Picture Fuzzy Environment Research Articles

Multiple-attribute decision-making based on picture fuzzy Archimedean power Maclaurin symmetric mean operators

In this paper, a novel multiple-attribute decision-making method based on a set of Archimedean power Maclaurin symmetric mean operators of picture fuzzy numbers is proposed. The Maclaurin symmetric mean operator, power average operator, and operational rules based on Archimedean T-norm and T-conorm are introduced into picture fuzzy environment to construct the aggregation operators. The formal definitions of the aggregation operators are presented. Their general and specific expressions are established. The properties and special cases of the aggregation operators are, respectively, explored and discussed. Using the presented aggregation operators, a method for solving the multiple-attribute decision-making problems based on picture fuzzy numbers is designed. The method is illustrated through example and experiments and validated by comparisons. The results of the comparisons show that the proposed method is feasible and effective that can provide the generality and flexibility in aggregation of values of attributes and consideration of interactions among attributes and the capability to lower the negative effect of biased attribute values on the result of aggregation.

A new picture fuzzy information measure based on shannon entropy with applications in opinion polls using extended VIKOR–TODIM approach

Picture fuzzy set theory developed by Cuong and Kreinovich is an extension of the fuzzy set theory and intuitionistic fuzzy set theory. In this paper, we proposed a new framework for picture fuzzy entropy from a probabilistic viewpoint. The justification of the proposed axiomatic structure is established by offering a new information measure based on Shannon entropy under picture fuzzy environment and also studied its mathematical properties. Besides, we developed an algorithm for picture fuzzy set with the help of TODIM (a Portuguese acronym for Interactive Multi-Criteria Decision Making) and VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) methods to explain the multi-criteria decision-making (MCDM) problems with picture fuzzy numbers. Finally, two numerical examples are given to verify the proposed approach based on opinion surveys to anticipate the election results and the output is reasonably compared with other MCDM method existing in the literature, what’s more, the viable experiment results are gotten.

Analysis of the effect of medicines over bacteria based on competition graphs with picture fuzzy environment

In this study, the concept of picture fuzzy competition graph along with its two subclasses such as picture fuzzy k-competition graphs and p-competition picture fuzzy graphs are introduced. Picture fuzzy competition graph is one of the generalization of competition graph. Several properties of picture fuzzy competition graphs have been investigated. Some new types of picture fuzzy graphs have been introduced like picture fuzzy open neighborhood graph and picture fuzzy closed neighborhood graph. In addition, the relationship between picture fuzzy k-competition graph and picture fuzzy k-neighborhood graph are established. An application of picture fuzzy competition graph in medical science is presented.

A new integrated approach for engineering characteristic prioritization in quality function deployment

As a customer-driven quality improvement tool, quality function deployment (QFD) can convert customer requirements (CRs) into appropriate engineering characteristics (ECs) in product design and development. However, the conventional QFD method has been criticized for a variety of drawbacks, which limit its efficiency and potential applications. In this study, a new QFD approach integrating picture fuzzy linguistic sets (PFLSs) and the evaluation based on distance from average solution (EDAS) method is proposed for the determination of ranking order of ECs. The PFLSs are utilized to express the judgements of experts on the relationships among CRs and ECs. Then, the EDAS method is extended under picture fuzzy linguistic environment for the prioritization of the ECs identified in QFD. Moreover, a combined weighing method based on technique for order of preference by similarity to ideal solution (TOPSIS) and maximum entropy theory is established to calculate the weights of experts objectively. Finally, a product-service system design is provided to illustrate the effectiveness of the proposed QFD approach. The result shows that the manufacturer should pay more attention to “Meantime before failure”, “Warning feature” and “Quality of product manual”. Feedback from domain experts indicates that the integrated approach being proposed in this paper is more suitable for assessing and prioritizing ECs in QFD.

Some novel aggregation operators for cubic picture fuzzy information: application in multi-attribute decision support problem

Cubic picture fuzzy set (CPFS) is the hybrid version of the interval-valued picture fuzzy set (IPVFS) and the picture fuzzy set (PFS) simultaneously. Clearly, the CPFS contains significantly more information than the general IVPFS and PFS in order to address the vulnerability of decision-making problems. Lamentably, the aggregation operators have not been researched so far on the basis of CPFS. In the techniques of group decision-making, aggregation operators are an important mathematical method to resolve ambiguity in decision-making problems. The present paper proposes few novel geometric mean aggregation operators, in particular, cubic picture fuzzy geometric and cubic picture fuzzy geometric star aggregation operators between cubic picture fuzzy numbers to aggregate the different predispositions of the decision maker. Then, based on the proposed operators in the cubic picture fuzzy environment, we developed a decision-making method and illustrated a numerical example. Finally, in order to demonstrate the supremacy of the proposed technique, classify its comparison with the existing approach. The results showed that the established decision-making technique was superior, accurate and effective.

A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment

The Picture Fuzzy Sets (PFS) are well suitable to capture inconsistent, imprecise and uncertain information in multiple-criteria decision-making problems. This communication is intended to introduce one such information measure defined on PFSs called R-norm picture fuzzy information measure. Moreover, a new set of axioms is proposed as a criteria for picture fuzzy entropy. Besides establishing the validity of proposed R-norm picture fuzzy information measure, some of its major properties are also discussed. In application part, the proposed information measure is applied in predicting the outcome of elections in a poll bound country through opinion polls and to solve an investment problem.

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.

影像模糊环境下基于证据合成的冷链物流服务供应商选择方法

影像模糊环境下基于证据合成的冷链物流服务供应商选择方法

Picture Fuzzy Decision-Making Approach for Sustainable Last-Mile Delivery

In light of the increasing importance of last-mile delivery (LMD) and the associated high costs, air pollution, and logistical challenges, research on sustainable LMD is highly trending and dynamic. The selection of sustainable LMD mode is an emerging problem for decision-makers in the logistics industry. The key question is how to determine the best LMD mode from a set of alternatives under numerous criteria with ambiguous, vague, and uncertain sustainability-related information. This paper aims to provide an advanced decision-making approach for sustainable LMD. Firstly, 20 sustainable LMD mode evaluation criteria are identified. Secondly, picture fuzzy sets (PFSs) are exploited to help decision-makers to more naturally express their preferences by voting. Thirdly, a hybrid picture fuzzy criteria weighting method based on the Direct rating and R-norm entropy is developed to compute the importance of evaluation criteria. Fourthly, a novel picture fuzzy Combined Compromise Solution method is formulated to rank alternative LMD modes. Fifthly, the presented picture fuzzy approach for sustainable LMD is implemented in the real-life decision-making context. The results show that “e-cargo bike” is the best alternative in the Pardubice context. The comparative analysis with three state-of-the-art PFS-based MCDM methods approved the high reliability of the provided approach. The sensitivity analyses of the trade-off parameter and balancing factor confirmed the high robustness of the presented approach. The introduced approach can help decision-makers in the logistics industry to elucidate sustainable LMD mode. It can solve not only the highlighted problem but also other MCDM problems under the picture fuzzy environment.

Multiple-Valued Picture Fuzzy Linguistic Set Based on Generalized Heronian Mean Operators and Their Applications in Multiple Attribute Decision Making

To better express and handle the increasing complicated fuzzy decision making information, we firstly put forward the concept of multiple-valued picture fuzzy linguistic set (MVPFLS), which is motivated by the advantages of hesitant fuzzy set (HFS), linguistic term set (LTS), and picture fuzzy set (PFS). First, the concepts concerning MVPFLS and the multiple-valued picture fuzzy linguistic element (MVPFLE) are proposed. Second, the operating rules of MVPFLEs on account of linguistic scale functions (LSFs) are given, and the compared functions for MVPFLE are also defined. Third, the traditional generalized Heronian mean (HM) operators capturing the correlation among attributes are extended to multiple-valued picture fuzzy linguistic environment, namely, the multiple-valued picture fuzzy linguistic generalized weighted Heronian mean (MVPFLGWHM) aggregating operator and the multiple-valued picture fuzzy linguistic generalized weighted geometric Heronian mean (MVPFLGWGHM) aggregating operator are proposed, their interesting characteristics and some particular instances are also given. Fourth, the method utilizing the proposed aggregating operators to settle multiple attribute decision making (MADM) issues is provided. Eventually, a practical instance is employed to validate the powerfulness of the new approach, and the sensitivity analysis is performed along with comparative analysis.

Similarity Measures of T-Spherical Fuzzy Sets Based on the Cosine Function and Their Applications in Pattern Recognition

In this manuscript, nine similarity measures of T-spherical fuzzy set (TSFS) considering the membership degree, the hesitancy degree, the non-membership degree and the refusal degree are developed according to the cosine function. Besides, the generalizations of existing similarity measures are the similarity measures of TSFS proposed in this paper, which indicates the breadth and novelty of the proposed similarity measures. More importantly, the nine similarity measures of TSFSs are applied to pattern recognition. Then, we make a comparative study, that is, we apply the nine similarity measures of TSFSs developed in this manuscript to picture fuzzy environment, and the results obtained are consistent with the previous results. This application make the problem of building material recognition better solved in the real world. Finally, two numerical examples show the validity of the proposed similarity measure between TSFSs.

Emergency decision making with extended axiomatic design approach under picture fuzzy environment

AbstractTimely and effective emergency decision making (EDM) is the key to control the spread of disasters and reduce the casualties and property losses caused by emergencies. However, due to limited time and insufficient data, it is difficult for decision makers to provide accurate information about emergency incidents. Moreover, the EDM problems become complicated and unstructured requiring the deployment of advanced mathematical techniques to derive the most acceptable response. In this paper, we propose a new EDM approach by using picture fuzzy sets and axiomatic design technique for determining the optimal rescue plan to reduce the damages of emergencies. The contribution of this paper is to apply the picture fuzzy sets to handle the uncertainty and ambiguity of decision makers' assessments on emergency alternatives, apply the picture fuzzy hybrid averaging operator to aggregate decision makers' opinions into a group evaluation matrix and extend the axiomatic design technique to identify the best emergency solution for EDM. Finally, a real example is provided, and the result is compared with existing methods to demonstrate the feasibility and practicability of our proposed EDM approach.

MULTIMOORA based MCDM model for site selection of car sharing station under picture fuzzy environment

The car sharing is an effective supplement to public transportation systems. However, how to select an appropriate site for building a car sharing station is a big challenge. Therefore, in this paper, a novel picture fuzzy multi-criteria decision making (MCDM) model is proposed to solve the site selection problem for car sharing stations. To this end, the definition of picture fuzzy sets is adopted to accurately portray the voting information. Then, a concept of knowledge measure is defined for PFNs and an objective method based on knowledge measure is proposed to derive the weight information of criteria. To rank the candidate sites for car sharing stations, an extended MULTIMOORA method based on novel score function and Borda rule is devised. The proposed MCDM model is applied to solve the site selection for car sharing stations in Bejing. Finally, comparative analyses are given to verify the superiority of the proposed MCDM model.

Picture fuzzy aggregation information based on Einstein operations and their application in decision making

The information aggregation operator plays a key rule in the group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely picture fuzzy Einstein weighted and Einstein ordered weighted operators are proposed in this paper. Some properties of these aggregation operators are discussed in detail. Further, a group decision making problem is illustrated and validated through a numerical example. A comparative analysis of the proposed and existing studies is performed to show the validity of the proposed operators.

Granulation of Hypernetwork Models under the q-Rung Picture Fuzzy Environment

In this paper, we define q-rung picture fuzzy hypergraphs and illustrate the formation of granular structures using q-rung picture fuzzy hypergraphs and level hypergraphs. Further, we define the q-rung picture fuzzy equivalence relation and q-rung picture fuzzy hierarchical quotient space structures. In particular, a q-rung picture fuzzy hypergraph and hypergraph combine a set of granules, and a hierarchical structure is formed corresponding to the series of hypergraphs. The mappings between the q-rung picture fuzzy hypergraphs depict the relationships among granules occurring at different levels. The consequences reveal that the representation of the partition of the universal set is more efficient through q-rung picture fuzzy hypergraphs and the q-rung picture fuzzy equivalence relation. We also present an arithmetic example and comparison analysis to signify the superiority and validity of our proposed model.

Some q-Rung Picture Fuzzy Dombi Hamy Mean Operators with Their Application to Project Assessment

The recently proposed q-rung picture fuzzy set (q-RPFSs) can describe complex fuzzy and uncertain information effectively. The Hamy mean (HM) operator gets good performance in the process of information aggregation due to its ability to capturing the interrelationships among aggregated values. In this study, we extend HM to q-rung picture fuzzy environment, propose novel q-rung picture fuzzy aggregation operators, and demonstrate their application to multi-attribute group decision-making (MAGDM). First of all, on the basis of Dombi t-norm and t-conorm (DTT), we propose novel operational rules of q-rung picture fuzzy numbers (q-RPFNs). Second, we propose some new aggregation operators of q-RPFNs based on the newly-developed operations, i.e., the q-rung picture fuzzy Dombi Hamy mean (q-RPFDHM) operator, the q-rung picture fuzzy Dombi weighted Hamy mean (q-RPFDWHM) operator, the q-rung picture fuzzy Dombi dual Hamy mean (q-RPFDDHM) operator, and the q-rung picture fuzzy Dombi weighted dual Hamy mean (q-RPFDWDHM) operator. Properties of these operators are also discussed. Third, a new q-rung picture fuzzy MAGDM method is proposed with the help of the proposed operators. Finally, a best project selection example is provided to demonstrate the practicality and effectiveness of the new method. The superiorities of the proposed method are illustrated through comparative analysis.

A Novel Description on Edge-Regular q-Rung Picture Fuzzy Graphs with Application

Picture fuzzy model is a generalized structure of intuitionistic fuzzy model in the sense that it not only assigns the membership and nonmembership values in the form of orthopair ( μ , ν ) to an element, but it assigns a triplet ( μ , η , ν ) , where η denotes the neutral degree and the difference π = 1 - ( μ + η + ν ) indicates the degree of refusal. The q-rung picture fuzzy set( q -RPFS) provides a wide formal mathematical sketch in which uncertain and vague conceptual phenomenon can be precisely and rigorously studied because of its distinctive quality of vast representation space of acceptable triplets. This paper discusses some properties including edge regularity, total edge regularity and perfect edge regularity of q-rung picture fuzzy graphs (q-RPFGs). The work introduces and investigates these properties for square q-RPFGs and q-RPF line graphs. Furthermore, this study characterizes how regularity and edge regularity of q-RPFGs structurally relate. In addition, it presents the concept of ego-networks to extract knowledge from large social networks under q-rung picture fuzzy environment with algorithm.

Q-rung picture fuzzy graphs: a creative view on regularity with applications

The q-rung picture fuzzy set model, superior to picture and spherical fuzzy set models, broaden the space of uncertain and vague information due to its outstanding feature of vast depiction space of admissible triplets. In this paper, we introduce the notion of q-rung picture fuzzy graphs and discuss regularity of these graphs. We present geometrical interpretation under q-rung picture fuzzy environment. We illustrate strongly regular, perfectly regular and regular uniform q-rung picture fuzzy graphs. Motivated by some real world situations, we propose the novel concept of m-partite q-rung picture fuzzy graphs with several insightful results on their regularity, named as m-regularity. Moreover, we introduce q-rung picture fuzzy line graphs and develop a necessary condition for regular q-RPFLGs. In addition, we present an application to investigate this broad representation space in graph-theoretical concepts.

Assessment of Enterprise Performance Based on Picture Fuzzy Hamacher Aggregation Operators

In the age of the knowledge-based economy and the rapid development of information technology, enterprise management is facing great challenges and has entered an era of prudent management. Traditional enterprise performance evaluation focuses on the interests of shareholders. Investors take financial data as their base and pay attention to the study of material attraction and the results; if they do not, they cannot adjust to a new economy period. Therefore, enterprise performance reflects the interests of shareholders and business strategists for the needs of stakeholders, which is important for the future of lively competition. With that in mind, aggregation of information is an important research tool that has recently drawn the attention of researchers for information analysis. In this paper, we have developed multiple-attribute decision-making methods for enterprise performance evaluation with picture fuzzy information. We have applied Hamacher aggregation operators such as the picture fuzzy Hamacher weighted averaging (PFHWA) operator and picture fuzzy Hamacher weighted geometric (PFHWG) operator in picture fuzzy environment for the assessment of the best enterprise selection. Finally, we justified the proposed approach with the existing methods for feasibility and effectiveness.

Performance Evaluation of Green Mine Using a Combined Multi-Criteria Decision Making Method With Picture Fuzzy Information

The construction of Green Mine has become an essential policy for the management of mineral resources in China. This study aims to propose a favorable approach to assess the performance of Green Mine. The evaluation criteria are recognized based on the specific characteristics of Green Mine. Considering that some of these criteria could not be mutually compensated, a novel multi-criteria decision making (MCDM) method is presented. It integrates the TODIM (an acronym in Portuguese of interactive and multi-criteria decision-making) method with the elimination and choice translating reality (ELECTRE) method in a picture fuzzy environment. In most existent methods, the evaluation information of Green Mine is described by real numbers. However, in this study, picture fuzzy numbers (PFNs) are first used to express such information to effectively indicate the uncertainty and fuzziness in the evaluation process. Another innovation is that the entropy weights model and the best-worst method (BWM) are combined to determine the comprehensive criteria weights. The practicability and advantages of the proposed method are verified by a case study and a comparative analysis with other methods. In addition, the influences of some parameters are discussed using sensitivity analysis to judge the flexibility and robustness of the proposed method. The results show that the proposed approach is feasible for solving the non-compensatory problems of evaluation criteria and can provide references for the performance evaluation and management of Green Mine.