Intuitionistic Hesitant Fuzzy Sets Research Articles

A new energy vehicle battery supplier selection using SWARA-MEREC-MARCOS approach under probabilistic triangular intuitionistic hesitant fuzzy environment

In this manuscript, we construct a Multi-Criteria Decision-Making (MCDM) model to study the new energy vehicle (NEV) battery supplier selection problem. Firstly, we select criteria to build an evaluation index system. Secondly, SAWARA and MEREC methods are used to calculate subjective and objective weights in the ranking process, respectively, and PTIHFS (Probabilistic Triangular Intuitionistic Hesitant Fuzzy Set) is employed to describe the decision maker’s accurate preferences in performing the calculation of subjective weights. Then, the game theory is used to find the satisfactory weights. We use TFNs to describe the original information in the MARCOS method to obtain the optimal alternative. Finally, a correlation calculation using Spearman coefficients is carried out to compare with existing methods and prove the model’s validity.

Novel Complex Intuitionistic Hesitant Fuzzy Distance Measures for Solving Decision-Support Problems

The key objective of this article is to introduce the innovative idea of a complex intuitionistic hesitant fuzzy set (CIHFS), which blends the intuitionistic hesitant fuzzy set with the complex fuzzy set to address the uncertain information in real-life complex problems. In CIHFS, the range of the membership functions is extended from the subset of the real number to the unit disc under the hesitant environment. To determine how well the CIHFSs can be distinguished from one another, we first propose generalized distance measures and weighted generalized distance measures based on the Hamming, Euclidean, and Hausdorff metrics. Some interesting properties and their relationships are thoroughly discussed. Furthermore, a decision-making framework for selecting the optimal option from the feasible set has been proposed, which is grounded in these distance metrics. For the purpose of proving the method’s efficacy, we included examples from pattern recognition and medical diagnostics.

Avenues of decarbonisation in the dynamics of processed food supply chains: Towards responsible production consumption

Nowadays, the demand for processed food items is surging. To fulfil the enhanced demand, a significant impact is laid on the environment, which enhances the carbon footprint being generated. Hence, to overcome this, the avenues of decarbonisation need to be explored. The presented work is aimed at promoting the decarbonisation of the existing practices within the processed food supply chains. It finds strong compliance with the sustainable development goal (SDG-12), focusing on responsible production-consumption mechanisms. For the same, key enactors of decarbonisation are identified and mapped with the practices at various stages of food supply chains, i.e. upstream, downstream, and other allied practices. Based upon these enactors, a relational, hierarchical framework is developed to provide a comprehensive perspective on complex intricacies. This framework is analysed with an innovative approach which comprises the fundamentals of Interval-Valued Intuitionistic Hesitant Fuzzy Set with the Entropy measures. It results in the outranking of the enactors relative to its importance in the decarbonisation of processed food supply chains. Furthermore, the empirical findings are validated by the sensitivity analysis to felicitate robust decision-making. The outcomes of the presented work provide a roadmap and stepped approach to achieve the decarbonisation goals and make production-consumption mechanisms sustainable. It finds implications in the development of the framework, policy formulation, and decisional attributes for the decarbonisation of food supply chains. It focuses on the adoption of strategies that align with global efforts to mitigate climate change and promote a sustainable future.

Multi-attribute decision-making based on dual probabilistic interval-valued intuitionistic hesitant fuzzy weighted heronian mean aggregation operator

Probabilistic interval-valued intuitionistic hesitant fuzzy sets (PIVIHFSs) can well describe the evaluation information of decision-makers (DMs) in multi-attribute decision-making (MADM) problems. However, PIVIHFSs only depict the situation where both membership and non-membership information occur with equal probability while ignoring the situations of non-equal possibility due to DMs’ subjective preferences. In this paper, we develop dual probabilistic interval-valued intuitionistic hesitant fuzzy sets (DPIVIHFSs) concept based on the truncated normal distribution. The DPIVIHFSs overcome the shortcomings of PIVIHFSs and are more interpretable. Then, the operations and ranking method of DPIVIHFSs are introduced. Furthermore, we study MADM methods in dual probabilistic interval-valued intuitionistic hesitant fuzzy environments by aggregation operators (AOs). We propose a series of AOs including the DPIVIHF heronian mean (DPIVIHFHM) operator and the DPIVIHF weighted heronian mean (DPIVIHFWHM) operator. The basic properties of the presented are discussed and proved. Finally, a novel method for solving the MADM problem is proposed based on the DPIVIHFWHM operator and a numerical example of express company selection strategy is used to illustrate the effectiveness of the method. The proposed method in this article can capture more fuzzy and uncertain information when solving MADM problems and have a wider application range.

A new type of cosine similarity measures based on intuitionistic hesitant fuzzy rough sets for the evaluation of volatile currency: evidence from the Pakistan economy

A new type of cosine similarity measures based on intuitionistic hesitant fuzzy rough sets for the evaluation of volatile currency: evidence from the Pakistan economy

An Innovative Decision Model Utilizing Intuitionistic Hesitant Fuzzy Aczel-Alsina Aggregation Operators and Its Application

The intuitionistic hesitant fuzzy set is a significant extension of the intuitionistic fuzzy set, specifically designed to address uncertain information in decision-making challenges. Aggregation operators play a fundamental role in combining intuitionistic hesitant fuzzy numbers into a unified component. This study aims to introduce two novel approaches. Firstly, we propose a three-way model for investors in the business domain, which utilizes interval-valued equivalence classes under the framework of intuitionistic hesitant fuzzy information. Secondly, we present a multiple-attribute decision-making (MADM) method using various aggregation operators for intuitionistic hesitant fuzzy sets (IHFSs). These operators include the IHF Aczel–Alsina average (IHFAAA) operator, the IHF Aczel–Alsina weighted average (IHFAAWAϣ) operator, and the IHF Aczel–Alsina ordered weighted average (IHFAAOWAϣ) operator and the IHF Aczel–Alsina hybrid average (IHFAAHAϣ) operators. We demonstrate the properties of idempotency, boundedness, and monotonicity for these newly established aggregation operators. Additionally, we provide a detailed technique for three-way decision-making using intuitionistic hesitant fuzzy Aczel–Alsina aggregation operators. Furthermore, we present a numerical case analysis to illustrate the pertinency and authority of the esteblished model for investment in business. In conclusion, we highlight that the developed approach is highly suitable for investment selection policies, and we anticipate its extension to other fuzzy information domains.

Evaluating the Quality of Medical Services Using Intuitionistic Hesitant Fuzzy Aczel–Alsina Aggregation Information

In modern civilization, individuals are increasingly concerned with evaluating the quality of medical services. Evaluation of the quality of medical services enables medical care providers to monitor and improve their service quality. The evaluation of medical service quality is efficiently addressed by the novel concept of Aczel–Alsina operators in an intuitionistic hesitant fuzzy (IHF) environment as multicriteria decision-making (MCDM) problem. Thus, this paper presents the IHF Aczel–Alsina weighted geometric operators for IHF information. We first apply the Aczel–Alsina norms to IHF scenarios and present novel operations of intuitionistic hesitant fuzzy sets. This article develops a unique strategy for evaluating the quality of medical services based on the specified operators, including a quantitative framework for evaluating medical service quality and a novel MCDM technique. Finally, this article presents a numerical example of the novel approach used to evaluate medical services for hospitals and compares it to conventional MCDM methods to highlight the suggested superiority method. According to the comparative results, our strategy outperforms the insufficiency of lacking decision flexibility in the existing MAGDM method.

Selection of Investment Policy Using a Novel Three-Way Group Decision Model under Intuitionistic Hesitant Fuzzy Sets

In today’s fast-paced and dynamic business environment, investment decision making is becoming increasingly complex due to the inherent uncertainty and ambiguity of the financial data. Traditional decision-making models that rely on crisp and precise data are no longer sufficient to address these challenges. Fuzzy logic-based models that can handle uncertain and imprecise data have become popular in recent years. However, they still face limitations when dealing with complex, multi-criteria decision-making problems. To overcome these limitations, in this paper, we propose a novel three-way group decision model that incorporates decision-theoretic rough sets and intuitionistic hesitant fuzzy sets to provide a more robust and accurate decision-making approach for selecting an investment policy. The decision-theoretic rough set theory is used to reduce the information redundancy and inconsistency in the group decision-making process. The intuitionistic hesitant fuzzy sets allow the decision makers to express their degrees of hesitancy in making a decision, which is not possible in traditional fuzzy sets. To combine the group opinions, we introduce novel aggregation operators under intuitionistic hesitant fuzzy sets (IHFSs), including the IHF Aczel-Alsina average (IHFAAA) operator, the IHF Aczel-Alsina weighted average (IHFAAWAϣ) operator, the IHF Aczel-Alsina ordered weighted average (IHFAAOWAϣ) operator, and the IHF Aczel-Alsina hybrid average (IHFAAHAϣ) operator. These operators have desirable properties such as idempotency, boundedness, and monotonicity, which are essential for a reliable decision-making process. A mathematical model is presented as a case study to evaluate the effectiveness of the proposed model in selecting an investment policy. The results show that the proposed model is effective and provides more accurate investment policy recommendations compared to existing methods. This research can help investors and financial analysts in making better decisions and achieving their investment goals.

A data-driven group emergency decision-making method based on interval-valued intuitionistic hesitant fuzzy sets and its application in COVID-19 pandemic

The outbreak of Corona Virus Disease 2019 (COVID-19) makes people more concerned about the validity and timeliness of emergency decision making. When an emergency occurs, it is difficult for decision makers (DMs) to give accurate assessment information in the early stage due to the urgency of time, the incompleteness of information, and the limitations of DMs’ cognition and knowledge. Hence, we use interval-valued intuitionistic hesitant fuzzy sets rather than exact numbers to better characterize the fuzziness and uncertainty of emergencies. In addition, the Internet has become a major platform for the public to express their opinions or concerns, so we can collect the user-generated content on social media to help DMs determine appropriate emergency decision-making criteria which are the premise and basis of scientific decisions. However, there is likely to be some correlation between the obtained criteria. To this end, we first extend the Bonferroni mean (BM) operator to the interval-valued intuitionistic hesitant fuzzy environment, and propose three interval-valued intuitionistic hesitant fuzzy BM operators to capture the interrelation of fuzzy input variables, including an interval-valued intuitionistic hesitant fuzzy BM operator, a simplified interval-valued intuitionistic hesitant fuzzy BM operator, and a simplified interval-valued intuitionistic hesitant fuzzy weighted BM (SIVIHFWBM) operator. Then, a new group emergency decision-making method based on the SIVIHFWBM operator and social media data is proposed, and the specific steps of ranking all emergency plans are put forward. Moreover, our method is applied to evaluate emergency plans for the prevention and control of COVID-19. Finally, the effectiveness and feasibility of the method are verified by the sensitivity analysis, validity test, and comparative analysis.

Multiple-Attribute Decision Making Based on Intuitionistic Hesitant Fuzzy Connection Set Environment

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of hesitant fuzzy sets (HFSs) that can cover both fuzzy sets (FSs) and intuitionistic fuzzy sets (IFSs). By assigning membership and non-membership grades as subsets of [0, 1], the IHFS can model and handle situations more proficiently. Another related theory is the theory of set pair analysis (SPA), which considers both certainties and uncertainties as a cohesive system and represents them from three aspects: identity, discrepancy, and contrary. In this article, we explore the suitability of combining the IHFS and SPA theories in multi-attribute decision making (MADM) and present the hybrid model named intuitionistic hesitant fuzzy connection number set (IHCS). To facilitate the design of a novel MADM algorithm, we first develop several averaging and geometric aggregation operators on IHCS. Finally, we highlight the benefits of our proposed work, including a comparative examination of the recommended models with a few current models to demonstrate the practicality of an ideal decision in practice. Additionally, we provide a graphical interpretation of the devised attempt to exhibit the consistency and efficiency of our approach.

Intuitionistic Hesitant Fuzzy UP (BCC)-Filters of UP (BCC)-Algebras

The concepts of intuitionistic hesitant fuzzy UP (BCC)-subalgebras, UP (BCC)-ideals, and UP (BCC)-filters of UP (BCC)-algebras are presented, some of their features are explained, and their extensions are demonstrated using the theory of hesitant fuzzy sets as a foundation. The necessary conditions for those intuitionistic hesitant fuzzy sets are provided and include their relation to their complement. The concept of prime and weakly prime of intuitionistic hesitant fuzzy sets was also introduced and studied. We also talk about the connections between intuitionistic hesitant fuzzy UP (BCC)-subalgebras (UP (BCC)-ideals, UP (BCC)-filters) and their level subsets. The homomorphic pre-images of intuitionistic hesitant fuzzy UP (BCC)-filters in UP (BCC)-algebras are also studied and some related properties are investigated.

A Telemedicine Decision-Making Model for Teleconsultation Decision Support System Based on Intuitionistic Hesitant Fuzzy Linguistic Term Sets

Teleconsultation is conducive to the rational use of health resources and plays a key role in the realization of hierarchical diagnosis and treatment. Previous research on telemedicine multicriteria decision making methods rarely consider the difference in responsibilities between remote experts and attending physicians. To show the difference precisely, this article first defines the intuitionistic hesitant fuzzy linguistic term set (IHFLTS) as an extended mathematical expression of the fuzzy set. We propose two kinds of correlation measuring methods and related hesitancy degrees based on information energy and statistics with different application scenarios. Based on information entropy and distance measurement, two criterion weight determination methods are studied. To formally implement the joint decision-making process of remote experts and attending physicians, a telemedicine decision-making model is established for designing the teleconsultation decision support system. We apply the proposed methods to a sinusitis teleconsultation case to demonstrate their effectiveness. The weight determination methods are applied, and the influence of parameter variation in the distance-based method is analyzed. Finally, the rationality and applicability of the proposed methods are verified by comparisons. The results show that by considering the importance and differences between the two roles of teleconsultation, IHFLTS can obtain a more realistic result for the referral problems.

Aczel-Alsina-based aggregation operators for intuitionistic hesitant fuzzy set environment and their application to multiple attribute decision-making process

<abstract> <p>An intuitionistic hesitant fuzzy set is an extension of the fuzzy set which deals with uncertain information and vague environments. Multiple-attribute decision-making problems (MADM) are one of the emerging topics and an aggregation operator plays a vital role in the aggregate of different preferences to a single number. The Aczel-Alsina norm operations are significant terms that handle the impreciseness and undetermined data. In this paper, we build some novel aggregation operators for the different pairs of the intuitionistic hesitant fuzzy sets (IHFSs), namely as Aczel-Alsina average and geometric operators. Several characteristics of the proposed operators are also described in detail. Based on these operators, a multi-attribute decision-making algorithm is stated to solve the decision-making problems. A numerical example has been taken to display and validate the approach. A feasibility and comparative analysis with existing studies are performed to show its superiority.</p> </abstract>

Interval Valued q- Rung Orthopair Hesitant Fuzzy Choquet Aggregating Operators in Multi-Criteria Decision Making Problems

Abstract: In this paper, we introduce Interval valued q- Rung Orthopair Hesitant fuzzy sets (IVq-ROHFS) with motivation of Interval valued pythagorean Hesitant fuzzy sets [44] as a new concept. Then, we give some basic operations as complement, union, intersection, addition, scalar multiplication, scalar power. Also, we combine to (IVq-ROHFS) and choquet integral , together with aggregating operators, and develop to Interval valued q- rung orthopair hesitant fuzzy Choquet averaging operator (IVq-ROHCA) and Interval valued q- rung orthopair hesitant fuzzy Choquet geometric operator (IVq-ROHCG). Then, we offer to indicate soft approach of proposed IVq-ROHCA and IVq-ROHCG an example adopted from Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS (IVIHCI) [43]. The obtained results are agreement with IVIHCI but presented IVq-ROHCA and IVq-ROHCG have more advantages than existing structures as Interval-valued intuitionistic hesitant fuzzy sets (IVIHFS), interval-valued Pythagorean Hesitant fuzzy sets (IVPHFS) with reasons changing according to need, requirement, prefer of decision makers and moreover, being IVIHFS and IVPHFS are special cases of IVq-ROHFS. It is open from comparative analysis that the while some of offered approaches are giving no solution for some values, our operators present to needed results.

Medical Diagnosis and Pattern Recognition Based on Generalized Dice Similarity Measures for Managing Intuitionistic Hesitant Fuzzy Information

Pattern recognition is the computerized identification of shapes, designs, and reliabilities in information. It has applications in information compression, machine learning, statistical information analysis, signal processing, image analysis, information retrieval, bioinformatics, and computer graphics. Similarly, a medical diagnosis is a procedure to illustrate or identify diseases or disorders, which would account for a person’s symptoms and signs. Moreover, to illustrate the relationship between any two pieces of intuitionistic hesitant fuzzy (IHF) information, the theory of generalized dice similarity (GDS) measures played an important and valuable role in the field of genuine life dilemmas. The main influence of GDS measures is that we can easily obtain a lot of measures by using different values of parameters, which is the main part of every measure, called DGS measures. The major influence of this theory is to utilize the well-known and valuable theory of dice similarity measures (DSMs) (four different types of DSMs) under the assumption of the IHF set (IHFS), because the IHFS covers the membership grade (MG) and non-membership grade (NMG) in the form of a finite subset of [0, 1], with the rule that the sum of the supremum of the duplet is limited to [0, 1]. Furthermore, we pioneered the main theory of generalized DSMs (GDSMs) computed based on IHFS, called the IHF dice similarity measure, IHF weighted dice similarity measure, IHF GDS measure, and IHF weighted GDS measure, and computed their special cases with the help of parameters. Additionally, to evaluate the proficiency and capability of pioneered measures, we analyzed two different types of applications based on constructed measures, called medical diagnosis and pattern recognition problems, to determine the supremacy and consistency of the presented approaches. Finally, based on practical application, we enhanced the worth of the evaluated measures with the help of a comparative analysis of proposed and existing measures.

Time-sequential hesitant fuzzy set and its application to multi-attribute decision making

The hesitant fuzzy set has been an important tool to address problems of decision making. There are several various improved hesitant fuzzy sets, such as dual hesitant fuzzy set, hesitant interval-valued fuzzy set, and intuitionistic hesitant fuzzy set, however, no one kind of improved fuzzy sets could reflect attitude characteristics of decision makers on time-sequences. In reality, time-sequence is one important sector to reflect hesitant situations as decision makers might have different knowledges of the same alternative at different moments. To perfect the description of such hesitant situations and obtain more reasonable results of decision making, we define a new kind of hesitant fuzzy set, namely, time-sequential hesitant fuzzy set. Meanwhile, its corresponding basic operators, score function and distance measures are proposed. We also propose the concept of fluctuated hesitant information to describe hesitant degrees of decision makers on time-sequences. By comprehensively utilizing the score function, fluctuated hesitant information and distance measures under time-sequential hesitant fuzzy set, a synthetic decision model is proposed. Two illustrated examples and one real-application are utilized to illustrate the effectiveness and advantage of the synthetic decision model under time-sequential hesitant fuzzy set.

Matrix game-based approach for MADM with probabilistic triangular intuitionistic hesitant fuzzy information and its application

This paper develops a zero-sum matrix game-based methodology for multi-attribute decision making (MADM) problems, where the attribute information is described by the probabilistic triangular intuitionistic hesitant fuzzy set (PTIHFS), and their weights are unknown. Firstly, we propose a new comprehensive rank method to measure PTIHFSs based on the concepts of the centroid value and the ambiguity value. Then, in order to obtain the rational attribute weights strategies (solutions) with DM's preferences/parameters, the transformed parameterized PTIHFS bilinear programming models are proposed for the zero-sum matrix. Next, the alternatives are sorted by the aggregation scores of each alternative with different parameters. Finally, we apply the zero-sum matrix game-based models and approach in a carrying capacity evaluation, the feasibility and superiority are demonstrated by comparing them with other methods. The proposed simple measure method of PTIHFSs, and it is used for interactive decision-making, which can much significantly promote the application of MADM.

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application.

Using advantages of interval-valued intuitionistic hesitant fuzzy sets (IVIHFS) for describing the hesitant and intuitionistic decisions of experts and identifying the limitations of previous research works about optimization techniques, this paper introduces a new optimization technique and provides a new computational algorithm, applicable in various real life multiobjective optimization problem (MOOP) of engineering and management sectors, and for this, a new operation between IVIHFSs is first introduced. On the basis of this concept, a stepwise computational algorithm is constructed, and it is an extension of both fuzzy and intuitionistic fuzzy optimization techniques. Finally, the proposed algorithm is illustrated using a production planning problem, and the obtained results are compared with the existing optimization techniques.

Distance measures on intuitionistic hesitant fuzzy set and its application in decision-making

Intuitionistic hesitant fuzzy set (IHFS) provides a valid mean for dealing with the uncertainty of complex problems. Information measures on IHFS can measure the uncertain information, so that we shall introduce a method to construct a class of distance measures for IHFS in this paper. For constructing more objective distance measures to reflect the actual situation, we consider the information content and information clarity of IHFS simultaneously and utilize different functions to adjust their contribution. Its superiority is evidenced by an example of pattern recognition that the proposed distance measure improves numerically results obtained with existing distance measures. In particular, we investigate the connection between distance measure, similarity measure, and entropy measure of IHFS, and prove that they can be constructed mutually under this axiomatic framework. On this basis, we apply the proposed entropy measure to determine criteria weights in multi-criteria decision-making problems and design an extended intuitionistic hesitant fuzzy technique for order preference by similarity to an ideal solution (TOPSIS) method, which effectiveness is presented by a practical application.

Power Aggregation Operators and Similarity Measures Based on Improved Intuitionistic Hesitant Fuzzy Sets and their Applications to Multiple Attribute Decision Making

Intuitionistic hesitant fuzzy set (IHFS) is a mixture of two separated notions called intuitionistic fuzzy set (IFS) and hesitant fuzzy set (HFS), as an important technique to cope with uncertain and awkward information in realistic decision issues. IHFS contains the grades of truth and falsity in the form of the subset of the unit interval. The notion of IHFS was defined by many scholars with different conditions, which contain several weaknesses. Here, keeping in view the problems of already defined IHFSs, we will define IHFS in another way so that it becomes compatible with other existing notions. To examine the interrelationship between any numbers of IHFSs, we combined the notions of power averaging (PA) operators and power geometric (PG) operators with IHFSs to present the idea of intuitionistic hesitant fuzzy PA (IHFPA) operators, intuitionistic hesitant fuzzy PG (IHFPG) operators, intuitionistic hesitant fuzzy power weighted average (IHFPWA) operators, intuitionistic hesitant fuzzy power ordered weighted average (IHFPOWA) operators, intuitionistic hesitant fuzzy power ordered weighted geometric (IHFPOWG) operators, intuitionistic hesitant fuzzy power hybrid average (IHFPHA) operators, intuitionistic hesitant fuzzy power hybrid geometric (IHFPHG) operators and examined as well their fundamental properties. Some special cases of the explored work are also discovered. Additionally, the similarity measures based on IHFSs are presented and their advantages are discussed along examples. Furthermore, we initiated a new approach to multiple attribute decision making (MADM) problem applying suggested operators and a mathematical model is solved to develop an approach and to establish its common sense and adequacy. Advantages, comparative analysis, and graphical representation of the presented work are elaborated to show the reliability and effectiveness of the presented works.