Hesitant fuzzy sets are very useful for dealing with group decision-making problems when experts have hesitation among several possible memberships for an element in a set. Recently, many researchers have used these concepts in clustering analysis and decision-making. In this article, the notions of Hesitant hybrid subsemigroups and Hesitant hybrid left(resp., right) ideals in a semigroup are introduced, and several properties are investigated. The concept of Hesitant hybrid product is also introduced, and properties of Hesitant hybrid subsemigroups and hybrid left (resp., right) ideals are considered using the notion of Hesitant hybrid product. Relations between Hesitant hybrid intersection and Hesitant hybrid product are exhibited. Additionally, we establish Hesitant hybrid interior ideals in semigroups and study theirproperties. Furthermore, we prove that in regular and intra-regular semigroups, the Hesitant hybrid ideal and the Hesitant hybrid interior ideals are coincide.

One of the attractive subjects in decision analysis is the in-vestigating of the uncertain data which is inevitable in many real-world applications. Fuzzy sets theory has been introduced to investigate the uncertain data which formulates the uncertainty by using the member-ship functions. However, in many real world applications, it is di, cult to determine the exact amount of the membership value and so the skepticism can be raised during the decision-making process. The new perspective manages the uncertainty caused by the skepticism and in this case, the most important issues are to collect the Hesitant fuzzy information and to select the optimal alternative. This study develops the deviation-oriented Hesitant fuzzy envelopment analysis (DHFEA) based on deviation values. The hybrid fuzzy DHFEA/AHP approach derives the AHP pair-wise comparisons by Hesitant fuzzy DEA and uti-lizes AHP to fully rank units. It shows that the proposed approach generates a logical ranking of units that has perfect compatibility with Hesitant fuzzy DEA ranking and there is no any form of subjective anal-ysis engaged within the methodology. The potential application of the proposed method is illustrated with a numerical example.

Optimizing airport security screening processes is imperative in the modern age, ensuring a delicate balance between stringent security measures and efficient, seamless travel experiences for passengers. This research presents an innovative paradigm for decision-making that optimizes airport security screening procedures. By utilizing sophisticated fuzzy concepts, particularly Fermatean Probabilistic Hesitant Fuzzy Sets, the research presents new hybrid aggregation techniques known as Fermatean Probabilistic Hesitant hybrid Weighted Averaging FePHHWA and hybrid Weighted Geometric FePHHWG. These procedures are intended to improve the decision-making process by providing a thorough method of addressing the intricacies of security screening. In addition to showcasing the flexibility and effectiveness of Fermatean Probabilistic Hesitant Fuzzy Sets, the suggested technique creates a strong foundation for resolving issues with airport security screening by utilizing the recently developed hybrid aggregation processes.

Optimizing airport security screening processes is imperative in the modern age, ensuring a delicate balance between stringent security measures and efficient, seamless travel experiences for passengers. This research presents an innovative paradigm for decision-making that optimizes airport security screening procedures. By utilizing sophisticated fuzzy concepts, particularly Fermatean Probabilistic Hesitant Fuzzy Sets, the research presents new hybrid aggregation techniques known as Fermatean Probabilistic Hesitant hybrid Weighted Averaging FePHHWA and hybrid Weighted Geometric FePHHWG. These procedures are intended to improve the decision-making process by providing a thorough method of addressing the intricacies of security screening. In addition to showcasing the flexibility and effectiveness of Fermatean Probabilistic Hesitant Fuzzy Sets, the suggested technique creates a strong foundation for resolving issues with airport security screening by utilizing the recently developed hybrid aggregation processes.

High dimensional microarray datasets are difficult to classify since they have many features with small number of instances and imbalanced distribution of classes. This paper proposes a filter-based feature selection method to improve the classification performance of microarray datasets by selecting the significant features. Combining the concepts of rough sets, weighted rough set, fuzzy rough set and Hesitant fuzzy sets for developing an effective algorithm is the main contribution of this paper. The mentioned method has two steps, in the first step, four discretization approaches are applied to discretize continuous datasets and selects a primary subset of features by combining of weighted rough set dependency degree and information gain via Hesitant fuzzy aggregation approach. In the second step, a significance measure of features (defined by fuzzy rough concepts) is employed to remove redundant features from primary set. The Wilcoxon Signed Ranked tes (A Non-parametric statistical test) is conducted for comparing the presented method with ten feature selection methods across seven datasets. The results of experiments show that the proposed method is able to select a significant subset of features and it is an effective method in the literature in terms of classification performance and simplicity.

This paper presents the introduction of two novel equation types: the partial Hesitant fuzzy equation and the half Hesitant fuzzy equation‎. Additionally, ‎ an efficient method is proposed to solve these equations by defining four solution categories: Controllable‎, ‎Tolerable Solution Set (TSS)‎, Controllable ‎Solution Set (CSS)‎, ‎and Algebraic Solution Set (ASS)‎. ‎ Furthermore, ‎ the paper establishes eight theorems that explore different types of solutions and lay out the conditions for the existence and non-existence of Hesitant fuzzy solutions‎. ‎ The practicality of the proposed method is demonstrated through numerical examples.

Nowadays, the fundamental role of having a purpose for life in physical and mental health has been confirmed. According to victor frankl, presence of a purpose in life gives life a meaning and increases resilience against pains and traumas. The importance of the purpose in life construct reveals the need for a reliable and valid tool to measure it. Crumbaugh and Maholick's purpose in life questionnaire is the first and one of the most applied tools for the assessment of life's purposefulness. The aim of this research is to determine the factor structure of purpose in life questionnaire. The questionnaire was administered on 206 students who were selected through random stratified sampling at Ferdowsi University of Mashhad. Exploratory factor analysis showed that there are two factors "comprehension" and "purpose" and this finding were confirmed by confirmatory factor analysis. Altogether results of this research showed factor validity of the purpose in life questionnaire with a two factor pattern

In the real world, in most cases, such as industry, management, and even in daily life, we encounter optimization and decision-making problems that require the opinions of experts and masters on the problem to be able to make the best decision. In these cases, it is necessary to use an optimization problem with Hesitant fuzzy parameters.There are few studies on Hesitant fuzzy linear programming (HFLP) problems. Therefore,in this paper, we  consider such problems.Especially, we study HFLP problems with Hesitant cost coefficients. For this purpose,we propose the simplex  method to solve the introduced optimization problems and draw a flowchart of the proposed  method.Finally, by solving two illustrative examples with Hesitant fuzzy information, we examine the applicability of the proposed method.

In recent years, industrial clusters have received considerable attention from economists and industry analysts because they are seen as the main reason for certain economic regions' economic growth and success. For many Industrial States Organization, the selection of industrial clusters has become a critical strategic consideration due to the Budget allocation priority. In this paper, an extended qualitative flexible multiple (QUALIFLEX) methods is used to solve problems regarding the priority among this cluster using probability Hesitant fuzzy information, which can lead to allocating the budget for industrial clusters more effectively. For more accuracy, we have applied a Hesitant fuzzy Topsis for prioritizing. Both rankings have been aggregated by the Copeland method. From our research results, the Larestan Muscat is of great importance, and Abade Inlaid Wood, Citrus packaging, Shiraz Marquetry, and Niriz stone have ranked respectively.