Interval-valued Hesitant Fuzzy Information Research Articles

Cloud model-based multi-stage multi-attribute decision-making method under probabilistic interval-valued hesitant fuzzy environment

Due to the complexity of multi-stage multi-attribute decision-making (MADM) problems, decision-makers (DMs) frequently provide incomplete and hesitant evaluation information. A crucial difficulty in multi-stage MADM problems is how to make a valid decision under uncertain environment. Firstly, we employ probabilistic interval-valued hesitant fuzzy set (PIVHFS) to characterize the hesitancy of DMs, and then build an optimization model to obtain the probability information based on the score function, deviation function of probabilistic interval-valued hesitant fuzzy element (PIVHFE) and information entropy. Secondly, cloud model is introduced to optimize the calculation process and an optimization model is developed to realize the transformation from PIVHFS to cloud model. Thirdly, a method to solve the stage weights is proposed by synthesizing the within-stage and between-stage decision information. Similarly, the attribute weights are obtained by constructing a mathematical model based on the within-attribute and between-attribute decision information. The noted method can utilize decision information to its fullest. Then, the regret theory is applied to a multi-stage MADM problem. Finally, the applicability and effectiveness of the method are illustrated through case analysis and methods comparison.

Bilateral Matching Decision Making of Partners of Manufacturing Enterprises Based on BMIHFIBPT Integration Methods: Evaluation Criteria of Organizational Quality-Specific Immunity

This study aims to examine how the bilateral matching decision making of manufacturing enterprises that are seeking partners in the manufacturing supply chain can be improved by taking into consideration evaluation criteria for organizational quality-specific immunity. This study constructs an evaluation indicator system to measure organizational quality-specific immunity based on immune theory. The system’s evaluation criteria are based on the key components of organizational quality-specific immunity. We also construct bilateral matching evaluation and decision-making models using interval-valued hesitant fuzzy information and bidirectional projection technology (BMIHFIBPT). The interval-valued bilateral fuzzy bidirectional projection technology is applied to solve a combination satisfaction and matching optimization model. Empirical analysis is carried out to assess both the supply and demand sides of representative manufacturing enterprises in the manufacturing supply chain, match the main supply and demand bodies of two subjects, and help manufacturing enterprises select the optimal cooperation partners. The empirical analysis results indicate that the bilateral matching evaluation and decision-making models based on BMIHFIBPT can overcome the lack of information to some extent and help solve interval-valued hesitant fuzzy decision-making problems. In turn, the models can provide a basis for manufacturing enterprises to effectively select the best cooperation partners and conduct bilateral matching decision making in the manufacturing supply chain area that supports organizational quality-specific immunity.

Dynamic updating approximations approach to multi-granulation interval-valued hesitant fuzzy information systems with time-evolving attributes

Since data is furious growth and rapid alteration, it is completely imperative to monitor and update real-time data promptly. There is no denying that calculating approximations by means of classical approach is pretty time-consuming for an information system with attribute sets varying constantly. Whereas, dynamic updating approximations method takes full advantage of previous knowledge instead of calculating from scratch, which saves a large amount of time. Enlightened by this idea, our work focuses on researching mechanisms of dynamic updating approximations caused by the variation of attributes in multi-granulation interval-valued hesitant fuzzy information system (MG-IVHFIS). To begin with, the average dominance relation which reduces the restriction of universal dominance relation in reality is recommended, then an average dominance rough set based on this relation is established in MG-IVHFIS. Additionally, we study four mechanisms for updating approximations from the perspective of optimism and pessimism in dynamic MG-IVHFIS when some attributes are removed or inserted, and improve corresponding dynamic algorithms. Furthermore, we test ten datasets from UCI and design contrastive experiments to assess dynamic and classical algorithms. In terms of computational efficiency, experimental results show that the dynamic method clearly precedes the classical method for handling with dynamic attribute sets in MG-IVHFIS.

Models for MADM with hesitant interval-valued fuzzy information under uncertain environment

This paper is a research of interval-valued fuzzy and Muirhead Mean algorithms. We deduced new algorithms named as hesitant interval-valued fuzzy Muirhead Mean (HIVFMM) and hesitant interval-valued fuzzy Muirhead Mean (HIVFWMM) with Muirhead Mean algorithms based on Hesitant interval-valued fuzzy set (HIVFS). Firstly, we introduced some concepts and operation laws of HIVFS and the formula form of MM, then we combined them both and gave the proof process of properties and theorems, a mathematic model applying to MADM and a numerical example was given to illustrate the effectively and practically.

A probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory

With the increasing complexity of the decision environment, the fuzzy theory has attracted the extensive attention of scholars. Probabilistic interval-valued hesitant fuzzy set, as a complex ambiguous information representation tool, dedicates to depict uncertain information as complete as possible. Thus, this paper proposes a probabilistic interval-valued hesitant fuzzy gained and lost dominance score method based on regret theory and interval evidential reasoning approach. In view of the uncertainties in evaluations, the interval evidential reasoning approach is an effective tool to deal with the fuzziness and ignorance, which is first applied in probabilistic interval-valued hesitant fuzzy information in this paper. Besides, an interval projection measure is proposed to consider both distance and direction simultaneously, so as to avoid the problem of information losses in the decision process. On this basis, a novel regret-rejoice function is developed. Then, an extended gained and lost dominance score method based on regret theory and interval evidential reasoning approach is developed, which considers the regret avoidance behavior of experts. Finally, a case study on supplier selection of epidemic prevention products is applied to elucidate and illustrate the application of the proposed method in this paper.

Frank Aggregation Operators and Their Application to Probabilistic Hesitant Fuzzy Multiple Attribute Decision-Making

The fuzzy aggregation information plays an important role in the group decision support system under the interval-valued hesitant fuzzy information and interval-valued probabilistic hesitant fuzzy information. Therefore, in this paper, we develop a new approach of the interval-valued hesitant fuzzy Frank aggregation (IVHFFA) and interval-valued probabilistic hesitant fuzzy aggregation (IVPHFFA) operators. First, we define some operational laws of IVHEs and IVPHFEs by using Frank t-norm and t-conorm. Furthermore, we develop a series of IVHFFA and IVPHFFA operators based on these operational laws under the IVHF and IVPHF information. Also, discuss some fundamental properties and relations of the proposed aggregation operators for IVHF and IVPHF information. In order to implement the proposed aggregation operators of IVHF and IVPHF information in group decision-making problem, we construct general algorithms for multi-attribute group decision-making problem based on the proposed IVHFFA and IVPHFFA. Finally, from the comparative and sensitivity analysis, the proposed fuzzy decision-making model is more effective and reliable as compared with existing method.

On weakly prioritized multicriteria decision analysis with interval-valued hesitant fuzzy information

On weakly prioritized multicriteria decision analysis with interval-valued hesitant fuzzy information

Reconfiguring IVHF-TOPSIS decision making method with parameterized reference solutions and a novel distance for corporate carbon performance evaluation

The hesitant and imprecise uncertainties widely exist in real decision-making problems. For solving the class of problems, this work is aimed at reconfiguring a novel method under the TOPSIS framework to solve the general uncertain decision problem that with both the ratings of alternatives and weights of criteria represented by interval-valued hesitant fuzzy (IVHF) information. Three novelties are proposed to support the reconfigured method. First, a parameterized approach for generating apt positive and negative IVHF reference solutions is proposed, which permits decision makers (DMs) to express their different aspiration strengths for fitting complex and uncertain decision scenarios and situations. Second, a novel distance for IVHF elements is constructed based on the modification of Wave-Hedges measurement to address the defects of the previous hesitant distances and to measure the separations of alternatives in TOPSIS. Third, a nine-step solution procedure of IVHF-TOSPSIS method is reconfigured to solve effectively the general problem that the ratings and weights are expressed with IVHF information. Finally, the reconfigured method is exploited to settle the carbon performance evaluation of industrial firms and some sensitivity and comparison analyses are conducted to validate the proposed method.

Research on the construction noise appraisal models with hesitant interval-valued fuzzy information

In this paper, we utilize induced Choquet ordered averaging operator to develop the induced hesitant interval-valued fuzzy choquet ordered averaging (IHIVFCOA) operator. Then, we have utilized this operator to develop the approach to solve the hesita

Weighted Interval-Valued Hesitant Fuzzy Sets and Its Application in Group Decision Making

The interval-valued hesitant fuzzy set, which allows decision makers to use several interval numbers to assess a variable, is a useful tool to deal with situations in which people are hesitant in providing their interval-valued assessments. In this paper, we introduce the concept of weighted interval-valued hesitant fuzzy set, in which different weights are designed to these possible membership degrees, and the weights indicate that the decision maker has different confidence in giving every possible assessment of the membership degree. Then we define some basic operations such as union, intersection, complement, multiplication and power operation of weighted interval-valued hesitant fuzzy sets and weighted interval-valued hesitant fuzzy elements, discuss their operation properties, and propose the score function of the weighted interval-valued hesitant fuzzy element to compare two weighted hesitant fuzzy elements. Furthermore, we introduce the concept of hesitance degree of weighted interval-valued hesitant fuzzy element, present four aggregation operators such as the weighted interval-valued hesitant fuzzy-weighted averaging operator, the weighted interval-valued hesitant fuzzy-weighted geometric operator, the generalized weighted interval-valued hesitant fuzzy-weighted averaging operator and the generalized weighted interval-valued hesitant fuzzy-weighted geometric operator to aggregate weighted interval-valued hesitant fuzzy information, and build the mathematical model of multi-criteria group decision making based on the expert weights (known and unknown). Finally, a numerical example is given to illustrate the effectiveness and feasibility of our proposed method.

Novel decision-making approach based on hesitant fuzzy sets and graph theory

Hesitant fuzzy set is a powerful and effective tool to express uncertain information in multi-attribute decision-making (MADM) process, as it permits the membership degree of an element to a set represented by several possible values in [0,1]. In this paper, we develop a new decision-making approach based on graph theory to deal with the MADM problems, in which the decision information is expressed by hesitant fuzzy elements. Meanwhile, we generalize this approach to make it suitable for processing interval-valued hesitant fuzzy and hesitant triangular fuzzy information. Moreover, we utilize the numerical examples concerning the energy project selection and software evaluation to show the detailed implementation procedure and reliability of our method in solving MADM problems under hesitant fuzzy, interval-valued hesitant fuzzy and hesitant triangular fuzzy environment.

Fusions and preference relations based on probabilistic interval-valued hesitant fuzzy information in group decision making

This paper proposes probabilistic interval-valued hesitant fuzzy set (P-IVHFS) by integrating the probability distribution into IVHFS. The concept can make some vital but seemingly repetitive information [such as the same memberships of interval forms given by different decision makers (DMs)], which is an important basis for decision-making rather than being discarded. Moreover, some operations and aggregation operators of probabilistic interval-valued hesitant fuzzy elements (P-IVHFEs) and probabilistic interval-valued hesitant fuzzy preference relation (P-IVHFPR) are put forward, based on which, a decision-making model is proposed. It can keep almost all information given by the DMs so that the results calculated with the model will be much more reliable than those calculated with approaches based on IVHFSs. Finally, a practical case concerning the evaluation of intelligent transportation systems is given to verify the advantages of the proposed decision-making approach based on P-IVHFPRs.

Probabilistic Interval-Valued Hesitant Fuzzy Information Aggregation Operators and Their Application to Multi-Attribute Decision Making

Based on the probabilistic interval-valued hesitant fuzzy information aggregation operators, this paper investigates a novel multi-attribute group decision making (MAGDM) model to address the serious loss of information in a hesitant fuzzy information environment. Firstly, the definition of probabilistic interval-valued hesitant fuzzy set will be introduced, and then, using Archimedean norm, some new probabilistic interval-valued hesitant fuzzy operations are defined. Secondly, based on these operations, the generalized probabilistic interval-valued hesitant fuzzy ordered weighted averaging (GPIVHFOWA) operator, and the generalized probabilistic interval-valued hesitant fuzzy ordered weighted geometric (GPIVHFOWG) operator are proposed, and their desirable properties are discussed. We further study their common forms and analyze the relationship among these proposed operators. Finally, a new probabilistic interval-valued hesitant fuzzy MAGDM model is constructed, and the feasibility and effectiveness of the proposed model are verified by using an example of supplier selection.

Solving group decision-making problems in manufacturing systems by an uncertain compromise ranking method

The purpose of this paper is to introduce a new modified compromise ranking method (VIKOR), known as sorting the possible alternatives and determining the compromise solution under interval-valued hesitant fuzzy sets (IVHFSs) for solving group decision-making problems in manufacturing systems. By using numerical measure and crisp data, the decision making is complex in real-life situations because the decision makers (DMs)' judgments are usually hesitant and vague. A more applicable and realistic approach based on interval-valued hesitant fuzzy elements (variables) is presented and defined as the inputs to the presented VIKOR method. The proposed interval-valued hesitant fuzzy modified VIKOR (IVHF-MVIKOR) method utilises the membership degrees to demonstrate the degrees of satisfiability for each possible alternative according to selected criteria for the manufacturing assessments. Then, a new index for relative importance of the DMs is introduced with the extended fuzzy sets. Also, some operations in the proposed IVHF-MVIKOR method are developed for manufacturing decision problems. Then, new indexes are presented with interval-valued hesitant fuzzy hamming distance measure for the purpose of rankings. Finally, by presenting a practical example in flexible manufacturing systems, the performance of IVHF-MVIKOR method is evaluated and compared with two well-known methods under interval-valued hesitant fuzzy information.

Solving group decision-making problems in manufacturing systems by an uncertain compromise ranking method

The purpose of this paper is to introduce a new modified compromise ranking method (VIKOR), known as sorting the possible alternatives and determining the compromise solution under interval-valued hesitant fuzzy sets (IVHFSs) for solving group decision-making problems in manufacturing systems. By using numerical measure and crisp data, the decision making is complex in real-life situations because the decision makers (DMs)' judgments are usually hesitant and vague. A more applicable and realistic approach based on interval-valued hesitant fuzzy elements (variables) is presented and defined as the inputs to the presented VIKOR method. The proposed interval-valued hesitant fuzzy modified VIKOR (IVHF-MVIKOR) method utilises the membership degrees to demonstrate the degrees of satisfiability for each possible alternative according to selected criteria for the manufacturing assessments. Then, a new index for relative importance of the DMs is introduced with the extended fuzzy sets. Also, some operations in the proposed IVHF-MVIKOR method are developed for manufacturing decision problems. Then, new indexes are presented with interval-valued hesitant fuzzy hamming distance measure for the purpose of rankings. Finally, by presenting a practical example in flexible manufacturing systems, the performance of IVHF-MVIKOR method is evaluated and compared with two well-known methods under interval-valued hesitant fuzzy information.

Grey relational projection method for multiple attribute decision making with interval-valued dual hesitant fuzzy information

Grey relational projection method for multiple attribute decision making with interval-valued dual hesitant fuzzy information

Interval-Valued Hesitant Fuzzy Multiattribute Group Decision Making Based on Improved Hamacher Aggregation Operators and Continuous Entropy

Under the interval-valued hesitant fuzzy information environment, we investigate a multiattribute group decision making (MAGDM) method with continuous entropy weights and improved Hamacher information aggregation operators. Firstly, we introduce the axiomatic definition of entropy for interval-valued hesitant fuzzy elements (IVHFEs) and construct a continuous entropy formula on the basis of the continuous ordered weighted averaging (COWA) operator. Then, based on the Hamachert-norm andt-conorm, the adjusted operational laws for IVHFEs are defined. In order to aggregate interval-valued hesitant fuzzy information, some new improved interval-valued hesitant fuzzy Hamacher aggregation operators are investigated, including the improved interval-valued hesitant fuzzy Hamacher ordered weighted averaging (I-IVHFHOWA) operator and the improved interval-valued hesitant fuzzy Hamacher ordered weighted geometric (I-IVHFHOWG) operator, the desirable properties of which are discussed. In addition, the relationship among these proposed operators is analyzed in detail. Applying the continuous entropy and the proposed operators, an approach to MAGDM is developed. Finally, a numerical example for emergency operating center (EOC) selection is provided, and comparative analyses with existing methods are performed to demonstrate that the proposed approach is both valid and practical to deal with group decision making problems.

Managing interval-valued multiplicative hesitant fuzzy information in GDM problems

Inspired by the idea of multiplicative preference relation as well as interval-valued hesitant fuzzy set, we introduce a new preference relation called interval-valued multiplicative hesitant fuzzy preference structure. It is a powerful technique to describe the preference information assessed by different appraise subjective. The predominant feature of it was allows decision makers to use the interval-valued hesitant fuzzy information in describing the preference structure. We focus on the information aggregation methods for interval-valued multiplicative hesitant fuzzy preference information and proposed a series of useful aggregation operators. Moreover, we propose a group decision making (GDM) method based on proposed aggregation operators under interval-valued multiplicative hesitant fuzzy environment. Real case about college application problem is presented to show the useful and effectiveness of our proposed method.

A Method for Interval-Valued Hesitant Fuzzy Multiple Attribute Decision Making and Their Application to Wireless Sensor Network Route Security Evaluation

Wireless sensor network, as an integrated network which can perform information gathering, processing and delivering, can connect the real world and logistic information world. It is greatly changing the interaction between people and nature. There are wide potential applications for wireless sensor network, such as industry, agriculture, military affairs, environment monitoring, biomedicine, city managing and disaster succoring. The problem of evaluating the security of wireless sensor network route with interval-valued hesitant fuzzy information is the multiple attribute decision making. In this paper, we extend the ELECTRE method to take into account interval-valued hesitant fuzzy information and propose the ELECTRE method to solve the multiple attribute decision making problems. Finally, a practical example for evaluating the wireless sensor network route security is given to verify the developed approach and to demonstrate its practicality and effectiveness.

On Extending Power-Geometric Operators to Interval-Valued Hesitant Fuzzy Sets and Their Applications to Group Decision Making

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some “false” or “biased” arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques.