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An introduction is presented in which the editor discusses various papers within the issue on topics including aggregation operators, analytic hierarchy process and support vector machines.

The fire-fighting system is one of the proactive technical barriers related to liquefied petroleum gas storage tank safety. This paper presents an integrated approach that uses fuzzy set theory, an improved-dependent uncertain ordered weighted averaging operator and fault tree analysis to handle uncertainty in the unavailability assessment of fire-fighting systems. In this study, the center of area is used to defuzzify triangular fuzzy numbers. Furthermore, for the fire-fighting system fault tree, importance analysis, including Fussell–Vesely importance measure and risk reduction worth of basic events, are performed to identify the weak links of the fire-fighting system. In addition, a real case study on a fire-fighting system for a liquefied petroleum gas storage system in an LPG unit in Algeria is provided to illustrate the effectiveness of the proposed methodology. The research results show that the proposed methodology makes it possible to assess the unavailability of the entire system by analyzing weak links. Consequently, some suggestions are given to take preventive–corrective actions in advance, in order to reduce the failure probability of fire-fighting system and assist the practitioners in setting priorities for improving safety procedures in liquefied petroleum gas storage tanks. The study provides references for analyzing safety barriers in a complex system. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate three new methods to regulate and analyze the spreading of coronavirus disease (COVID-19). COVID-19 started in the city of Wuhan, China at the end of 2019 and spread to the whole world in a short time. This infection caused millions of infected cases globally and still poses a disturbing situation for the people. Recently, some mathematical models have been constructed for better understanding of the coronavirus infection. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. So, at the current position, it is a challenge for the world to control the spreading of COVID-19. Therefore, the aim of this paper is to utilize fuzzy logic to control the transmission and spreading of COVID-19. Here, we develop three new methods such as the generalized interval-valued intuitionistic fuzzy Einstein weighted geometric (GIVIFEWG) operator, the generalized interval-valued intuitionistic fuzzy Einstein ordered weighted geometric (GIVIFEOWG) operator, and the generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric (GIVIFEHG) operator. Intuitionistic fuzzy information for interval-valued is the moral and decent method to precise the fuzzy information for judgment or decision and Einstein operations are the best approximations, and the generalized aggregation operators are a generalization of most aggregation operators so, in these notes, we can spread the Einstein operations to aggregate the interval-valued intuitionistic fuzzy information based on the generalized aggregation operators. At the end of the paper, an illustration of the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested approach, showing the feasibility and reliability of the new methods. [ABSTRACT FROM AUTHOR]

In this paper, we want to investigate some theorems about -cubic sets in [Sh. Rashid, M. Gulistan, Y. B. Jun, S. Khan and S. Kadry, -cubic sets and aggregation operators, J. Intell. Fuzzy Syst.37(4) (2019) 5009–5023] and while correcting these theorems, we get new results in this issue and at the end we present an application regarding decision making. First, by using some examples, we show that the conditions of some theorems in above-mentioned paper are not true in general and then we attempt to correct these theorems and proofs. Moreover, we discuss some new related results in -cubic sets. Finally, we discuss the score function and -cubic weighted average operator of -cubic sets for application in physical and different engineering regions. [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses various reports within the issue on topics including decision support approach, multiple criteria decision making, and aggregation operators.

Confidence level plays an important role in decision making in daily life. Therefore, the focus of our paper is to develop the idea of confidence level. With the help of confidence level in this paper, we explore some new operators, namely confidence intuitionistic trapezoidal fuzzy Einstein weighted averaging (abbreviated as CITFEWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted averaging (abbreviated as CITFEOWA) operator, confidence intuitionistic trapezoidal fuzzy Einstein hybrid averaging (abbreviated as CITFEHA) operator, confidence intuitionistic trapezoidal fuzzy Einstein weighted geometric (abbreviated as CITFEWG) operator, confidence intuitionistic trapezoidal fuzzy Einstein ordered weighted geometric (abbreviated as CITFEOWG) operator and confidence intuitionistic trapezoidal fuzzy Einstein hybrid geometric (abbreviated as CITFEHG) operator. The benefit of the confidence approaches is that these techniques not only deliver evidence of the problems to the experts, but these operators and methods also develop the grades of the decision makers of that these experts are familiar with the option for the selection. To develop the proposed operators, we investigate and study some of their basic properties. To show the importance and efficiency of the new methods, these methods are applied to decision making. Lastly, an example is given for the confirmation of the viability and availability of the proposed approaches and methods. [ABSTRACT FROM AUTHOR]

Due to the complexity of the problem in the actual group management decision, the ambiguity of the information of all parties and the uncertainty of the decision environment, it is often difficult for decision-makers to describe the decision information by quantitative methods, but to give uncertain linguistic variables. Based on the analysis of previous research results, this paper proposes a group management decision-making aggregation model based on relative entropy and norm operator. First, the model uses the operation of T -norm and new T -norm operator to make the fuzzy set satisfy the ranking rate and contradiction rate. Then, based on the reliability of relative entropy, the attribute weights of different expert decisions are obtained, and the optimal assembly model of the corresponding group decision is established, respectively. The optimal solution and decision algorithm are given for each optimization model. The last example of the algorithm proves the validity and feasibility of the model, and can effectively avoid the distortion and distortion in the process of group management decision preference aggregation. [ABSTRACT FROM AUTHOR]

The cloud model (CM) is an important tool to describe qualitative concept by the quantitative method, and the Maclaurin symmetric mean (MSM) can capture the interrelationship among the multi-inputs and it can generalize most of existing operators. In this paper, we firstly convert the uncertain linguistic variables (ULVs), which are easily used to express the qualitative information, to CM. Then, we combine the MSM with the CM, and propose the cloud MSM (CMSM) operator and cloud weighted MSM (CWMSM) operator. In addition, we explore some of their desirable features and develop a new approach to deal with some multi-attribute group decision-making (MAGDM) problems under the uncertain environment based on the proposed operators. Finally, by comparing with other approaches, an illustrative example is arranged to demonstrate the usability of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, we are mainly to solve the functional equations given by the modularity condition. Modularity condition between disjunctive (resp. conjunctive) uni-nullnorms and some most studied classes of binary aggregation operators (i.e., t-norms, t-conorms, uninorms and semi-t-operators) are discussed. Both positive and negative results of modularity condition for uni-nullnorms are obtained. Since uni-nullnorms are an extension of nullnorms and uninorms, previous results about modularity condition for nullnorms and uninorms in max and min can be obtained as simple corollaries. [ABSTRACT FROM AUTHOR]

The early diagnosis of the glaucoma disease in the eye is crucial to avoid vision loss. This paper proposes an efficient computer-aided detection (CAD) system for diagnosing glaucoma based on fundus images, deep transfer learning and fuzzy aggregation operators. Specifically, the proposed CAD system includes three stages: (1) Detection of the region of interest of the optic disc using an efficient deep learning network, (2) Classification of images based on different pre-trained deep convolutional neural networks and support vector machines, and (3) Use of fuzzy aggregation operators to fuse the predictions of glaucoma classifiers. We used three popular yet robust aggregators: ordered weighted averaging (OWA) operator, weighted power mean (WPM), and exponential mean (EXM). We assessed the efficacy of the proposed glaucoma CAD system on three public datasets: DRISHTI-GS1, RIM-ONE, and REFUGE. The proposed conjunctive OWA aggregation method (Conj-OWA) achieves the best glaucoma classification results. Specifically, it achieves accuracy values of 90.2%, 97.8%, and 94.3% and area under the curve (AUC) values of 95.3%, 99.8%, and 96.2%, respectively, on DRISHTI-GS1, RIM-ONE, and REFUGE databases. [ABSTRACT FROM AUTHOR]

Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set for handling the uncertainties in the data. Under this environment, in this paper we introduce the notion of induced interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (I-IVPFEOWG) operator and induced interval-valued Pythagorean fuzzy Einstein hybrid geometric (I-IVPFEHG) operator along with their some basic properties such as, idempotency, boundedness, commutatively, monotonicity. The main advantage of the induced aggregation operators is that, these operators are more suitable to aggregate the individual preference relations into a collective preference relation. Therefore these methods play a vigorous role in daily life problems. Furthermore, a method for multi-attribute group decision-making (MAGDM) problems based on these operators was developed, and the operational procedures were explained in detail. [ABSTRACT FROM AUTHOR]

This paper presents the ordered weighted average weighted average inflation (OWAWAI) and some extensions using induced and heavy aggregation operators and presents the generalized operators and some of their families. The main advantage of these new formulations is that they can use two different sets of weighting vectors and generate new scenarios based on the reordering of the arguments with the weights. With this idea, it is possible to generate new approaches that under- or overestimate the results according to the knowledge and expertise of the decision-maker. The work presents an application of these new approaches in the analysis of the inflation in Chile, Colombia, and Argentina during 2017. [ABSTRACT FROM AUTHOR]

This paper introduces a modified DLA model, based on a fractional diffusion mechanism, as a novel approach to modeling fractal growth. The specific memory performance of fractional operators can be reflected macroscopically in aggregated patterns eventually. The influence of the model's order on the structure and behavior of its pattern is further quantitatively described by anisotropy index and fractal dimension. Some simulations are provided to illustrate the correctness and effectiveness of the main results. [ABSTRACT FROM AUTHOR]

In this paper we study some modifications and generalizations of additivity in the case of aggregation functions on the unit interval [0, 1]. We prove that some common properties of aggregation functions can be viewed as modifications of additivity — additivity with constraints.We also generalize additivity into pseudo-additivity and k-pseudo-additivity, and provide characterization of pseudo-additive and k-pseudo-additive aggregation functions, including maxitive and k-maxitive aggregation functions. [ABSTRACT FROM AUTHOR]

Grouping functions, as one new case of not necessarily associative particular binary aggregation functions, have been proposed in the literature for their vast applications in fuzzy community detection problems, image processing and decision making. On the other hand, due to the wide applications in fuzzy reasoning, fuzzy control and approximate reasoning, the investigations of fuzzy implications derived from specific binary aggregation functions become a natural and hot research topic. In this paper, we focus on this research area and consider the ℐ , -implications induced from quasi-grouping functions and negations on bounded lattices. To be precise, firstly, by removing the continuity condition, we extend the notion of grouping functions on the unit closed interval to the so-called quasi-grouping functions on bounded lattices. Secondly, we give some basic properties and two construction methods of quasi-grouping functions on bounded lattices. Finally, we give the concept of ℐ , -implications and focus on the conditions under which they can satisfy the certain algebraic properties possessed by implications on bounded lattices. [ABSTRACT FROM AUTHOR]

The most preferred OWA (MP-OWA) operator is a new method to aggregate preference information with crisp numbers, whose weights are related with the frequency of the most preferred assessment to each criteria. However, people are usually not able to estimate their preference degrees with crisp number, since they have a vague knowledge about the preference assessment. In this paper, we propose a 2-tuple linguistic MP-OWA (LMP-OWA) operator. It is useful because it can be used to make decision with linguistic preference relations, and the weighting vector is not only connected to the maximum frequency of the assessment to the criteria, but also to the assessment values. Meanwhile, we introduce the parameterized 2-tuple LMP-OWA operator and the parameterized 2-tuple LMP-OWA operator with power function, which provide multiple aggregation results for decision makers to select. The paper ends up with an example of decision making with linguistic preference relations in movie recommender system. [ABSTRACT FROM AUTHOR]

In many real-life decision making (DM) situations, the available information is vague or imprecise. To adequately solve decision problems with vague or imprecise information, fuzzy set theory and aggregation operator theory have become powerful tools. In last three decades, DM theories and methods under fuzzy aggregation operator have been proposed and developed for effectively solving the DM problems and numerous applications have been reported in the literature. While various aggregation operators have been suggested and developed, there is a lack of research regarding systematic literature review and classification of study in this field. Regarding this, Web of Science database has been nominated and systematic and meta-analysis method called 'PRISMA' has been proposed. Accordingly, a review of 312 published articles appearing in 33 popular journals related to fuzzy set theory, aggregation operator theory and DM approaches between July 1986 and June 2017 have been attained to reach a comprehensive review of DM methods and aggregation operator environment. Consequently, the selected published articles have been categorized by name of author(s), the publication year, technique, application area, country, research contribution and journals in which they appeared. The findings of this study found that, ordered weighted averaging (OWA) has been the highest frequently accessed more than other areas. This systematic review shows that the DM theories under fuzzy aggregation operator environment have received a great deal of interest from researchers and practitioners in many disciplines. [ABSTRACT FROM AUTHOR]

The concept of moving average is studied. We analyze several extensions by using generalized aggregation operators, obtaining the generalized moving average. The main advantage is that it provides a general framework that includes a wide range of specific cases including the geometric and the quadratic moving average. This analysis is extended by using the generalized ordered weighted averaging (GOWA) and the induced GOWA (IGOWA) operator. Thus, we get the generalized ordered weighted moving average (GOWMA) and the induced GOWMA (IGOWMA) operator. Some of their main properties are studied. We further extend this approach by using distance measures suggesting the concept of distance moving average and generalized distance moving average. We also consider the case with the OWA and the IOWA operator, obtaining the generalized ordered weighted moving averaging distance (GOWMAD) and the induced GOWMAD (IGOWMAD) operator. The paper ends with an application in multi-period decision making. [ABSTRACT FROM AUTHOR]

Combining outputs of a pool of individual classifiers appropriately, as a hot research topic of pattern classification, can generate statistically significant increase in classification perfor-mances. During the last decades, several fusion algorithms were presented, but few of those focus on two-class classification which possesses wide application area such as sentiment clas-sification, cancer differentiation and so on. Thus the main purpose of this paper is to develop a highly effective fusion algorithm, i.e. intuitionistic fuzzy reasoning fusion algorithm, to increase the performance of a multiple two-class classifiers system. The outputs of component classifiers are represented by a set of intuitionistic fuzzy values at first and the fusion process is interpreted as aggregation of intuitionistic fuzzy information. The proposed algorithm includes three ver-sions using the intuitionistic fuzzy arithmetic average operator, intuitionistic fuzzy weighted average operator and induced intuitionistic fuzzy ordered weighted average aggregation oper-ator, respectively. The proposed fusion algorithm can combine both evidences of the hypothesis that a test pattern belongs to a class and evidences of the hypothesis that the test pattern does not belong to the class at the same time. We compare the versions of ora algorithm with four other fusion techniques on five open-access datasets. The proposed algorithm exhibits good predictive abilities, compared to the best individual classifiers and other comparable fusion techniques. Further, the experiments show some interesting results about measuring and weighting component classifiers. [ABSTRACT FROM AUTHOR]

We introduce the uncertain generalized OWA (UGOWA) operator. This operator is an extension of the OWA operator that uses generalized means and uncertain information represented as interval numbers. By using UGOWA, it is possible to obtain a wide range of uncertain aggregation operators such as the uncertain average (UA), the uncertain weighted average (UWA), the uncertain OWA (UOWA) operator, the uncertain ordered weighted geometric (UOWG) operator, the uncertain ordered weighted quadratic averaging (UOWQA) operator, the uncertain generalized mean (UGM), and many specialized operators. We study some of its main properties, and we further generalize the UGOWA operator using quasi-arithmetic means. The result is the Quasi-UOWA operator. We end the paper by presenting an application to a decision-making problem regarding the selection of financial strategies. [ABSTRACT FROM AUTHOR]

In this paper we analyze a group decision procedure that follows a recursive pattern. In the first stage, the members of a group show their opinions on all the individuals of that group, regarding a specific attribute, by means of assessments within an ordered set, e.g. the unit interval or a finite scale. Taking into account this information, some aggregation operators and a family of thresholds, a subgroup of individuals is selected: those members whose collective assessment reach a specific threshold. Now only the opinions of this qualified subgroup are taken into account and a new subgroup emerges in the implementation of the aggregation phase. We analyze how to put in practice this recursive procedure in order to provide a final subgroup of qualified members. We have considered the minimum as aggregation operator. Thus, the collective assessment is just the worst of the individual assessments. This idea corresponds to qualify individuals whenever all the individual assessments reach the fixed threshold. [ABSTRACT FROM AUTHOR]

In this paper, we present some methods for constructing copulas with a given diagonal section that are not necessarily symmetric. An interesting application for the construction of copulas with given tail dependence coefficients is, hence, provided. [ABSTRACT FROM AUTHOR]

This paper describes an approach to pointwise construction of general aggregation operators, based on monotone Lipschitz approximation. The aggregation operators are constructed from a set of desired values at certain points, or from empirically collected data. It establishes tight upper and lower bounds on Lipschitz aggregation operators with a number of different properties, as well as the optimal aggregation operator, consistent with the given values. We consider conjunctive, disjunctive and idempotent n-ary aggregation operators; p-stable aggregation operators; various choices of the neutral element and annihilator; diagonal, opposite diagonal and marginal sections; bipolar and double aggregation operators. In all cases we provide either explicit formulas or deterministic numerical procedures to determine the bounds. The findings of this paper are useful for construction of aggregation operators with specified properties, especially using interpolation schemata. [ABSTRACT FROM AUTHOR]

In this paper, we perform the analysis of temporalized structure of a body of evidence and possibilistic Extremal Fuzzy Dynamic System (EFDS) for the construction of more precise decisions based on the expert knowledge stream. The process of decision precision consists of two stages. In the first stage the relation of information precision is defined on a monotone sequence of bodies of evidence. The principle of negative imprecision is developed, as the maximum principle of knowledge ignorance measure of a body of evidence. Corresponding mathematical programming problem is constructed. On the output of the first stage we receive the expert knowledge precision stream of the criteria with respect to any decision. In the second stage the constructed stream is an input trajectory for the finite possibilistic model of EFDS. A genetic algorithm approach is developed for identifying of the EFDS finite model. The modelling process gives us the more precise decisions as a prediction of a temporalization procedure. The constructed technology is applied in the non-probabilistic utility theory for the information technology management problem. [ABSTRACT FROM AUTHOR]

The problem of distributivity was posed many years ago and it has been investigated for families of certain operations, such as t-norms, t-conorms, uninorms and nullnorms. In this paper, we continue to investigate the same topic as the above by focusing on semi-nullnorms and semi-t-operators, which are generalization of nullnorms and t-operators by omitting commutativity and associativity, and commutativity, respectively. The obtained results are not only the full characterization of this kind of distributivity equation, but also extensions of distributivity for nullnorms and for semi-nullnorms. Moreover, this paper finishes the full characterization of distributivity between semi-nullnorms and semi-t-operators together with Refs. 6 and 20. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to propose a new approach to interactive multi-attribute group decision making with triangular Atanassov's intuitionistic fuzzy numbers (TAIFNs). The contribution of this study is fivefold: (1) Minkowski distance between TAIFNs is firstly defined; (2) We define the possibility attitudinal expected values of TAIFNs and thereby present a novel risk attitudinal ranking method of TAIFNs which can sufficiently consider the risk attitude of decision maker; (3) The weighted average operator (TAIFWA) and generalized ordered weighted average (TAIFGWA) operator of TAIFNs are defined as well as the hybrid ordered weighted average (TAIFHOWA) operator; (4) To study the interaction between attributes, we further develop the generalized Choquet (TAIF-GC) integral operator and generalized hybrid Choquet (TAIF-GHC) integral operator of TAIFNs. Their desirable properties are also discussed; (5) The individual overall value of alternative is obtained by TAIF-GC operator and the collective one is derived through TAIFWA operator. Fuzzy measures of attribute subsets and expert weights are objectively derived through constructing multi-objective optimization model which is transformed into the goal programming model to solve. The system analyst selection example verifies effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Bonferroni mean (BM) is a very useful aggregation operator, which can consider the correlations between the aggregated arguments and the multi-valued neutrosophic set can be much more convenient to denote the incomplete, indeterminate and inconsistent information, in this paper, we applied the Bonferroni mean to the multi-valued neutrosophic set, and proposed some Bonferroni mean operators of multi-valued neutrosophic numbers (MVNNs). First, we gave some operational laws and a comparison method of MVNNs, then we presented the weighted Bonferroni mean (WBM) operator and weighted geometric Bonferroni mean (WGBM) operator. Further, we proposed the multi-valued neutrosophic weighted Bonferroni mean (MVNWBM) operator and the multi-valued neutrosophic weighted geometric Bonferroni mean (MVNWGBM) operator and some properties of them are also investigated. Finally, the decision making methods are developed based on MVNWGBM operator and MVNWBM operator, and an example about investment selection is given to illustrate the applications of the developed methods and the influence of different parameter values on the decision-making results. [ABSTRACT FROM AUTHOR]

Developing aggregation operators for interval-valued hesitant fuzzy sets (IVHFSs) is a technological task we are faced with, because they are specifically important in many problems related to the fusion of interval-valued hesitant fuzzy information. This paper develops several novel kinds of power geometric operators, which are referred to as variable power geometric operators, and extends them to interval-valued hesitant fuzzy environments. A series of generalized interval-valued hesitant fuzzy power geometric (GIVHFG) operators are also proposed to aggregate the IVHFSs to model mandatory requirements. One of the important characteristics of these operators is that objective weights of input arguments are variable with the change of a non-negative parameter. By adjusting the exact value of the parameter, the influence caused by some 'false' or 'biased' arguments can be reduced. We demonstrate some desirable and useful properties of the proposed aggregation operators and utilize them to develop techniques for multiple criteria group decision making with IVHFSs considering the heterogeneous opinions among individual decision makers. Furthermore, we propose an entropy weights-based fitting approach for objectively obtaining the appropriate value of the parameter. Numerical examples are provided to illustrate the effectiveness of the proposed techniques. [ABSTRACT FROM AUTHOR]

In this paper, new generalizations of the probabilistic averaging operator - Associated Fuzzy Probabilistic Averaging (As-PA and As-FPA) and Immediate Probabilistic Fuzzy Ordered Weighted Averaging (As-IP-OWA and As-IP-FOWA) operators are presented in the environment of fuzzy uncertainty. An uncertainty is presented by associated probabilities of a fuzzy measure. Expert's evaluations as arguments of the aggregation operators are described by a variable, values of which are compatibility levels on the states of nature defined in positive real or triangular fuzzy numbers (TFNs). Two propositions on the As-FPA operator are proved: (1) The As-FPA operator for the fuzzy measure - capacity of order two coincides with the finite Choquet Averaging (CA) Operator; (2) the As-FPA operator coincides with the FPA operator when a probability measure is used in the role of a fuzzy measure. Analogous propositions for the As-IP-FOWA operator are proved. Some propositions on the connection of the As-FPA and As-IP-FOWA operators are also proved. Information measures - Orness and Divergence for the constructed operators are defined. Some propositions on the connections of these parameters with the corresponding parameters of the finite CA Operator are proved. Two illustrative examples on the applicability of the As-FPA and As-IP-FOWA operators are presented: (1) Several variants of the As-FPA and As-IP-FOWA operators are used for comparison of decision-making results for the problems regarding the fiscal policy of a country; (2) The As-FPA operator is used in the Multi-attribute decision-making (MADM) problem of choosing the best version of the students' project. [ABSTRACT FROM AUTHOR]

Aggregation operators play a key role in multiple criteria decision-making (MCDM). Extensions of aggregation operators to intuitionistic fuzzy sets (IFSs) usually involve replacing the standard arithmetic operations with those defined over the membership and nonmembership of IFS, which is essentially a pair of special Archimedean triangular norm (t-norm) and triangular conorm (t-conorm), called probabilistic sum t-conorm and product t-norm, on the membership and nonmembership of IFS, respectively. In this paper, we first introduce some operations on IFSs by means of Archimedean t-norm and t-conorm. Then some generalized Archimedean intuitionistic fuzzy aggregation operators are proposed, such as generalized Archimedean intuitionistic fuzzy weighted averaging operator, generalized Archimedean intuitionistic fuzzy ordered weighted averaging (GAIFOWA) operator, and generalized Archimedean intuitionistic fuzzy hybird averaging operator. Some desirable properties of these operators are investigated. The relations between these operators and the existing intuitionistic fuzzy aggregation operators are discussed. Finally, applying these proposed operators, we develop an approach for multi-criteria decision-making with intuitionistic fuzzy information, an illustrative example is used to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

As a generalization of intuitionistic fuzzy set, the Pythagorean fuzzy set is interesting and very useful in modeling uncertain information in real-world decision-making problems. In this paper, we develop a new method for Pythagorean fuzzy multiple-criteria decision-making (MCDM) problems with aggregation operators and distance measures. First, we present the Pythagorean fuzzy ordered weighted averaging weighted average distance (PFOWAWAD) operator. The main advantage of the PFOWAWAD operator is that it uses distance measures in a unified framework between the ordered weighted averaging (OWA) operator and weighted average (WA) that considers the degree of importance of each concept in the aggregation. Some of its main properties and special cases are studied. Then, based on the proposed operator, a hybrid TOPSIS method, called PFOWAWAD-TOPSIS is introduced for Pythagorean fuzzy MCDM problem. Finally, a numerical example is provided to illustrate the practicality and feasibility of the developed method. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy sets can describe the uncertainty and complexity of the world flexibly, so it has been widely used in multi-attribute decision making. Traditional intuitionistic fuzzy aggregation operators are usually based on the probability measure, namely, they consider that the attributes of objects are independent. But in actual situations, it is difficult to ensure the independence of attributes, so these operators are unsuitable in such situations. Fuzzy measure is able to depict the relationships among the attributes more comprehensively, so it can complement the traditional probability measure in dealing with the multi-attribute decision making problems. In this paper, we first analyze the existing intuitionistic fuzzy operators based on fuzzy measure, then introduce two novel additive intuitionistic fuzzy aggregation operators based on the Shapley value and the Choquet integral, respectively, and show their advantages over other ones. [ABSTRACT FROM AUTHOR]

The intuitionistic fuzzy set (A-IFS) was introduced by Atanassov to generalize the concept of Zadeh's fuzzy set. The basic elements of an A-IFS are the intuitionistic fuzzy numbers (IFNs). In this paper, we deal with the intuitionistic fuzzy set with the help of Einstein operations. First we introduce some operations of A-IFS, such as the Einstein sum, Einstein product, Einstein scalar multiplication and Einstein exponentiation, and redefine two new and important operation as Einstein subtraction and Einstein division. Then we investigate the limit, continuity and derivatives of intuitionistic fuzzy functions (IFFs) based on the Einstein operations. Furthermore and what is more, some infinite and definite integrals for the IFFs are discussed importantly, and an aggregation method based on the definite integral was introduced to solve some actual decision making problems, which focus on the original data and obtain better overall evaluations in information aggregation. [ABSTRACT FROM AUTHOR]

Hesitant fuzzy sets, permitting the membership of an element to be a set of several possible values, can be used as an efficient mathematical tool for modeling people's hesitancy in daily life. The aim of this paper is to present a consensus support model for group decision making with hesitant fuzzy information. This model is composed of two processes: a consensus process and a selection process. The consensus process is carried out to reach a high level of consensus among experts' opinions before applying a selection process. We first aggregate the hesitant fuzzy decision matrix into a group decision matrix by using the additive aggregation (AA) operator. Then the consensus measure is used to design a feedback mechanism that generates advice to the experts on how they should change their preferences to obtain a solution with a high consensus degree. In the selection process, based on the consentaneous group decision matrix, the additive weighted aggregation (AWA) operator is utilized to derive the overall attribute values of alternatives, by which the most desirable alternative can be found out. Finally, a practical example is proposed to illustrate the application of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, two uncertain linguistic Choquet aggregation operators called the induced uncertain linguistic hybrid generalized Shapley Choquet weighted averaging (IULHGSCWA) operator and the induced uncertain linguistic hybrid generalized Shapley Choquet geometric mean (IULHGSCGM) operator are defined. To reduce the complexity of solving a fuzzy measure, the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet weighted averaging (IULHAGSCWA) operator and the induced uncertain linguistic hybrid 2-additive generalized Shapley Choquet geometric mean (IULHAGSCGM) operator are presented. When the weight information is incompletely known, models for the optimal fuzzy measures on an expert set, on an attribute set and on their ordered sets are built, respectively. Furthermore, an approach to multi-attribute group decision making under uncertain linguistic environment is developed, which can cope with the interdependent or correlative characteristics between elements. Finally, a practical application is selected to illustrate the validity and practicability of the developed procedure. [ABSTRACT FROM AUTHOR]

In this paper, we perform the analysis of temporalized structure of bodies of evidence to construct more precise decisions based on the mathematical model of experts' evaluations. The relation of information precision is defined on a monotone sequence of the bodies of evidence. For determining of a body of evidence the maximum principles of nonspecificity measure, the Shannon and Shapley entropies are applied. Corresponding mathematical programming problems are constructed. A new approach for the numerical solution of these problems is developed. The temporalized structure of bodies of evidence is used for precising the decision in the well-known Kaufmann's theory of expertons. A measure of increase of decision precision is introduced, which takes into account all steps of temporalization. The temporalized method of expertons is applied to the problem of decision risk management, where the investment fund expert commission provides evaluation of competition results. In our specially created decision-making model, the goal of the expert technology is to aggregate and refine subjective evaluations provided by the expert commission members. The model performs as an adviser that assists the expert commission in selecting of decision with a minimum risks. The results of developed method are then compared with other well-known methods and aggregation operators such as: mean, median, ordered weighed averaging (OWA) and method of expertons. [ABSTRACT FROM AUTHOR]

Consider the various types of uncertain preference information provided by the decision makers and the importance of determining the associated weights for the aggregation operator, the multiple attribute group decision making (MAGDM) methods based on some dependent interval 2-tuple linguistic aggregation operators are proposed in this paper. Firstly some operational laws and possibility degree of interval 2-tuple linguistic variables are introduced. Then, we develop a dependent interval 2-tuple weighted averaging (DITWA) operator and a dependent interval 2-tuple weighted geometric (DITWG) operator, in which the associated weights only depend on the aggregated interval 2-tuple arguments and can relieve the influence of unfair arguments on the aggregated results by assigning low weights to them. Based on the DITWA and the DITWG operators, some approaches for multiple attribute group decision making with interval 2-tuple linguistic information are proposed. Finally, an illustrative example is given to demonstrate the practicality and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the use of weighted averaging aggregation operators as techniques for time series smoothing. We analyze the moving average, exponential smoothing methods, and a new class of smoothing operators based on linearly decaying weights from the perspective of ordered weights averaging to estimate a constant model. We examine two important features associated with the smoothing processes: the average age of the data and the expected variance, both defined in terms of the associated weights. We show that there exists a fundamental conflict between keeping the variance small while using the freshest data. We illustrate the flexibility of the smoothing methods with real datasets; that is, we evaluate the aggregation operators with respect to their minimal attainable variance versus average age. We also examine the efficiency of the smoothed models in time series smoothing, considering real datasets. Good smoothing generally depends upon the underlying method's ability to select appropriate weights to satisfy the criteria of both small variance and recent data. [ABSTRACT FROM AUTHOR]

While Multi-Criteria Decision Making (MCDM) models are focused on selecting the best alternative from a finite number of feasible solutions according to a set of criteria, in Dynamic Multi-Criteria Decision Making (DMCDM) the selection process also takes into account the temporal performance of such alternatives during different time periods. In this paper a new discrete time variable index is proposed, to handling differences in temporal behavior of alternatives, which are not discriminated in preceding dynamic approaches, also considering rating-based perspectives for discrimination of the decision maker by modeling different attitudes to deal with the rating changes along different time periods. Moreover a DMCDM for supplier selection example is provided to illustrate the feasibility and effectiveness of the proposed index. [ABSTRACT FROM AUTHOR]

As we may have a set of possible values when comparing alternatives (or criteria), the hesitant fuzzy preference relation becomes a suitable and powerful technique to deal with this case. This paper mainly focuses on the multiplicative consistency of the hesitant fuzzy preference relation. First of all, we explore some properties of the hesitant fuzzy preference relation and develop some new aggregation operators. Then we introduce the concepts of multiplicative consistency, perfect multiplicative consistency and acceptable multiplicative consistency for a hesitant fuzzy preference relation, based on which, two algorithms are given to improve the inconsistency level of a hesitant fuzzy preference relation. Furthermore, the consensus of group decision making is studied based on the hesitant fuzzy preference relations. Finally, several illustrative examples are given to demonstrate the practicality of our algorithms. [ABSTRACT FROM AUTHOR]

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice. [ABSTRACT FROM AUTHOR]

In the process of group decision making (GDM), preference relations (e.g. fuzzy preference relation and multiplicative preference relation) are very popular tools to express decision makers' preferences, especially when a set of alternatives (or criteria) are compared. However, most of the existing preference relations don't consider the hesitancy information, which allows the decision makers to provide all the possible values when comparing two alternatives (or criteria), and is a common situation in daily life. In this paper, we first define the concept of hesitant fuzzy preference relation and study its properties, based on which we give an approach to GDM. Motivated by the multiplicative preference relation and the hesitant fuzzy set, we introduce the hesitant multiplicative set and develop a series of hesitant multiplicative aggregation operators. Hesitant multiplicative preference relation is also defined to provide decision makers a very useful tool to express their hesitant preferences over alternatives, and then is applied to GDM. Additionally, an example is given to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Motivated by the idea of prioritized aggregation operators (R. R. Yager, Prioritized aggregation operators, Int. J. Approximate Reasoning 48 (2008) 263-274.), we develop some prioritized aggregation operators for aggregating uncertain linguistic information, and then apply them to develops some models for uncertain linguistic multiple attribute group decision making (MAGDM) problems in which the attributes and experts are in different priority level. Finally, a practical example about talent introduction is given to verify the developed approach and to demonstrate its practicality and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we present a new intuitionistic fuzzy decision-making technique based on similarity measures and the ordered weighted average (OWA) operator. We develop the intuitionistic fuzzy ordered weighted similarity (IFOWS) measure. The main advantage of the IFOWS measure is that it can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Moreover, it provides a very general formulation that includes a wide range of aggregation similarity measures and aggregates the input arguments taking the form of intuitionistic fuzzy values rather than exact numbers. We further develop the interval-valued intuitionistic fuzzy ordered weighted similarity (IVIFOWS) measure. Then we apply the developed similarity measures for consensus analysis in group decision-making with intuitionistic fuzzy information. Finally, a practical case is used to illustrate the developed procedures. [ABSTRACT FROM AUTHOR]