Hesitant Sets Research Articles

Time-sequential probabilistic fermatean hesitant approach in multi-objective green solid transportation problems for sustainable enhancement

In order to delineate the randomness and imprecision in a single framework of time-sequential information, we proposed the notion of a time-sequential probabilistic fermatean hesitant set (TS-PFHS). Triangular time-sequential probabilistic fermatean hesitant number (Tr-TS-PFHN) is also initiated as a triangular version of TS-PFHS along with its fundamental operations and a ranking function. For the employment of our proposed set, we formulated a solid transportation problem (STP) with multiple objectives with TS-PFHS parameters for a sustainable green environment. Consequently, we proposed an algorithm by utilizing fuzzy programming (FP) and weighted sum technique (WST) to address proposed green transportation model. Additionally, to highlight the significance of the suggested technique, a numerical instance based on the transportation of electric vehicles in India is also investigated. Finally, conclusion along with the future prospects and limitations of the work done are discussed.

Three-way decisions based on hesitant sets over three-way decision spaces

The concept of hesitant set was introduced by Hu, which purpose is to unify hesitant fuzzy sets, interval-valued hesitant fuzzy sets, shadowed sets etc. This paper discusses the construction of decision evaluation functions and three-way decisions based on hesitant sets over three-way decision spaces. First, this paper presents the construction methods of decision evaluation functions based on hesitant sets over semi-three-way decision spaces and quasi-three-way decision spaces. Second, this paper presents some transformation methods of decision evaluation functions based on hesitant sets from semi-three-way decision spaces and quasi-three-way decision spaces to three-way decision spaces. Third, this paper presents three-way decisions based on hesitant sets. Numerous examples are given to support this paper’s argument on the existence of semi-(quasi-)decision evaluation functions and significance of the transformation methods.

Fermatean Hesitant Fuzzy Choquet Integral Aggregation Operators

Fermatean fuzzy hesitant sets provide a flexible and powerful tool for decision making, allowing decision makers to incorporate uncertainty and hesitation into their decision making process, and enabling them to make more informed and effective decisions in complex and uncertain environments. Considering that many factors are interdependent in reality while existing methods cannot solve this problem, we propose Fermatean hesitant fuzzy Choquet integral ordered aggregation operators based on the Fermatean hesitant fuzzy set and Choquet integral, and establish their related properties. These operators including averaging and geometric operators not only handle situations where decision criteria or preferences are interdependent, but also provides the decision under ideal and non-ideal situation. Additionally, we present a multi-attribute decision-making method for Fermatean hesitant fuzzy information using these operators. We have validated the proposed method, and its practicality and effectiveness are demonstrated through numerical examples from previous research regarding Fermatean Hesitant Fuzzy set, including sensitivity analysis and comparison.

Neutrosophic statistics is an extension of interval statistics, while plithogenic statistics is the most general form of statistics (third version)

In this paper we prove that Neutrosophic Statistics is an extension of the Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities, andhas more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some applications, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics that are the most general forms of Multi Variate Probability and Multi Variate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses).

Neutrosophic Statistics is an extension of Interval Statistics, while Plithogenic Statistics is the most general form of statistics (second version)

In this paper, we prove that Neutrosophic Statistics is more general than Interval Statistics, since it may deal with all types of indeterminacies (with respect to the data, inferential procedures, probability distributions, graphical representations, etc.), it allows the reduction of indeterminacy, and it uses the neutrosophic probability that is more general than imprecise and classical probabilities and has more detailed corresponding probability density functions. While Interval Statistics only deals with indeterminacy that can be represented by intervals. And we respond to the arguments by Woodall et al. [1]. We show that not all indeterminacies (uncertainties) may be represented by intervals. Also, in some cases, we should better use hesitant sets (that have less indeterminacy) instead of intervals. We redirect the authors to the Plithogenic Probability and Plithogenic Statistics which are the most general forms of MultiVariate Probability and Multivariate Statistics respectively (including, of course, the Imprecise Probability and Interval Statistics as subclasses).

A novel hesitant-fuzzy-based group decision approach for outsourcing risk

Outsourcing is recognized as a strategic instrument for companies to move towards diversified operation advantages and efficient global market. However, outsourcing agreements may fail due to insufficient risk consideration and evaluation. This requires an effective risk evaluation approach that necessitates an entire comprehension of the system, its requirements and dimensions. This paper proposes a novel fuzzy group multiple-criteria decision-making approach through integrating triangular fuzzy hesitant sets (TFHS), Failure Mode and Effect Analysis (FMEA) and combined compromise solution (CoCoSo) algorithm. This approach (F-FMEA-CoCoSo, henceforth) analyzes and evaluates the possible risks level of alternative outsourcing providers. It hereby provides measurable information for managers according to the linguistic opinions of industrial experts. Utilization of hesitant fuzzy variables allows decision making participants to state their opinion more precisely. A case study of an Iranian chemical company is used to exemplify the applicability and suitability of the proposed F-FMEA-CoCoSo approach. The model reflects an analytical approach while experts are experiencing considerable uncertainty in risky conditions of outsourcing operations. CoCoSo contains an integrated approach of compromise solutions and its utilization enables investigators to assure results reliability which is proven via the sensitivity analysis. Through this study, we found that risk evaluation of outsourcing providers must consider four key-factors: multi-experts, multi-criteria, multi-uncertainties and measurability.

Warhead power assessment based on double hierarchy hesitant fuzzy linguistic term sets theory and gained and lost dominance score method

Warhead power assessment of the anti-ship missile plays a vital role in determining the optimal design of missile, thus having important strategic research significance. However, in the assessment process, expert’s judgement will directly affect the assessment accuracy. In addition, there are many criteria involved in the missile design alternatives. Some criteria with poor performance may be compensated by other criteria with excellent performance, and then it is impossible to find the truly optimal alternative. Aimed at solving these problems, this paper proposes a synthetical assessment process based on fuzzy hesitant linguistic term set and the Gained and Lost Dominance Score (GLDS) method. In order to improve the assessment accuracy of experts and solve the problem that experts generate different opinions, combined with the advantages of fuzzy hesitant sets and linguistic term sets, the double hierarchy hesitant fuzzy linguistic term sets are used in this paper to improve the accuracy of expert’s judgement. In order to effectively combine expert’s experience with the data of criteria, the evidence theory and entropy weight method are used to transfer the expert’s judgement to the weight. In order to avoid selecting defective alternative of missile design, the GLDS is used to fuse expert information and criteria information. Sensitivity analysis shows that the assessment process has sensitivity to some extent. However, when the fluctuation of expert’s assessment makes the fluctuation of θ in the range of −5% to 5%, the impact on the results is not quite conspicuous. The analysis of calculation result and comparative analysis show that the assessment process proposed in this paper is accurate enough, has great advantage in selecting the current and potential optimal alternative of missile design, and avoids the alternatives with low criteria performance that cannot be compensated by other criteria being selected.

On Unification of Methods in Theories of Fuzzy Sets, Hesitant Fuzzy Set, Fuzzy Soft Sets and Intuitionistic Fuzzy Sets

The main goal of this publication is to show that the basic constructions in the theories of fuzzy sets, fuzzy soft sets, fuzzy hesitant sets or intuitionistic fuzzy sets have a common background, based on the theory of monads in categories. It is proven that ad hoc defined basic concepts in individual theories, such as concepts of power set structures in these theories, relations or approximation operators defined by these relations are only special examples of applications of the monad theory in categories. This makes it possible, on the one hand, to unify basic constructions in all these theories and, on the other hand, to verify the legitimacy of ad hoc definitions of these constructions in individual theories. This common background also makes it possible to transform these basic concepts from one theory to another.

Sustainable development evaluation on wind power compressed air energy storage projects based on multi-source heterogeneous data

According to the requirement of energy sustainable development strategy in Jilin province, this paper evaluates the performance of wind power coupling compressed air energy storage projects for a wind farm in Jilin from the perspective of sustainability. Firstly, a sustainable criteria system is established from economic, social and ecological dimensions, and 10 secondary criteria are given. Secondly, to fully express the hesitancy and fuzziness of experts, linguistic fuzzy hesitant sets (LFHSs) are used to describe the subjective evaluation information. And then, the cloud model is developed to deal with the randomness and fuzziness of LFHS. Thirdly, a multi criteria decision-making model based on improved Choquet fuzzy integral and deviation degree is proposed for a multi criteria evaluation problem with initial data in the form of crisp values, interval numbers and linguistic fuzzy hesitant sets. The deviation degree can deal with multi-source heterogeneous data and Choquet fuzzy integral improved with Mobius transformation can eliminate the overlap information between criteria. Finally, the case study in Jilin is given to illustrate the effective of the proposed evaluation criteria and technique. From the results, the project 4: wind power coupling compressed air energy storage system with meshing switch is the most suitable alternative for the wand farm, followed by the project of wind power coupling compressed air energy storage system with variable configuration. Moreover, the sensitivity analysis reveals that the project 4 always occupies its top ranking when its weight is floating within a certain range. At last, some policy implications to promote wind power industry are given for the government.

Utility-Numbers Theory

Fuzzy theory defined by Zadeh has been developed through both analytical and computational categories of diverse sciences in light of time. The goal of applying fuzzy theory is to incorporate uncertainties with conventional deterministic calculations to enhance the reliability of results. Since fuzzy theory has been developed and carried out by so many researchers, various types of generalizations, including Z-numbers, type-2 fuzzy sets, intuitionistic sets, and hesitant sets, have been revealed to estimate real-world variables more accurately. Toward these goals, utility-numbers or H-numbers theory is proposed with an ordered set of (n, M (n), N(n)), to assign satisfaction degrees to corresponding uncertain numbers. The first component, n, is a constraint on the values, which a stochastic real-structured variable, X, may take. The following components, M (n), N(n), represent the maximum and minimum utilities assigned to the first component, respectively. This paper first substantiates immediate H-numbers as (n, M (n)), and the mathematical operations over them; then, these H-numbers are elaborated to (n, M (n), N(n)) in which both the minimum and maximum utility values are considered. Meanwhile, the main contribution of the proposed model leads to obtain satisfaction value for each fuzzy number component and helps practitioners to concentrate on total satisfaction that is aggregated by each alternative. The proposed model is validated by comparison tables and reasonable values over conventional fuzzy sets.

Sustainable Assessment for Selecting the Best Alternative of Reclaimed Water Use Under Hesitant Fuzzy Multi-Criteria Decision Making

Reuse of wastewater is considered a major source of water retention and improvement in drought prone areas. The water recovered from renewable water resource project is used for many utilities. Here, every application is considered to be an alternative. When assessing, it is necessary to evaluate and assume that all users are safe and helpful. In this way, every alternative assessment is evaluated based on the social acceptance, environmental protection, economy, technology and operation and health risk. Then the best alternative is chosen. When recycled water is recovered and we reuse in water management plants, it can lead to multi-criteria decision making processes related to uncertain critical assessments. In general hesitant fuzzy set is represented by a number of possible values for each of element in a set. Hesitant set is used as a powerful tool to express uncertainty and hesitant information in the decision processor. The aim of this research article is to propose a new methodology of MCDM in hesitant fuzzy (HF) namely, HF-CRITIC (Hesitant Fuzzy Criteria Importance Through Inter-criteria Correlation) and HF-MAUT (Hesitant Fuzzy Multi Attribute Utility Theory) to get hesitant fuzzy information in order to select the best alternative for using reclaimed water use in India. Here, five reclaimed water plants have been identified as alternatives. These alternatives are evaluated with five criteria namely social, economic, environmental, technical/operation and health risk. After evaluation, the result shows that ground water recharge is the best alternative for reclaimed water use.

Prospect Theory and Interval-Valued Hesitant Set for Safety Evacuation Model

The study applies the research results of prospect theory and multi attribute decision making theory, combined with the complexity, uncertainty and multifactor influence of the underground mine fire system and takes the decision makers’ psychological behavior of emotion and intuition into full account to establish the intuitionistic fuzzy multiple attribute decision making method that is based on the prospect theory. The model established by this method can explain the decision maker’s safety evacuation decision behavior in the complex system of underground mine fire due to the uncertainty of the environment, imperfection of the information and human psychological behavior and other factors.

Hesitant sets and hesitant relations

Hesitant sets and hesitant relations

A Novel Multiple Attribute Decision Making Framework based on Hamacher Operations in Patron Driven Acquisitions Mode of Library Management

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. Some new hesitant fuzzy operational rules are introduced based on the Hamacher t-conorm and t-norm, whereby we present a multi attribute decision making method under hesitant fuzzy information. In the daily management of library, book selection problem usually is very complex and unstructured, because variety of uncontrollable and unpredictable factors affects the evaluation and decision-making process at different levels. By integrating the multiple attribute decision making method with (Patron Driven Acquisitions, PDA) mode, a novel multiple attribute decision making framework based on Hamacher operations in PDA mode is proposed to select the best book providing the highest satisfaction for the attributes determined in this paper. Finally, a case study is so demonstrated to verify the reliability and applicability of the proposed framework.

The Generalized Hybrid Weighted Average Operator Based on Interval Neutrosophic Hesitant Set and Its Application to Multiple Attribute Decision Making

The Neutrosophic set and Hesitant set are the important tools to describe the fuzzy information, in this paper, we combine the interval neutrosophic sets (INSs) and interval valued hesitant fuzzy sets (IVHFSs), and propose the concept of the interval neutrosophic hesitant fuzzy set (INHFS) in order to use the advantages of them.

The Generalized Hybrid Weighted Average Operator Based on Interval Neutrosophic Hesitant Set and Its Application to Multiple Attribute Decision Making

The Generalized Hybrid Weighted Average Operator Based on Interval Neutrosophic Hesitant Set and Its Application to Multiple Attribute Decision Making

Hesitant fuzzy Hamacher aggregation operators for multicriteria decision making

As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. We first introduce some new operational rules of hesitant fuzzy sets based on the Hamacher t-norm and t-conorm, in which a family of hesitant fuzzy Hamacher operators is proposed for aggregating hesitant fuzzy information. Some basic properties of these proposed operators are given, and the relationships between them are shown in detail. We further discuss the interrelations between the proposed aggregation operators and the existing hesitant fuzzy aggregation operators. Applying the proposed hesitant fuzzy operators, we develop a new technique for hesitant fuzzy multicriteria decision making problems. Finally, the effectiveness of the proposed technique is illustrated by mean of a practical example.

The generalized hybrid weighted average operator based on interval neutrosophic hesitant set and its application to multiple attribute decision making

The Neutrosophic set and Hesitant set are the important and effective tools to describe the uncertain information. In this paper, we combine the interval neutrosophic sets and interval-valued hesitant fuzzy sets, and propose the concept of the interval neutrosophic hesitant fuzzy set (INHFS) in order to use the advantages of them. Then, we present the operations and comparison method of INHFS, and develop some new aggregation operators for the interval neutrosophic hesitant fuzzy information, including interval neutrosophic hesitant fuzzy generalized weighted operator, interval neutrosophic hesitant fuzzy generalized ordered weighted operator, and interval neutrosophic hesitant fuzzy generalized hybrid weighted operator, and discuss some properties. Furthermore, we propose the decision-making method for multiple attribute group decision making with interval neutrosophic hesitant fuzzy information, and give the detail decision steps. Finally, we give an illustrate example to show the process of decision making.

Typical Hesitant Fuzzy Negations

Since the seminal paper of fuzzy set theory by Zadeh in 1965, many extensions have been proposed to overcome the difficulty for assigning the membership degrees. In recent years, a new extension, the hesitant fuzzy sets, has attracted a lot of interest due to its usefulness to handle those problems in which it is difficult to provide accurately a single membership value; since for hesitant sets, membership values are given by a whole set of values. On the other hand, since fuzzy negations have an important role in applications as well as in the theoretical approach to of fuzzy logics, it is important to study an extension of the concept of fuzzy negation for hesitant fuzzy degrees (elements). In this paper, we propose such a definition and we study some of the main properties of this new concept.