Evaluation of the product quality of the online shopping platform using t-spherical fuzzy preference relations

2021 ◽  
pp. 1-18
Author(s):  
Choonkil Park ◽  
Shahzaib Ashraf ◽  
Noor Rehman ◽  
Saleem Abdullah ◽  
Muhammad Aslam
Keyword(s):  
Decision Making ◽  
Product Quality ◽  
Fuzzy Sets ◽  
Online Shopping ◽  
Score Function ◽  
Decision Makers ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

As a generalization of Pythagorean fuzzy sets and picture fuzzy sets, spherical fuzzy sets provide decision makers more flexible space in expressing their opinions. Preference relations have received widespread acceptance as an efficient tool in representing decision makers’ preference over alternatives in the decision-making process. In this paper, some new preference relations are investigated based on the spherical fuzzy sets. Firstly, the deficiency of the existing operating laws is elaborated in detail and three cases are described to identify the accuracy of the proposed operating laws in the context of t-spherical fuzzy environment. Also, a novel score function is proposed to obtain the consistent value in ranking of the alternatives. The backbone of this research, t-spherical fuzzy preference relation, consistent t-spherical fuzzy preference relations, incomplete t-spherical fuzzy preference relations, consistent incomplete t-spherical fuzzy preference relations, and acceptable incomplete t-spherical fuzzy preference relations are established. Additionally, some ranking and selection algorithms are established using the proposed novel score function and preference relations to tackle the uncertainty in real-life decision-making problems. Finally, evaluation of the product quality of the online shopping platform problem is demonstrated to show the applicability and reliability of proposed technique.

Decision making based on intuitionistic fuzzy preference relations with additive approximate consistency

2020 ◽  
Vol 39 (3) ◽  
pp. 4041-4058
Author(s):  
Fang Liu ◽  
Xu Tan ◽  
Hui Yang ◽  
Hui Zhao
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Real Interval ◽  
Preference Relations ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Fuzzy Preference Relations ◽  
Novel Concept ◽  
Fuzzy Weights ◽  
Fuzzy Preference

Intuitionistic fuzzy preference relations (IFPRs) have the natural ability to reflect the positive, the negative and the non-determinative judgements of decision makers. A decision making model is proposed by considering the inherent property of IFPRs in this study, where the main novelty comes with the introduction of the concept of additive approximate consistency. First, the consistency definitions of IFPRs are reviewed and the underlying ideas are analyzed. Second, by considering the allocation of the non-determinacy degree of decision makers’ opinions, the novel concept of approximate consistency for IFPRs is proposed. Then the additive approximate consistency of IFPRs is defined and the properties are studied. Third, the priorities of alternatives are derived from IFPRs with additive approximate consistency by considering the effects of the permutations of alternatives and the allocation of the non-determinacy degree. The rankings of alternatives based on real, interval and intuitionistic fuzzy weights are investigated, respectively. Finally, some comparisons are reported by carrying out numerical examples to show the novelty and advantage of the proposed model. It is found that the proposed model can offer various decision schemes due to the allocation of the non-determinacy degree of IFPRs.

scholarly journals Consensus-Based Multi-Person Decision Making with Incomplete Fuzzy Preference Relations Using Product Transitivity

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 185 ◽  
Author(s):  
Atiq-ur Rehman ◽  
Mustanser Hussain ◽  
Adeel Farooq ◽  
Muhammad Akram
Keyword(s):  
Decision Making ◽  
Preference Relation ◽  
Selection Procedure ◽  
Feedback Mechanism ◽  
Decision Makers ◽  
Consensus Process ◽  
Preference Relations ◽  
Priority Weights ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In this paper, a consensus-based method for multi-person decision making (MPDM) using product transitivity with incomplete fuzzy preference relations (IFPRs) is proposed. Additionally, an average aggregation operator has been used at the first level to estimate the missing preference values and construct the complete fuzzy preference relation (FPR). Then it is confirmed to be product consistent by using the transitive closure formula. Following this, weights of decision makers (DMs) are evaluated by merging consistency weights and predefined priority weights (if any). The consistency weights for the DMs are estimated through product consistency investigation of the information provided by each DM. The consensus process determines whether the selection procedure should be initiated or not. The hybrid comprises of a quitting process and feedback mechanism, and is used to enhance the consensus level amongst DMs in case of an inadequate state. The quitting process arises when some DMs decided to leave the course, and is common in MPDM while dealing with a large number of alternatives. The feedback mechanism is the main novelty of the proposed technique which helps the DMs to improve their given preferences based on this consistency. At the end, a numerical example is deliberated to measure the efficiency and applicability of the proposed method after the comparison with some existing models under the same assumptions. The results show that proposed method can offer useful comprehension into the MPDM process.

scholarly journals A new group decision making approach based on incomplete probabilistic dual hesitant fuzzy preference relations

2021 ◽  
Author(s):  
Juan Song ◽  
Zhiwei Ni ◽  
Feifei Jin ◽  
Ping Li ◽  
Wenying Wu
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Membership Degree ◽  
Hesitant Fuzzy Sets ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
The Impact ◽  
Fuzzy Preference

AbstractAs an enhanced version of probabilistic hesitant fuzzy sets and dual hesitant fuzzy sets, probabilistic dual hesitant fuzzy sets (PDHFSs) combine probabilistic information with the membership degree and non-membership degree, which can describe decision making information more reasonably and comprehensively. Based on PDHFSs, this paper investigates the approach to group decision making (GDM) based on incomplete probabilistic dual hesitant fuzzy preference relations (PDHFPRs). First, the definitions of order consistency and multiplicative consistency of PDHFPRs are given. Then, for the problem that decision makers (DMs) cannot provide the reasonable associated probabilities of probabilistic dual hesitant fuzzy elements (PDHFEs), the calculation method of the associated probability is given by using an optimal programming model. Furthermore, the consistency level for PDHFPRs is tested according to the weighted consistency index defined by the risk attitude of DMs. In addition, a convergent iterative algorithm is proposed to enhance the unacceptable consistent PDHFPRs’ consistency level. Finally, a GDM approach with incomplete PDHFPRs is established to obtain the ranking of the alternatives. The availability and rationality of the proposed decision making approach are demonstrated by analyzing the impact factors of haze weather.

A Natural Method for Ranking Objects from Hesitant Fuzzy Preference Relations

2017 ◽  
Vol 16 (06) ◽  
pp. 1611-1646 ◽  
Author(s):  
Jie Tang ◽  
Qingxian An ◽  
Fanyong Meng ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
Group Consensus ◽  
Preference Relations ◽  
Additive Consistency ◽  
Mixed Programming ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

Hesitant fuzzy preference relations (HFPRs) are efficient tools to denoting the decision maker’s judgements that permit the decision makers to compare objects using several values in [0, 1], and the number of elements in different hesitant fuzzy elements may be different. After reviewing the previous researches about decision making with HFPRs, one can find that there are several limitations. To avoid these issues and to guarantee the reasonable ranking order, this paper introduces a new additive consistency concept for HFPRs. Different from the previous consistency concepts, the new concept neither needs to add values into hesitant fuzzy elements nor disregards any information offered by the decision makers. To measure the additive consistency of HFPRs, two 0-1 mixed programming models are constructed. Meanwhile, an additive consistency based 0-1 mixed programming model is established to determining the missing values in incomplete HFPRs that can address the situation where ignored objects exist. Then, an algorithm to obtaining the hesitant fuzzy priority weight vector from (incomplete) HFPRs is provided. Considering group decision making, a new group consensus index is defined, and an interactive approach to improving the group consensus level of individual HFPRs is offered. Furthermore, a probability distance measure between two HFPRs is defined to deriving the weights of the decision makers. According to the additive consistency and consensus analysis, an approach to group decision making with incomplete and inconsistent HFPRs is performed. Finally, two practical numerical examples are provided, and comparison analysis is offered.

scholarly journals A Group Decision-Making Model Based on Regression Method with Hesitant Fuzzy Preference Relations

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Min Xue ◽  
Yifei Du
Keyword(s):  
Decision Making ◽  
Regression Method ◽  
Fuzzy Linear Programming ◽  
Decision Makers ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Decision Making Model ◽  
Supplier Selection Problem ◽  
Original Information ◽  
Fuzzy Preference

In recent years, the decision-making models with hesitant fuzzy preference relations (HFPRs) have received a lot of attention by some researchers. Meanwhile, the previous studies normally adopt normalization technical means to ensure the same number for all elements, which biases original information of decision-makers. In order to overcome this problem, in this paper, the multiplicative consistency of HFPRs is defined and the highest consistent reduced HFPRs are obtained by means of fuzzy linear programming method from given HFPRs. The proposed regression method eliminates the unreasonable information and retains the reasonable information from a given HFPR. In addition, the proposed method overcomes drawbacks of Zhu and Xu’s regression method and is more simple and effective. On account of the obtained reduced HFPRs by the proposed regression method, a GDM model is established. Finally, a supplier selection problem was researched to present the effectiveness and pragmatism of the proposed approach, which proved that the method could offer beneficial insights into the GDM procedure.

scholarly journals Decision support model with Pythagorean fuzzy preference relations and its application in financial early warnings

2021 ◽  
Author(s):  
Wenying Wu ◽  
Zhiwei Ni ◽  
Feifei Jin ◽  
Ying Li ◽  
Juan Song
Keyword(s):  
Decision Making ◽  
Decision Support ◽  
Fuzzy Sets ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Support Model ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference ◽  
Support Model

AbstractPythagorean fuzzy sets (PFSs) retain the advantages of intuitionistic fuzzy sets (IFSs), while PFSs portray 1.57 times more information than IFSs. In addition, Pythagorean fuzzy preference relations (PFPRs), as a generalization of intuitionistic fuzzy preference relations (IFPRs), are more flexible and applicable. The objective of this paper is to propose a novel decision support model for solving group decision-making problems in a Pythagorean fuzzy environment. First, we define the concepts of ordered consistency and multiplicative consistency for PFPRs. Then, aiming at the group decision-making problem of multiple PFPRs, a consistency improving model is constructed to improve the consistency of group preference relations. Later, a consensus reaching model is developed to reach the degree of group consensus. Furthermore, a decision support model with PFPRs is established to derive the normalized weights and output the final result. Holding these features, this paper builds a decision support model with PFPRs based on multiplicative consistency and consensus. Finally, the described method is validated by an example of financial risk management, and it is concluded that the solvency of a company is an important indicator that affects the financial early warning system.

AN APPROACH TO GROUP DECISION MAKING BASED ON INCOMPLETE FUZZY PREFERENCE RELATIONS

2008 ◽  
Vol 16 (01) ◽  
pp. 83-94 ◽  
Author(s):  
YAN-PING JIANG ◽  
ZHI-PING FAN
Keyword(s):  
Decision Making ◽  
Group Decision Making ◽  
Group Decision ◽  
Decision Makers ◽  
New Approach ◽  
Preference Relations ◽  
Fuzzy Preference Relations ◽  
Ranking Of Alternatives ◽  
Collective Ranking ◽  
Fuzzy Preference

In this paper, a new approach is proposed to solve group decision making (GDM) problems where the preference information on alternatives provided by decision makers (DMs) is represented in incomplete fuzzy preference relations. In order to make the collective opinion close each decision maker's opinion as near as possible, an optimization model is constructed to integrate the incomplete fuzzy preference relations and to compute the collective ranking values of alternatives. The ranking of alternatives or selection of the most desirable alternative(s) is directly obtained from the derived collective ranking values. A numerical example is also used to illustrate the applicability of the proposed approach.

scholarly journals Sustainable Decision Making Using a Consensus Model for Consistent Hesitant Fuzzy Preference Relations—Water Allocation Management Case Study

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1957
Author(s):  
Atiq-ur Rehman ◽  
Jarosław Wątróbski ◽  
Shahzad Faizi ◽  
Tabasam Rashid ◽  
Małgorzata Tarczyńska-Łuniewska
Keyword(s):  
Decision Making ◽  
Decision Makers ◽  
Preference Relations ◽  
Priority Weights ◽  
Fuzzy Preference Relations ◽  
Consensus Measure ◽  
Symmetrical Matrices ◽  
Management Case Study ◽  
Fuzzy Preference

This paper presents an improved consensus-based procedure to handle multi-person decision making (MPDM) using hesitant fuzzy preference relations (HFPRs) which are not in normal format. At the first level, we proposed a ukasiewicz transitivity (TL-transitivity) based scheme to get normalized hesitant fuzzy preference relations (NHFPRs), subject to which, a consensus-based model is established. Then, a transitive closure formula is defined to construct TL-consistent HFPRs and creates symmetrical matrices. Following this, consistency analysis is made to estimate the consistency degrees of the information provided by the decision-makers (DMs), and consequently, to assign the consistency weights to them. The final priority weights vector of DMs is calculated after the combination of consistency weights and predefined priority weights (if any). The consensus process concludes whether the aggregation of data and selection of the best alternative should be originated or not. The enhancement mechanism is indulged in improving the consensus measure among the DMs, after introducing an identifier used to locate the weak positions, in case of the poor consensus reached. In the end, a comparative example reflects the applicability and the efficiency of proposed scheme. The results show that the proposed method can offer useful comprehension into the MPDM process.

scholarly journals Triangular hesitant fuzzy preference relations and their applications in multi-criteria group decision-making

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 917-930 ◽  
Author(s):  
Yan Yang ◽  
Junhua Hu ◽  
Yongmei Liu ◽  
Xiaohong Chen
Keyword(s):  
Decision Making ◽  
Group Decision ◽  
Aggregation Operators ◽  
Decision Makers ◽  
Decision Making Process ◽  
Scientific Evaluation ◽  
Preference Relations ◽  
Fuzzy Environment ◽  
Fuzzy Preference Relations ◽  
Fuzzy Preference

In this paper, we present a novel multi-criteria decision-making (MCDM) methodology for assessing several alternatives under the triangular hesitant fuzzy environment. A scientific evaluation and prioritization approach is proposed by solving the MCDM problems with triangular hesitant fuzzy preference relations (THFPRs). Firstly, the concepts of THFPRs are defined, and a series of aggregation operators is introduced and their corresponding properties are discussed. Then, we define the consistency of the THFPRs and propose two methods to measure consistency. Furthermore, we construct an MCDM model using THFPR (MCDM-THFPR) to help decision makers assess and prioritise alternatives in the decision making process. Lastly, the validity and feasibility of the proposed MCDM-THFPR method for the MCDM are verified by a comparison with two previous approaches, along with certain discussions.

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