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The Pythagorean fuzzy sets conveniently capture unreliable, ambiguous, and uncertain information, especially in problems involving multiple and opposing criteria. Pythagorean fuzzy sets are one of the popular generalizations of the intuitionistic fuzzy sets. They are instrumental in expressing and managing hesitant under uncertain environments, so they have been involved extensively in a diversity of scientific fields. This paper proposes a new Pythagorean entropy for Multi-Criteria Decision-Analysis (MCDA) problems. The entropy measures the fuzziness of two fuzzy sets and has an influential position in fuzzy functions. The more comprehensive the entropy, the more inadequate the ambiguity, so the decision-making established on entropy is beneficial. The COmplex PRoportional ASsessment (COPRAS) method is used to tackle uncertainty issues in MCDA and considers the singularity of one alternative over the rest of them. This can be enforced to maximize and minimize relevant criteria in an assessment where multiple opposing criteria are considered. Using the Pythagorean sets, we represent a decisional problem solution by using the COPRAS approach and the new Entropy measure. [ABSTRACT FROM AUTHOR]

Multi-criteria decision-analysis (MCDA) methods have been widely applied by many researchers in various fields of study. One of the numerous MCDA methods, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) under fuzzy environment, namely fuzzy TOPSIS, has been successfully applied in many practical, real-world challenges. This paper provides a short review of fuzzy TOPSIS applications. The research is based on 25 studies conducted in the years 2009 - 2018. Most relevant and most cited papers concerned with fuzzy TOPSIS technique were analyzed and categorized into application areas, such as supply chain, environment, energy sources, business, healthcare. Fuzzy TOPSIS implementations are examined and compared by approaches used, such as fuzzy sets, hesitant fuzzy sets or intuitionistic fuzzy sets, by other methods combined with fuzzy TOPSIS, such as fuzzy Analytic Hierarchic Process (AHP) or enhancements for group decision-making and by a number of alternatives and criteria used. Finally, insights into ongoing trends, most popular approaches, and directions of study concerning the fuzzy TOPSIS method are presented. [ABSTRACT FROM AUTHOR]

The preference of one alternative over another is a useful way to express the opinion of the decision-maker. In the process of group decision-making, preference relations are used in preference modeling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty and, in many scenarios of decision-making problems, the probabilities of different events affect the decision-making process directly. In order to deal with this issue, the hesitant probabilistic multiplicative preference relation (HPMPR) is defined in this paper. Furthermore, consistency of the HPMPR and consensus among decision makers are studied here. In this respect, many algorithms are developed to achieve consistency of HPMPRs, reasonable consensus between decision-makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision-making. Lastly, we present a case study with complete illustration of the proposed model and discuss the effects of probabilities on decision-making validating the importance of the introduction of probability in hesitant multiplicative preference relations. [ABSTRACT FROM AUTHOR]

The correlation between two different variables possesses an important place in the field of statistics. Correlation is used to estimate the change in one variable associated with another variable. The concept of correlation is well known but it is not used within intuitionistic 2-tuple fuzzy linguistic (I2TFL) information. To investigate the best alternative among different alternatives in multi-criteria group decision-making (MCGDM) problems, our aim is to propose a formula for the correlation coefficient based on I2TFL information. A new type of information energy for I2TFL element is defined first and then the correlation coefficient between I2TFL information are discussed based on this information energy. In addition, considering that different I2TFL elements may have different criteria weights, the weighted correlation coefficients are further investigated. Some of the properties of the proposed correlation coefficient are also mentioned and verified. Furthermore, best-worst method (BWM) is expanded to uncertain situations like I2TFL BWM, where the data is expressed in I2TFL form. Utilizing the idea of BWM, linearly constrained optimization problems are framed to acquire weights of criteria in the context of I2TFL environment. Two numerical illustrations are described to confirm the effectiveness of the proposed work in the cases where the criteria weights are either known or unknown. Finally, comparative discussions between the proposed approach and existing practices are taken to reveal the importance of our work. • Multi-criteria group decision-making based on the correlation coefficient. • Intuitionistic 2-tuple fuzzy linguistic environment (I2TFL). • Correlation coefficient between I2TFL. • Best-Worst method. [ABSTRACT FROM AUTHOR]

• Priority vector construction ways in BWM method under I2TL information are proposed. • Hamacher aggregation operations for I2TL are introduced. • MCGDM framework under I2TL information is proposed. Sometimes in the sense of intuitionist 2-tuple linguistic (I2TL) sets, experts may not be able to decide the most suitable criterion weight vector for multicriteria decision making (MCDM). To avoid this situation, the decision-makers (DMs) can use the Best-Worst method (BWM), in which DMs choose the best (most significant) criterion and the worst (least significant) criterion and then provide two preference vectors by comparing criteria best to other (BO) and other to worst (OW). In the Nonlinear Best-Worst Method (NBWM) it is more complicated to find the unique solution of the model. Therefore, the main goal of this study is to propose two approaches to BWM, namely, Linear Best-Worst Method (LBWM) and Euclidean Best-Worst method (EBWM) to achieve the best criteria priority vector for Multi-Criteria Group Decision Making (MCGDM) problems in the context of I2TL information. In the computational process of MCDM problems, we have to aggregate I2TL elements into a global one. Consequently, under certain critical properties, we are creating some operational laws for I2TL elements based on Hamacher operations. Also, the intuitionistic 2-tuple linguistic Hamacher weighted average (I2TLHWA), and the intuitionistic 2-tuple linguistic Hamacher weighted geometric (I2TLHWG) operators are introduced with the assistance of Hamacher operations and I2TL elements. Subsequently, we analyze some of the I2TLHWA operator's related properties and we propose MCGDM framework under I2TL information. Finally, we demonstrate the validity and efficiency of our method and operations. [ABSTRACT FROM AUTHOR]

Ambiguous and uncertain facts can be handled using a hesitant 2-tuple linguistic set (H2TLS), an important expansion of the 2-tuple linguistic set. The vagueness and uncertainty of data can be grabbed by using aggregation operators. Therefore, aggregation operators play an important role in computational processes to merge the information provided by decision makers (DMs). Furthermore, the aggregation operator is a potential mechanism for merging multisource data which is synonymous with cooperative preference. The aggregation operators need to be studied and analyzed from various perspectives to represent complex choice situations more readily and capture the diverse experiences of DMs. In this manuscript, we propose some valuable operational laws for H2TLS. These new operational laws work through the individual aggregation of linguistic words and the collection of translation parameters. We introduced a hesitant 2-tuple linguistic weighted average (H2TLWA) operator to solve multi-criteria group decision-making (MCGDM) problems. We also define hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator, hesitant 2-tuple linguistic geometric Bonferroni mean (H2TLGBM) operator, hesitant 2-tuple linguistic Heronian mean (H2TLHM) operator, and a hesitant 2-tuple linguistic geometric Heronian mean (H2TLGHM) operator based on the novel operational laws proposed in this paper. We define the aggregation operators for addition, subtraction, multiplication, division, scalar multiplication, power and complement with their respective properties. An application example and comparison analysis were examined to show the usefulness and practicality of the work. [ABSTRACT FROM AUTHOR]

The multi-criteria decision-making (MCDM) problem has a solution whose quality can be affected by the experts' inclinations. Under essential conditions, the fuzzy MCDM method can provide more acceptable and efficient outcomes to select the best alternatives. This work consists of a consensus-based technique for selecting and evaluating suppliers in an incomplete fuzzy preference relations (IFPRs) environment utilizing T L -transitivity (Lukasiewicz transitivity). The suggested method is developed based on the criteria of the Analytical Hierarchy Process (AHP) Fframework, and the decision matrix is construtced using consistent fuzzy preference relations (FPRs). We use the symmetrical decisional matrix approach. A variety of numerical explanations and an analysis of quantitative results illustrate the suggested methodology's logic and effectiveness. [ABSTRACT FROM AUTHOR]

Over the past few decades, several researchers and professionals have focused on the development and application of multi-criteria group decision making (MCGDM) methods under a fuzzy environment in different areas and disciplines. This complex research area has become one of the more popular topics, and it seems that this trend will be increasing. In this paper, we propose a new MCGDM approach combining intuitionistic fuzzy sets (IFSs) and the Characteristic Object Method (COMET) for solving the group decision making (GDM) problems. The COMET method is resistant to the rank reversal phenomenon, and at the same time it remains relatively simple and intuitive in practical problems. This method can be used for both symmetric and asymmetric information. The Triangular Intuitionistic Fuzzy Numbers (TIFNs) have been used to handle uncertain data. This concept can ensure the preference information about an alternative under specific criteria more comprehensively and allows for easy modelling of symmetrical or asymmetrical linguistic values. Each expert provides the membership and non-membership degree values of intuitionistic fuzzy numbers (IFNs). So this approach deals with a different kind of uncertainty than with hesitant fuzzy sets (HFSs). The proposed combination of COMET and IFSs required an adaptation of the matrix of expert judgment (MEJ) and allowed to capture the behaviour aspects of the decision makers (DMs). Therefore, we get more reliable solutions while solving MCGDM problems. Finally, the proposed method is presented in a simple academic example. [ABSTRACT FROM AUTHOR]