation of the proposed method and its application could afford to the theoretical development of linguistic MAGDM, as well as the practical expansion in the domain of supplier selection.

Hesitant Fuzzy Network Approach for Alternatives Selection with Incomplete Weight Information

Networked rule bases in fuzzy system, acknowledged as fuzzy network, carries multiple stages of development in decision making processes that involves the uncertainty in the data used as medium in various field. Fuzzy network promotes transparency in multicriteria decision making (MCDM) whereby the criteria are divided into subsystems of cost and benefit to ensure good assessment performance. By considering Hesitant fuzzy sets (HFS), which gives the permission of a set of possible values to present the membership degree of an element, we develop a novel approach that applies fuzzy network and the maximizing deviation method in solving MCDM problem. Fuzzy network addresses transparency in the formulation and maximizing deviation method can restore weight information in MCDM problems whether partially known or fully unknown. The proposed method is applied in case study of stock evaluation that carries opinion evaluated by several decision makers and compared in terms of performance using Spearman rho correlation.

Spherical Cubic Fuzzy Extended TOPSIS Method and Its Application in Multicriteria Decision-Making

This paper aims to propose a new methodology for spherical cubic fuzzy (SCF) multicriteria decision-making (MCDM) utilizing the TOPSIS method that uses incomplete weight information. At first, the maximum deviation model is suggested to determine the criteria of weight values. An MCDM methodology is introduced using SCF information, based on the proposed method. Also, to validate the effectiveness of the proposed information, a numerical example is given. Finally, a comprehensive and structured analysis of existing work in comparison with previous work is given.

Heterogeneous multi-attribute case retrieval method based on group decision making using incomplete weight information

Case-based reasoning (CBR) is one of the most popular methods used in emergency decision making (EDM). Case retrieval plays a key role in EDM processes based on CBR and usually functions by retrieving similar historical cases using similarity measurements. Decision makers (DMs), thus, choose the most appropriate historical cases. Although uncertainty and fuzziness are present in the EDM process, in-depth research on these issues is still lacking. In this study, a heterogeneous multi-attribute case retrieval method based on group decision making (GDM) with incomplete weight information is developed. First, the case similarities between historical and target cases are calculated, and a set of similar historical cases is constructed. Six formats of case attributes are considered, namely crisp numbers, interval numbers, linguistic variables, intuitionistic fuzzy numbers, single-valued neutrosophic numbers (NNs) and interval-valued NNs. Next, the evaluation information from the DMs is expressed using single-valued NNs. Additionally, the evaluation utilities of similar historical cases are obtained by aggregating the evaluation information. The comprehensive utilities of similar historical cases are obtained using case similarities and evaluation utilities. In this process, the weights of incomplete information are determined by constructing optimization models. Furthermore, the most appropriate similar historical case is selected according to the comprehensive utilities. Finally, the proposed method is demonstrated using two examples; its performance is then compared with those of other similar methods to demonstrate its validity and efficacy.

Regret Theory-Based Case-Retrieval Method with Multiple Heterogeneous Attributes and Incomplete Weight Information

Regret Theory-Based Case-Retrieval Method with Multiple Heterogeneous Attributes and Incomplete Weight Information

Two-sided matching decision making with multi-granular hesitant fuzzy linguistic term sets and incomplete criteria weight information

Two-sided matching decision making (TSMDM) problems exist widely in human being’s daily life. For practical TSMDM problems, matching objects with different culture and knowledge backgrounds usually tend to provide linguistic assessments using different linguistic term sets (i.e., multi-granular linguistic information). Moreover, for TSMDM problems with high uncertainty, it is possible that matching objects may have some hesitancy and thus provide hesitant fuzzy linguistic term sets (HFLTSs). To model these situations, an approach to TSMDM with multi-granular HFLTSs is developed in the paper. In the proposed approach, some optimization models are first constructed to determine criteria weights for matching objects who do not provide clear criteria weight vectors. Afterwards, each matching object’s hesitant fuzzy linguistic decision matrix is aggregated to obtain his/her collective assessments over matching objects on the other side, which are denoted by multi-granular linguistic distribution assessments. These multi-granular linguistic distribution assessments are unified to obtain matching objects’ satisfaction degrees. Furthermore, an optimization model which aims to maximize the overall satisfaction degree of matching objects by considering the stable matching condition is then established and solved to determine the matching between matching objects. Eventually, an example for the matching of green building technology supply and demand is provided to demonstrate the characteristics of the proposed approach. Compared with previous studies, the proposed approach allows matching objects to provide linguistic assessments flexibly and can deal with the situations when incomplete criteria weight information is provided.

An evolutionary strategic weight manipulation approach for multi-attribute decision making: TOPSIS method

Weight information of the attributes plays a pivotal role in multi-attribute decision making (MADM) problems. Oftentimes, a decision maker may try to manipulate this weight information to persuade a particular rank order of the alternatives of his/her interest. In the literature, this type of manipulation is known as strategic manipulation of the weight information. In this study, we consider the manipulation of weight information strategically in a TOPSIS MADM method under two scenarios: (1) completely unknown weight information i.e. the decision maker does not provide any weight information; (2) incomplete weight information i.e. the decision maker provides only partial preference information over the attributes. This weight manipulation problem is formulated as a mixed integer non-linear programming (MINLP) problem which is highly constrained. Therefore, for solving the MINLP model, a genetic algorithm based solution procedure is developed. A practical example is presented to illustrate the strategic manipulation procedure.

Multiple attribute decision making problem using GRA method with incomplete weight information based on picture hesitant fuzzy setting

Multiple attribute decision making problem using GRA method with incomplete weight information based on picture hesitant fuzzy setting

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

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 novel methodology to select sustainable municipal solid waste management scenarios from three-way decisions perspective

Selecting a sustainable municipal solid waste management (MSWM) scenario can reduce greenhouse gas emissions and deal with the energy crisis, effectively. However, traditional decision approaches only rank alternative scenarios but fail to manage them. Implementing effective management for alternative MSWM scenarios can save decision costs and improve efficiency. Thus, this paper aims to construct a novel multi-criteria group decision-making (MCGDM) methodology to manage and rank sustainable scenarios. To evaluate sustainable MSWM scenarios, a comprehensive evaluation index system is constructed from five dimensions including economy, environment, society, technology, and energy. The hesitant fuzzy linguistic term set is employed to articulate evaluation information. Given the importance of experts and the incomplete criteria weight information, an inclusion measure-based approach is proposed to obtain expert weights, and the grey relational analysis linear programming model with incomplete criteria weight information is constructed to determine criteria weights. An inclusion measure-based hesitant fuzzy linguistic multigranulation three-way decisions over two universes approach is developed to manage and rank alternative MSWM scenarios. The feasibility of the proposed methodology is illustrated by a numerical case. Triple sensitivity analysis is performed from the perspectives of decision-makers’ risk appetite, expert weight fluctuations, and criteria weight fluctuations. A comparative analysis is implemented to demonstrate the effectiveness and superiority of the proposed methodology. This study provides a novel insight to solve MSWM scenario selection and can extensively be applied to handle other MCGDM problems.

Selecting the Optimal Green Agricultural Products Supplier: A Novel Approach Based on GBWM and PROMETHEE II

Due to the uncertainty of natural factors and a larger global population, the work of supplying sustainable agricultural materials, especially green agricultural products, faces enormous challenges. How to effectively evaluate and select the most desirable green agricultural material supplier is an urgent issue for both agribusiness and government. In this paper, an integrated q-rung orthopair fuzzy (q-ROF) group best–worst method (GBWM) and the PROMETHEE II was introduced to availably solve such issue. Firstly, by taking similarity degree into account to solve incomplete weight information, a novel technique was constructed to determine the experts’ weight reasonably under the q-ROF context. Secondly, to improve consistency for group decision making and obtain a highly reliable selection result, the GBWM was used to derive criteria weights. Then, based on the proposed generalized p-norm knowledge-based score function, the PROMETHEE II was further improved to rank the feasible alternatives. After that, a representative case under the background of green agricultural material supplier selection was investigated in depth. Finally, the detailed comparative technique was conducted to verify the validity and superiority of the improved method.