Interval-valued Pythagorean Fuzzy Environment Research Articles

An investment decision framework for offshore wind-solar-seawater pumped storage power project under interval-valued Pythagorean fuzzy environment

Offshore wind-solar-seawater pumped storage (wind-PV-SPS) power system will be a very competitive offshore new energy project in the future because it can realize the complementarities of wind and photovoltaic resources in the dimensions of time and space, and reduce the waste of resources caused by voltage instability. In order to promote the sustainable development of offshore wind-PV-SPS system, it is particularly important to construct a scientific and reasonable investment decision-making framework. Firstly, a comprehensive criteria system is established in this paper, which includes economy, resource, environment, supporting conditions and market. Secondly, the interval-valued Pythagorean fuzzy set (IVPFS) is introduced to describe the uncertainty and fuzziness of information in the process of investment decision, and the expert weight correction model is established based on the similarity of IVPFSs. At the same time, IVPF-DEMATEL method is utilized to determine the weight of criteria, which takes the interaction between criteria into account. In addition, considering the decision-maker's risk preference psychology, we introduce the GOWUA-HARA operator into the PROMETHEE II method, and extend it to the interval-valued Pythagorean fuzzy environment to choose the optimal investment alternative. Finally, the proposed framework is applied to a case study. Then sensitivity analysis and comparative analysis are carried out to verify its feasibility and robustness.

Enhancing Interval-Valued Pythagorean Fuzzy Decision-Making through Dombi-Based Aggregation Operators

The success of any endeavor or process is heavily contingent on the ability to reconcile and satisfy balance requirements, which are often characterized by symmetry considerations. In practical applications, the primary goal of decision-making processes is to efficiently manage the symmetry or asymmetry that exists within different sources of information. In order to address this challenge, the primary aim of this study is to introduce novel Dombi operation concepts that are formulated within the framework of interval-valued Pythagorean fuzzy aggregation operators. In this study, an updated score function is presented to resolve the deficiency of the current score function in an interval-valued Pythagorean fuzzy environment. The concept of Dombi operations is used to introduce some interval-valued Pythagorean fuzzy aggregation operators, including the interval-valued Pythagorean fuzzy Dombi weighted arithmetic (IVPFDWA) operator, the interval-valued Pythagorean fuzzy Dombi ordered weighted arithmetic (IVPFDOWA) operator, the interval-valued Pythagorean fuzzy Dombi weighted geometric (IVPFDWG) operator, and the interval-valued Pythagorean fuzzy Dombi ordered weighted geometric (IVPFDOWG) operator. Moreover, the study investigates many important properties of these operators that provide new semantic meaning to the evaluation. In addition, the suggested score function and newly derived interval-valued Pythagorean fuzzy Dombi aggregation (IVPFDA) operators are successfully employed to select a subject expert in a certain institution. The proposed approach is demonstrated to be successful through empirical validation. Lastly, a comparative study is conducted to demonstrate the validity and applicability of the suggested approaches in comparison with current techniques. This research contributes to the ongoing efforts to advance the field of evaluation and decision-making by providing novel and effective tools and techniques.

Interval-valued Pythagorean fuzzy multi-criteria decision-making method based on the set pair analysis theory and Choquet integral

This paper proposes a novel fuzzy multi-criteria decision-making method based on an improved score function of connection numbers and Choquet integral under interval-valued Pythagorean fuzzy environment. To do so, we first introduce a method to convert interval-valued Pythagorean fuzzy numbers into connection numbers based on the set pair analysis theory. Then an improved score function of connection numbers is proposed to make the ranking order of connection numbers more in line with reality in multi-criteria decision-making process. In addition, some properties of the proposed score function of connection numbers and some examples have been given to illustrate the advantages of conversion method proposed in the paper. Then, considering interactions among different criteria, we propose a fuzzy multi-criteria decision-making approach based on set pair analysis and Choquet integral under interval-valued Pythagorean fuzzy environment. Finally, a case of online learning satisfaction survey and a brief comparative analysis with other existing approaches are studied to show that the proposed method is simple,convenient and easy to implement. Comparing with previous studies, the method in this paper, from a new perspective, effectively deals with multi-criteria decision-making problems that the alternatives cannot be reasonably ranked in the decision-making process under interval-valued Pythagorean fuzzy environment.

An improved $$A^*$$ search algorithm for the shortest path under interval-valued Pythagorean fuzzy environment

An improved $$A^*$$ search algorithm for the shortest path under interval-valued Pythagorean fuzzy environment

Site selection framework of rail transit photovoltaic power station under interval-valued Pythagorean fuzzy environment

Different from centralized and large-scale photovoltaic power station, the sites selection of rail transit photovoltaic power station (RTPPS) concerns more on sustainability rather than profit and there is a lack of selection index system for RTPPS sites selection. Besides that, the decision model cannot deal with the uncertainty, the independence assumption problem and the solving problem of multi-objective programming (MOP) model in scenarios with more goals. The contributions of this paper are as follows: ① a selection index system of RTPPS site selection is established based on RTPPS’s characteristics to provide the scientific decision-making direction; ② the interval-valued Pythagorean fuzzy number (IVPFN) is used to deal with uncertainty in decision information; ③ the fuzzy measure were used to avoid the assumption of independence, which make the decision model is more in line with the reality; ④ the IVPFN-TOPSIS was used to decrease the number of goals, so the MOP model can be solved in scenarios with more goals. The effectiveness of this framework is proved by a China case study. According to the sensitivity analysis and comparative analysis, the decision result calculated by the proposed decision model has good robustness and the site selection framework can better serve the enterprise.

Correction to: Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment

Correction to: Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment

Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment

Multiple attribute group decision-making based on generalized aggregation operators under linguistic interval-valued Pythagorean fuzzy environment

Group decision making by a last aggregation approach under interval-valued Pythagorean fuzzy environment for sustainable project decision

Interval-valued Pythagorean fuzzy sets (IVPFSs) as enhanced type of Pythagorean fuzzy sets (PFSs) improve the expression of the degrees of membership, non-membership and hesitancy in comparison with intuitionistic fuzzy sets (IFSs). In this paper, to use the advantages of IVPFSs a new group decision-making method is introduced based on linear assignment method (LAM). In this approach, subjective and objective weights of criteria are taken into account. Moreover, the method applies a new ranking method for IVPFSs. To avoid the shortcomings of first aggregation methods, the introduced decision-making approach involves a last aggregation approach. Finally, the method is used in a case study of sustainable project evaluation in order to depict the applicability of this method.

A Novel Two-Stage Multi-Criteria Decision-Making Method Based on Interval-Valued Pythagorean Fuzzy Aggregation Operators with Self-Confidence Levels

Due to insufficient information in multi-criteria decision-making (MCDM) problems, the decision values given by experts are often fuzzy and uncertain. As an extension of Pythagorean fuzzy set (PFS), interval-valued Pythagorean fuzzy (IPF) set is a more effective and powerful tool to handle fuzzy information in decision problems. But, there are two key issues that needed to be solved: weights of experts in the IPF environment and IPF aggregation operators. For these issues, a two-stage MCDM method is constructed in the IPF environment. In the first stage, a novel method for determining the weights of experts is proposed by introducing IPF set (IPFS) into social networks. To do that, the concepts of trust function (TF) and trust score (TS) in the IPF environment are defined to obtain the objective weights of experts. Meanwhile, the subjective weights of experts are obtained from the number of experts. Afterward, the objective weight and subjective weight of each expert are combined to derive the weight of each expert. In the second stage, a novel weighted sum model (WSM) with novel IPF aggregation operators is constructed to rank alternatives. Considering the psychological behavior of experts, that is, self-confidence level, four IPF aggregation operators with self-confidence levels are defined, namely, the self-confidence interval-valued Pythagorean fuzzy weighted averaging (SC-IPFWA) and ordered weighted averaging (SC-IPFOWA) operator, the self-confidence interval-valued Pythagorean fuzzy weighted geometric (SC-IPFWG) and ordered weighted geometric (SC-IPFOWG) operator. Finally, a numerical case is used to verify the effectiveness of the proposed two-stage MCDM method.

A novel approach to emergency risk assessment using FMEA with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment

PurposeThe application of the traditional failure mode and effects analysis (FMEA) technique has been widely questioned in evaluation information, risk factor weights and robustness of results. This paper develops a novel FMEA framework with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment to solve these problems.Design/methodology/approachThis paper introduces innovatively interval-value Pythagorean fuzzy weighted averaging (IVPFWA) operator, Tchebycheff metric distance and interval-value Pythagorean fuzzy weighted geometric (IVPFWG) operator into the MULTIMOORA submethods to obtain the risk ranking order for emergencies. Finally, an illustrative case is provided to demonstrate the practicality and feasibility of the novel fuzzy FMEA framework.FindingsThe feasibility and validity of the proposed method are verified by comparing with the existing methods. The calculation results indicate that the proposed method is more consistent with the actual situation of project and has more reference value.Practical implicationsThe research results can provide supporting information for risk management decisions and offer decision-making basis for formulation of the follow-up emergency control and disposal scheme, which has certain guiding significance for the practical popularization and application of risk management strategies in the infrastructure projects.Originality/valueA novel approach using FMEA with extended MULTIMOORA method is developed under IVPF environment, which considers weights of risk factors and experts. The method proposed has significantly improved the integrity of information in expert evaluation and the robustness of results.

Hydrogen production facility location selection for Black Sea using entropy based TOPSIS under IVPF environment

Parallel with the globally increment in energy demand, governments and responsible authorities’ environmental awareness increases and they have been taking several preventions not to harm environment while energy demand is satisfied. For this purpose decision makers turn their faces to satisfy energy demand via renewable energy sources such as wind, wave, solar, hydro, biomass, hydrogen etc. Before this awareness human was satisfying energy demand via nonrenewable energy sources such as natural gas, coal etc. Even though not being one of these energy sources, hydrogen energy is a primary energy carrying form which is known one of the energy carrier [1]. This study aims to select the most appropriate site in the northern of Turkey for establishing a hydrogen energy hydrogen-sulphide (H2S) decomposition plant. Based on the researches, Black Sea is determined as one of the richest water to get H2S from. Since selecting the facility location for hydrogen energy production plant requires strategical decisions, Multi Criteria Decision Making (MCDM), as a powerful and efficient tool, is preferred in this study. Accordingly, Entropy and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methodologies are integrated and applied under Interval Valued Pythagorean Fuzzy (IVPF) environment to deal with uncertain information better. The developed method is shown to be useful and effective in terms of applicability and ease of usage. As a result, the best suitable location is determined and sensitivity analysis is conducted to analyze the dynamics of the developed methodology.

Interval-Valued Pythagorean Normal Fuzzy Information Aggregation Operators for Multi-Attribute Decision Making

The interval-valued Pythagorean fuzzy (IVPF) sets, describing the membership and non-membership degrees from interval values, can address uncertain information, while the normal fuzzy number (NFN) can depict normal distribution information in anthropogenic activity and natural environment. By combining the advantages of both operations, in this study, we proposed the interval-valued Pythagorean normal fuzzy (IVPNF) sets by introducing the NFN into IVPF environment. Firstly, we defined the conception, the operational laws, score function, accuracy function of IVPNF sets. Secondly, we presented four information aggregation operators to aggregate IVPNF information, including the IVPNF weighted averaging (IVPNFWA) operator, IVPNF weighted geometric (IVPNFWG) operator, the generalized IVPNFWA operator, and the generalized IVPNFWG operator. In addition, we analyzed some desirable properties of monotonicity, commutativity, and idempotency for the proposed four operators. Finally, a numerical example on multi-attribute decision-making problem is given to verify the practicality of the proposed operators, and the comparative and sensitive analysis are used to show the effectiveness and flexibility of our proposed approach.

Interval-valued pythagorean fuzzy power average-based MULTIMOORA method for multi-criteria decision-making

ABSTRACT In the multi-criteria decision-making (MCDM), multi-objective optimisation by ratio analysis (MOORA) plus the full multiplicative form (MULTIMOORA) are a useful method, which has the flexibility and robustness properties. The aim of this paper is to present a more robust method of MULTIMOORA to solve the MCDM evaluations with interval-valued Pythagorean fuzzy sets (IVPFSs). More specifically, considering the mutual support relationship among the input arguments, we firstly extend the power average (PA) and power geometric (PG) operators to accommodate the interval-valued Pythagorean fuzzy environment. For this, we propose four aggregation operators, including the interval-valued Pythagorean fuzzy power average (IVPFPA), the weighted interval-valued Pythagorean fuzzy power average (WIVPFPA), the interval-valued Pythagorean fuzzy power geometric (IVPFPG) and the weighted interval-valued Pythagorean fuzzy power geometric (WIVPFPG). With the aid of WIVPFPA and WIVPFPG, we further put forward a new robustness of the ranking method, i.e., the interval-valued Pythagorean fuzzy power average-based MULTIMOORA (IVPFPA-MULTIMOORA). Due to the availability and vast diversity among open-source electronic health record (EHR) systems, choosing an appropriate system is a challenge for many health-care institutions under the interval-valued Pythagorean fuzzy environment. Based on these above-mentioned research findings, we successfully utilise the IVPFPA-MULTIMOORA method to solve the selection problem of hospital open-source EHRs systems for MedLab in Ghana. Meanwhile, the effectiveness of the proposed method is verified by some comparative analyses.

A new decision approach for the sustainable transport investment selection based on the generalized entropy and knowledge measure under an interval-valued Pythagorean fuzzy environment

Finding the most suitable transport project is one of the most important tasks in transport planning. This task gets more complicated as the sustainable criteria get involved in the process. In this paper, a new multi-criteria group decision-making method with unknown expert and attribute weights is proposed to address the sustainable transport investment selection problem. To make the method more powerful in dealing with uncertain elements, an Interval-Valued Pythagorean Fuzzy (IVPF) set is used as an attractive and useful tool to handle uncertainty. First, a generalized entropy measure under an IVPF environment is introduced, which enables the method to determine the fuzziness of the attribute values, which are expressed by Interval-Valued Pythagorean Fuzzy Numbers (IVPFNs). To determine the fuzziness of IVPFNs with identical membership and non-membership degrees, a generalized knowledge measure of the IVPFNs is also introduced. Based on this measure and considering the deviation between attribute assessments, a new optimization model is presented to obtain unknown attribute weights. In addition, based on the extension of the VIKOR method, a new algorithm is presented to determine the unknown expert weights. Finally, a real case study is considered to show the efficiency of the proposed methods.

A Pearson-like correlation-based TOPSIS method with interval-valued Pythagorean fuzzy uncertainty and its application to multiple criteria decision analysis of stroke rehabilitation treatments

This paper extends one of the most extensively used multiple criteria decision analysis (MCDA) methods, the technique for order preference by similarity to ideal solutions (TOPSIS), to adapt to highly complicated uncertain environments based on interval-valued Pythagorean fuzzy (IVPF) sets. In contrast to classical TOPSIS methods, this paper develops a novel concept of Pearson-like IVPF correlation coefficients instead of distance measures to not only construct a useful and effective association measure between two IVPF characteristics but also depict the outranking relationship of IVPF information. Moreover, this paper proposes the (weighted) IVPF correlation-based closeness coefficients to establish a Pearson-like correlation-based TOPSIS model to manage MCDA problems within the IVPF environment. In particular, there is a definite improvement in determining the closeness coefficient required in the TOPSIS procedure. This paper considers anchored judgments with respect to the positive- and negative-ideal IVPF solutions and provides new approach- and avoidance-oriented definitions for the IVPF correlation-based closeness coefficient, which is entirely different from the traditional definition of relative closeness in TOPSIS. Furthermore, this paper proposes a comprehensive IVPF correlation-based closeness index to balance the consequences between ultra-approach orientation and ultra-avoidance orientation and acquire the ultimate compromise solution for decision support and aid. The feasibility and practicability of the developed methodology are illustrated by a practical MCDA problem of rehabilitation treatment for hospitalized patients with acute stroke. The application results, along with experimentations and comparative analyses, demonstrate that the developed methods are rational and effective.

Green Supplier Selection Based on DEA Model in Interval-Valued Pythagorean Fuzzy Environment

The green supplier selection has gradually become a hot topic around the world. To achieve the purpose of optimal decision-making, it is of great importance to process the imprecise and ambiguous information that may exist in the evaluation and selection of green suppliers. In the present article, first, converting the imprecise and ambiguous information into interval-valued Pythagorean fuzzy numbers (IVPFNs) through the Likert scale. Then, using the interval-valued Pythagorean fuzzy weighted average (IVPFWA) operator and multiplicative theory to introduce the IVPFNs into the non-radial SE-BCC model of Data Envelopment Analysis (DEA), we developed the DEA model in the interval-valued Pythagorean fuzzy environment. Later, ranking all decision-making units (DMUs) to be evaluated and selecting the best of them. Moreover, The proposed model can not only deal with the case where the quantitative indicators are interval-valued numbers, but also solve the problem of qualitative analysis in the evaluation process. Finally, a numerical example of green suppliers selection is provided to demonstrate the feasibility and usefulness of the model.

A group decision making sustainable supplier selection approach using extended TOPSIS under interval-valued Pythagorean fuzzy environment

Due to the increasing awareness of environmental and social issues, sustainable supplier selection becomes an important problem. The aim of this paper is to develop a novel group decision making sustainable supplier selection approach using extended Techniques for Order Preferences by Similarity to Ideal Solution (TOPSIS) under interval-valued Pythagorean fuzzy environment. Sustainable supplier selection often involves uncertain information due to the subjective nature of human judgments, and the interval-valued Pythagorean fuzzy set (IVPFS) has great ability to address strong fuzziness, ambiguity and inexactness during the decision-making process. The first contribution of this research is to use the IVPFS to capture the uncertain information of decision makers. Moreover, sustainable supplier selection often involves multiple decision makers from different groups. The second contribution of this research is to develop a group decision making approach for sustainable supplier selection. TOPSIS is the most commonly used technique in sustainable supplier selection. The third contribution of this research is to propose an extended TOPSIS method by integrating distance and similarity between alternatives concurrently to evaluate performances of suppliers. In this research, the group decision making approach and extended TOPSIS method is also extended to IVPFSs. Finally, experiments are conducted to verify the feasibility and efficiency of the proposed sustainable supplier selection approach. Experiments results show that the proposed approach is effective and efficient to help decision makers to select optimal sustainable suppliers. Therefore, the proposed approach can be applied by managers to evaluate and determine appropriate suppliers in sustainable supplier selection process.

Dijkstra algorithm for shortest path problem under interval-valued Pythagorean fuzzy environment

Pythagorean fuzzy set as an extension of fuzzy set has been presented to handle the uncertainty in real-world decision-making problems. In this work, we formulate a shortest path (SP) problem in an interval-valued Pythagorean fuzzy environment. Here, the costs related to arcs are taken in the form of interval-valued Pythagorean fuzzy numbers (IVPFNs). The main contributions of this paper are fourfold: (1) the interval-valued Pythagorean fuzzy optimality conditions in directed networks are described to design of solution algorithm. (2) To do this, an improved score function is used to compare the costs between different paths with their arc costs represented by IVPFNs. (3) Based on these optimality conditions and the improved score function, the traditional Dijkstra algorithm is extended to find the cost of interval-valued Pythagorean fuzzy SP (IVPFSP) and corresponding IVPFSP. (4) Finally, a small sized telecommunication network is provided to illustrate the potential application of the proposed method.

The linear assignment method for multicriteria group decision making based on interval-valued Pythagorean fuzzy Bonferroni mean

The interval-valued Pythagorean fuzzy sets can easily handle uncertain information more flexibly in the process of decision making. Considering the interrelationship among the input arguments, we extend the Bonferroni mean and the geometric Bonferroni mean to the interval-valued Pythagorean fuzzy environment and solve its practical application problems. First, we develop the interval-valued Pythagorean fuzzy Bonferroni mean and the weighted interval-valued Pythagorean fuzzy Bonferroni mean (WIVPFBM) operators. The properties of these aggregation operators are investigated. Then, we also develop the interval-valued Pythagorean fuzzy geometric Bonferroni mean and the weighted interval-valued Pythagorean fuzzy geometric Bonferroni mean (WIVPFGBM) operators and analyze their properties. Third, we utilize the WIVPFBM and WIVPFGBM operators to fuse the information in the interval-valued Pythagorean fuzzy multicriteria group decision making (IVPFMCGDM) problem, which can obtain much more information in the process of group decision making. With the aid of the linear assignment method, we present its extension and further design a new algorithm for the application of IVPFMCGDM. Finally, an example is given to elaborate our proposed algorithm and validate its excellent performance.

Failure Mode and Effects Analysis Considering Consensus and Preferences Interdependence

Failure mode and effects analysis is an effective and powerful risk evaluation technique in the field of risk management, and it has been extensively used in various industries for identifying and decreasing known and potential failure modes in systems, processes, products, and services. Traditionally, a risk priority number is applied to capture the ranking order of failure modes in failure mode and effects analysis. However, this method has several drawbacks and deficiencies, which need to be improved for enhancing its application capability. For instance, this method ignores the consensus-reaching process and the correlations among the experts’ preferences. Therefore, the aim of this study was to present a new risk priority method to determine the risk priority of failure modes under an interval-valued Pythagorean fuzzy environment, which combines the extended Geometric Bonferroni mean operator, a consensus-reaching process, and an improved Multi-Attributive Border Approximation area Comparison approach. Finally, a case study concerning product development is described to demonstrate the feasibility and effectiveness of the proposed method. The results show that the risk priority of failure modes obtained by the proposed method is more reasonable in practical application compared with other failure mode and effects analysis methods.