Fermatean Hesitant Fuzzy Sets with Medical Decision Making Application

Fermatean fuzzy set idea obtained by combining fermatean fuzzy sets and hesitant fuzzy sets can be used in practice to simplify the solution of complicated multi-criteria decision-making (MCDM) problems. Initially, the notion of fermatean hesitant fuzzy set is given and the operations related to this concept are presented. Aggregation operators according to fermatean hesitant fuzzy sets are given and basic properties of these operators are studied. To choose the best alternative in practice, a novel MCDM method that is obtained with operators has been created. Finally, an example of infectious diseases was examined to indicate the effectiveness of the suggested techniques.

Analysis and Impact Evaluation of Entrepreneurs’ Improvisational Behavior Trigger Patterns

How entrepreneurial firms can enhance the level of exploratory and exploitative improvisation in a balanced manner to enhance organizational dynamics has become an important research topic. Current research on the triggers of duality entrepreneurial improvisation has just started, exploring mainly abstract characteristic variables, and has not paid attention to the impact of entrepreneurs’ daily behaviors. In order to make up for the shortcomings of current research, the research goal of this paper is to construct a triggering model of entrepreneurs’ improvisation based on the research of entrepreneurs’ daily behaviors and then to evaluate the influence of the improvisational behavior trigger patterns. Based on the paradoxical and theoretical perspective of duality, a structured observation method is used to explore which behavioral patterns of entrepreneurs tend to trigger dual improvisational behaviors in themselves, their teams, and their organizations. After observing and recording the creators and collecting phenomenal data, six entrepreneurial behavior patterns containing 39 specific operational behaviors have been extracted from the phenomenal data by drawing on the rooted theory approach. In addition, the influence of entrepreneurial patterns is evaluated and ranked using the pairwise hesitant fuzzy set evaluation method. This study reveals the relationship between entrepreneurs’ daily behaviors and dyadic entrepreneurial improvisation at the operational level and provides guiding plans for entrepreneurs to improve their own and their organizations’ improvisation levels.

Decision-Making Approach Based on Generalized Aggregation Operators with Complex Single-Valued Neutrosophic Hesitant Fuzzy Set Information

A strategic decision-making technique can help the decision maker to accomplish and analyze the information in an efficient manner. However, in our real life, an uncertainty will play a dominant role during the information collection phase. To handle such uncertainties in the data, we present a decision-making algorithm under the single-valued neutrosophic (SVN) environment. The SVN is a powerful way to deal the information in terms of three degrees, namely, “truth,” “falsity,” and “indeterminacy,” which all are considered independent. The main objective of this study is divided into three folds. In the first fold, we state the novel concept of complex SVN hesitant fuzzy (CSVNHF) set by incorporating the features of the SVN, complex numbers, and the hesitant element. The various fundamental and algebraic laws of the proposed CSVNHF set are described in details. The second fold is to state the various aggregation operators to obtain the aggregated values of the considered CSVNHF information. For this, we stated several generalized averaging operators, namely, CSVNHF generalized weighted averaging, ordered weighted average, and hybrid average. The various properties of these operators are also stated. Finally, we discuss a multiattribute decision-making (MADM) algorithm based on the proposed operators to address the problems under the CSVNHF environment. A numerical example is given to illustrate the work and compare the results with the existing studies’ results. Also, the sensitivity analysis and advantages of the stated algorithm are given in the work to verify and strengthen the study.

Probabilistic Hesitant Fuzzy Recognition Method Based on Comprehensive Characteristic Distance Measure

The probabilistic hesitant fuzzy set (PHFS) and probabilistic hesitant fuzzy element (PHFE) have drawn the attention of scholars in recent years and have been applied in several disciplines. However, existing PHFE distance measures have several shortcomings. Therefore, in this study, we propose a new PHFE multi-attribute decision-making (MADM) method, based on the comprehensive characteristic distance measure. First, we devise a new PHFE comparison method and then define the comprehensive characteristic distance measure, based on four characteristics. Finally, based on the traditional TODIM method and prospect theory, we propose a new PHFE recognition method. The comprehensive characteristic distance measure avoids the introduction of errors, including an unequal number of elements and order adjustment. Meanwhile, the four characteristics make the measurement results more comprehensive and reasonable, and applicable to a variety of situations while avoiding counterintuitive phenomena. Compared with traditional approaches, the method in this article selects appropriate parameters according to actual situations to obtain more objective conclusions, which results in better flexibility and operability. Besides, the simulation results verify the effectiveness of this recognition method.

Fixed points of hesitant fuzzy set-valued maps with applications

In this paper, the notion of hesitant fuzzy fixed points is introduced. To this end, we define Suzuki-type $(\alpha,\beta)$-weak contractions in the framework of hesitant fuzzy set-valued maps, thereby establishing some corresponding fixed point theorems. The presented concept herein is an extension of fuzzy set-valued and multi-valued mappings in the corresponding literature. Examples are provided to support the assertions and generality of our obtained ideas. Moreover, one of our results is applied to investigate sufficient conditions for existence of a class of functional equation arising in dynamic programming.

The cross-entropy and improved distance measures for complex q-rung orthopair hesitant fuzzy sets and their applications in multi-criteria decision-making

The complex q-rung orthopair fuzzy set (Cq-ROFS) is the extension of complex Pythagorean fuzzy set (CPFS) in which the sum of the q-power of the real part (imaginary part) of the support for and the q-power of the real part (imaginary part) of the support against is limited by one; however, it is difficult to express the hesitant information. In this study, the conception of complex q-rung orthopair hesitant fuzzy set (Cq-ROHFS) by combining the Cq-ROFS and hesitant fuzzy set (HFS) is proposed, and its properties are discussed, obviously, Cq-ROHFS can reflect the uncertainties in structure and in detailed evaluations. Further, some distance measures (DMs) and cross-entropy measures (CEMs) are developed based on complex multiple fuzzy sets. Moreover, these proposed measures are utilized to solve a multi-criteria decision-making problem based on TOPSIS (technique for order preference by similarity to ideal solution) method. Then, the advantages and superiority of the proposed measures are explained by the experimental results and comparisons with some existing methods.

Normal Wiggly Probabilistic Hesitant Fuzzy Information for Environmental Quality Evaluation

As a valuable tool for representing uncertain information, probabilistic hesitant fuzzy sets (PHFS) have gained considerable recognition and in-depth discussion in recent years to increase the flexibility and manifest hesitant information in decision-making problems. However, decision-makers (DMs) cannot express all preferences only through a few probabilistic terms in actual decision-making. Much critical information is hidden behind the original information provided by the DMs. Keeping that in mind, we are interested in mining deeper uncertain information from the original probabilistic hesitant fuzzy evaluation data. To achieve the target, we put forward a novel representation tool called the normal wiggly probabilistic hesitant fuzzy set (NWPHFS) to extract deeper uncertain preferences from original probabilistic information. NWPHFS retains the original evaluation information and carries and assesses the potential uncertain details for increasing the rationality of decision-making outcomes. Herein, we propose some fundamental concepts of NWPHFS, for instance, some elementary operational laws, distance measures between two NWPHFSs, and score function. We also suggest two new aggregation operators, that is, the normal wiggly probabilistic hesitant fuzzy weighted averaging (NWPHFWA) and normal wiggly probabilistic hesitant fuzzy weighted geometric (NWPHFWG). A novel mechanism is proposed here to work out multiattribute decision-making (MADM) in solving normal wiggly probabilistic decision-making problems. Through a practical example of environmental quality assessment, the specific calculation steps of this method are epitomized. Finally, we have demonstrated the feasibility and advancement of the proposed approach via a comprehensive comparative study.

Cosine Similarity Measure of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Set and Their Applications to Multi-Attribute Decision-Making Process

Cosine similarity measure plays a significant role in various fields. Literature consultation confirms that the theory of cosine similarity measure has received a great interest and attention from the researchers in the world. The concept of Interval Valued Bipolar Neutrosophic Hesitant Fuzzy Sets (IVBNHFS) is recently presented and very interesting. Every element in IVBNHFS is characterized by six independent membership functions (three positive and three negative). There is no investigation on the Cosine Similarity Measure (CSM) of IVBNHFS. In this study, we firstly define a CSM and a weighted CSM between two IVBNHFS and their applications to Multi-Attribute Decision Making (MADM) process in the Interval Valued Bipolar Neutrosophic Hesitant Fuzzy (IVBNHF) setting. And, we establish some properties of CSM and a weighted CSM. We use this strategy to find out the best alternative in MADM case. Then, the new approach to clarify MADM problems in IVBNHF setting is presented in algorithmic form. And, we solve an illustrative case of MADM to demonstrate the effectiveness, workability, and appropriateness of the proposed approach. Finally, the main conclusion and future opportunity of research paper are overviewed and compiled.