Interval-Valued Hesitant Research Articles

Achieving strategic excellence: Integrating balanced scorecard and IVHF-DEMATEL for strategic management of a medical device SME

Nowadays, strategic planning and the establishment of long-term objectives are pivotal for companies from diverse economies based on geographical location, demographic distribution, financial challenges, and distinct customer portfolios. Defining strategic goals is vital more than ever however requires acceptance, adoption, and execution by the entire workforce. In this sense, this paper presents an integrated methodology that combines the Balanced Scorecard and the Interval-Valued Hesitant Fuzzy DEMATEL approaches to enhance strategic management in a Medical Device SME located in Istanbul-Turkey. The proposed approach aims to provide a holistic perspective on organizational performance and facilitate decision-making processes for sustainable growth and competitive advantage.

Undergraduate Teaching Audit and Evaluation Using an Extended ORESTE Method with Interval-Valued Hesitant Fuzzy Linguistic Sets

Undergraduate teaching audit and evaluation (UTAE) plays a substantial role in the teaching quality assurance and monitoring of universities. It achieves the goal of selecting the best university for promoting the quality of higher education in China. Generally, the UTAE is a complex decision-making problem by considering competing evaluation criteria. Moreover, the evaluation information on the teaching quality of universities is often ambiguous and hesitant because of the vagueness existing in human judgments. Previous studies on UTAE have paid subtle attention towards the managing of linguistic expressions and the performance priority of universities. The interval-valued hesitant fuzzy linguistic sets (IVHFLSs) can effectively describe uncertainty, hesitancy, and inconsistency inherent in decision-making process. The ORESTE (organísation, rangement et Synthèse de données relarionnelles, in French) is a new outranking decision-making method which can show detailed distinctions between alternatives. Therefore, in this study, we propose a new UTAE approach based on the VHFLSs and ORESTE method to resolve the prioritization of universities for selecting the optimal university to benchmark. Specifically, the presented method handles the hesitant and uncertain linguistic expressions of experts by adopting the IVHFLSs and determines the ranking of universities with an extended ORESTE approach. Finally, a practical UTAE example illustrates the feasibility the proposed approach and a comparison analysis provides grounding for the superiority of the integrated approach. When the obtained results are evaluated, U2 has been determined as the best university. The results indicate the good performance of the proposed UTAE approach in evaluating and improving the teaching quality of universities.

The Generalized Similarity Measures Based on Complex Interval-Valued Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

The Generalized Similarity Measures Based on Complex Interval-Valued Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

A New Approach to Correspondence Analysis Based on Interval-Valued Hesitant Fuzzy Sets

Correspondence Analysis (CA), a multivariate statistical technique, allows a visual representation of the association between categorical variables through a contingency table consisting of frequencies representing the existence of relationships. Despite being a widely used statistical technique, the classical CA is not able to demonstrate the uncertainty in real-life problems. To address this issue, a new Interval-valued Hesitant Fuzzy CA approach is proposed to represent the uncertainty caused by human doubt. Due to the nature of operations defined on Hesitant Fuzzy Sets, it is hard to integrate the fuzzy calculations directly into the classical CA. Thus, a new hesitant expected value method is proposed to reveal the independence between two categorical variables. As the output of the proposed approach, an interval-valued hesitant fuzzy correspondence map consisting of rectangles of different sizes representing the amount of the hesitancy is constructed. The applicability of the proposed approach is demonstrated by a simple but effective illustrative example.

An Efficiency-Based Interactive Dynamic Technique with Interval-Valued Hesitant Fuzzy Constraint Cone for Rescue Route Planning

An Efficiency-Based Interactive Dynamic Technique with Interval-Valued Hesitant Fuzzy Constraint Cone for Rescue Route Planning

A Congruent Approach to Normal Wiggly Interval-Valued Hesitant Pythagorean Fuzzy Set for Thermal Energy Storage Technique Selection Applications

Thermal energy is the energy from a substance in which molecules and atoms vibrate faster because of an increase in temperature. Thermal energy storage (TES) is an available energy resource for renewable energy platforms that enables them to meet sustainable technical requirements. The TES technique is divided into three categories; sensible TES, latent-heat TES, and thermo-chemical TES. The best of these techniques is selected in this research paper. Here the Interval-Valued Hesitant Pythagorean Fuzzy Set (IVPHFS) under the Normal Wiggly Mathematical Methodology is proposed and described for application to multi-criteria decision making (MCDM) technology. The MCDM methods, the Step-wise Weight Assessment Ratio Analysis (SWARA) method for determining weight values, and the Weighted Aggregated Sum Product Assessment (WASPAS) method for ranking alternative values are used employed here. The alternative values are selected based on the following criteria: capacity, efficiency, storage period, charging and discharging times, and cost

An effective similarity measurement under epistemic uncertainty

The epistemic uncertainty stems from the lack of knowledge and it can be reduced when the knowledge increases. Such interpretation works well with data represented as a set of possible states and therefore, multivalued similarity measures. Unfortunately, set-valued extensions of similarity measures are not computationally feasible even when the data is finite. Measures with properties that allow efficient calculation of their extensions, need to be found. Analysis of various similarity measures indicated logic-based (additive) measures as an excellent candidate. Their unique properties are discussed and efficient algorithms for computing set-valued extensions are given. The work presents results related to various classes of fuzzy set families: general ones, intervals of fuzzy sets, and their finite sums. The first case is related to the concept of the Fuzzy Membership Function Family, the second corresponds to the Interval-Valued Fuzzy Sets, while the third class is equivalent to the concept of Typical Interval-Valued Hesitant Fuzzy Sets.

Generalized interval-valued hesitant intuitionistic fuzzy soft sets

This paper aims to extend the Interval-valued Intuitionistic Hesitant Fuzzy Set to a Generalized Interval-valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS). Definition of a GIVHIFSS and some of their operations are defined, and some of their properties are studied. In these GIVHIFSSs, the authors have defined complement, null, and absolute. Soft binary operations like operations union, intersection, a subset are also defined. Here is also verified De Morgan’s laws and the algebraic structure of GIVHIFSSs. Finally, by using the comparison table, a different approach to GIVHIFSS based decision-making is presented.

Interval-Valued Hesitant Fuzzy TOPSIS Decision Making Method with Group Consistency

Interval-Valued Hesitant Fuzzy TOPSIS Decision Making Method with Group Consistency

Ancient Chinese Character Image Segmentation Based on Interval-Valued Hesitant Fuzzy Set

To address the low segmentation accuracy caused by the rich glyph styles of ancient Chinese characters and the complex layout of ancient Chinese books, which affects the retrieval and recognition results, an algorithm for the layout image analysis of ancient Chinese books and Chinese character image segmentation is proposed. The initial segmentation results were obtained through the projection method of the layout of ancient Chinese books, and the connected component analysis of the above results was carried out to determine the rough divided blocks of under-segmentation and over-segmentation. Considering under-segmentation of adhesive Chinese characters, the improved K-means clustering method was used to segment adhesive blocks to obtain single-character images. To address the over-segmentation of character components separation, a method based on interval-valued hesitant fuzzy set is proposed. This method analyzed the features of the connected component in the block, characterized the over-segmentation connected component. The hesitant fuzzy distances between other connected components and the standard merge evaluation interval number were calculated in sequence. The connected component with the smallest distance was preferentially merged with the over-segmentation connected component until no over-segmentation connected component remained in the block. The experimental segmentation accuracy was 89.94%.

A Prospect Theory Based Probabilistic Interval-Valued Hesitant Fuzzy Sets with Interval Reference Point and Incomplete Weight Information for Multi-Criteria Decision Making

In this paper, we introduce probabilistic interval-valued hesitant fuzzy sets (PIVHFS) and probabilistic interval-valued hesitant fuzzy elements (PIVHFE), then define correlation operations. At the same time, the hybrid distance measures of PIVHFE and interval fuzzy number are defined, and the hybrid distance measures of two PIVHFEs are also defined. Considering the psychological behavior of decision makers, we use interval fuzzy number decision makers' psychological interval reference points to calculate the gains and losses of evaluation value. Furthermore, based on incomplete weight information, the grey relational analysis (GRA) method is extended to calculate the optimal weight. Then, based on the traditional TOPSIS method, the decision-making method is proposed. Finally, the proposed method is applied to an example, and the sensitivity analysis and stability analysis of the proposed method are also discussed.

Multiple Criteria Decision Making Based on Probabilistic Interval-Valued Hesitant Fuzzy Sets by Using LP Methodology

Probabilistic interval-valued hesitant fuzzy sets (PIVHFSs) are an extension of interval-valued hesitant fuzzy sets (IVHFSs) in which each hesitant interval value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. PIVHFSs describe the belonging degrees in the form of interval along with probabilities and thereby provide more information and can help the decision makers (DMs) to obtain precise, rational, and consistent decision consequences than IVHFSs, as the correspondence of unpredictability and inaccuracy broadly presents in real life problems due to which experts are confused to assign the weights to the criteria. In order to cope with this problem, we construct the linear programming (LP) methodology to find the exact values of the weights for the criteria. Furthermore these weights are employed in the aggregation operators of PIVHFSs recently developed. Finally, the LP methodology and the actions are then applied on a certain multiple criteria decision making (MCDM) problem and a comparative analysis is given at the end.

Comment on “Corrigendum to ‘On Interval-Valued Hesitant Fuzzy Soft Sets’” and “Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis”

Comment on “Corrigendum to ‘On Interval-Valued Hesitant Fuzzy Soft Sets’” and “Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis”

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.

The Stably Multiplicative Consistency of Fuzzy Preference Relation and Interval-Valued Hesitant Fuzzy Preference Relation

Preference relations are generally used to cope with multi-attribute group decision making (MAGDM), which express the experts’ preference information through pairwise comparisons. To make decision rationale, one of the vital issues related to preference relations is how to make the preference information logical. The logicality level of preference information is usually described by the consistency of preference relation. Thus, developing methods to check and improve the consistency of preference relations is necessary and significant. In this paper, we give a general description of multiplicative transitivity property for fuzzy preference relation (FPR). Then, based on the new multiplicative transitivity function which can repair some counterintuitive cases of the traditional one, we define the stably multiplicative consistency, the stably mean multiplicative consistency (SMMC), and the acceptable SMMC for interval-valued hesitant FPR (IVHFPR). Additionally, several algorithms are developed to improve the SMMC of IVHFPR. A practical example concerning the respiratory illness diagnosis is given to demonstrate the applicability of IVHFPR with SMMC.

A Multiple Attribute Decision Making Approach Based on New Similarity Measures of Interval-valued Hesitant Fuzzy Sets

Hesitant fuzzy sets, as an extension of fuzzy sets to deal with uncertainty, have attracted much attention since its introduction, in both theory and application aspects. The present work is focused on the interval-valued hesitant fuzzy sets (IVHFSs) to manage additional uncertainty. Now that distance and similarity as a kind of information measures are essential and important numerical indexes in fuzzy set theory and all their extensions, the present work aims at investigating distance and similarity measures in the IVHFSs and then employing them into multiple attribute decision making application. To begin with, II-type generalized interval-valued hesitant fuzzy distance is firstly introduced in the IVHFS, along with its properties and its relationships with the traditional Hamming-Distance and the Euclidean distance. Afterwards, another interval-valued hesitant fuzzy Lp distance based on Lp metric is proposed and its relationship with the Hausdorff distance is discussed. In addition, different from most of similarity measures with dependent on the corresponding distances, a new similarity measure based on set-theoretic approach for IVHFSs is introduced and its properties are discussed; especially, a relative similarity measure is proposed based on the positive ideal IVHFS and the negative ideal IVHFS. Finally, we describe how the IVHFS and its relative similarity measure can be applied to multiple attribute decision making. A numerical example is then provided to illustrate the effectiveness of the proposed method.

Lattice ordered interval-valued hesitant fuzzy soft sets in decision making problem

In 2015, Haidong Zhang enhanced the idea of Hesitant Fuzzy Sets and Soft Sets into Interval-Valued Hesitant Fuzzy Soft Sets along with its properties. In this present work, we establish the Lattice Ordered Interval-Valued Hesitant Fuzzy Soft Sets and examined its vital properties with examples. Eventually the application of Lattice Ordered Interval-Valued Hesitant Fuzzy Soft Set to decision making problem is established by means of elegant algorithm.

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.

A New Method of Multiattribute Decision-Making Based on Interval-Valued Hesitant Fuzzy Soft Sets and Its Application

Combining interval-valued hesitant fuzzy soft sets (IVHFSSs) and a new comparative law, we propose a new method, which can effectively solve multiattribute decision-making (MADM) problems. Firstly, a characteristic function of two interval values and a new comparative law of interval-valued hesitant fuzzy elements (IVHFEs) based on the possibility degree are proposed. Then, we define two important definitions of IVHFSSs including the interval-valued hesitant fuzzy soft quasi subset and soft quasi equal based on the new comparative law. Finally, an algorithm is presented to solve MADM problems. We also use the method proposed in this paper to evaluate the importance of major components of the well drilling mud pump.

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.