Showing papers presented at "Granular Computing in 2021"

Intuitionistic fuzzy Dombi aggregation operators and their application to multiple attribute decision-making

Abstract: The purpose of this paper is to introduce the concepts of Dombi t-norm and Dombi t-conorm to aggregate intuitionistic fuzzy information. First, we have proposed some new operational laws of intuitionistic fuzzy numbers (IFNs) based on Dombi t-norm and t-conorm. Furthermore, based on these operational laws, we have introduced intuitionistic fuzzy Dombi weighted averaging (IFDWA) operator, intuitionistic fuzzy Dombi order weighted averaging (IFDOWA) operator, intuitionistic fuzzy Dombi hybrid averaging (IFDHA) operator, intuitionistic fuzzy Dombi weighted geometric (IFDWG) operator, intuitionistic fuzzy Dombi order weighted geometric (IFDOWG) operator, and intuitionistic fuzzy Dombi hybrid geometric (IFDHG) operator. Moreover, some suitable properties of these operators are also discussed. Then, utilizing these proposed operators, we have presented an algorithm to solve multiattribute decision-making (MADM) problems under an intuitionistic fuzzy environment. Finally, we have utilized a numerical example to compare the flexibility of the proposed method with the other existing methods.

Event abstraction in process mining: literature review and taxonomy

Abstract: The execution of processes in companies generates traces of event data, stored in the underlying information system(s), capturing the actual execution of the process. Analyzing event data, i.e., the focus of process mining, yields a detailed understanding of the process, e.g., we are able to discover the control flow of the process and detect compliance and performance issues. Most process mining techniques assume that the event data are of the same and/or appropriate level of granularity. However, in practice, the data are extracted from different systems, e.g., systems for customer relationship management, Enterprise Resource Planning, etc., record the events at different granularity levels. Hence, pre-processing techniques that allow us to abstract event data into the right level of granularity are vital for the successful application of process mining. In this paper, we present a literature study, in which we assess the state-of-the-art in the application of such event abstraction techniques in the field of process mining. The survey is accompanied by a taxonomy of the existing approaches, which we exploit to highlight interesting novel directions.

Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making

Abstract: The notion of generalized orthopair fuzzy sets, as a natural extension of both intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a more flexible framework for expressing and processing uncertain information. In intelligent decision making based on generalized orthopair fuzzy sets, it is a pivotal issue to compare or rank q-rung orthopair membership grades. In this work, we investigate the ranking issue of q-rung orthopair membership grades from a geometric point of view. We propose the regular Minkowski distance of q-rung orthopair membership grades which strengthens or extends some useful distance measures in the literature. By virtue of the regular Minkowski distance, we define a generic class of novel score functions called the Minkowski score function of q-rung orthopair membership grades. This new type of score functions not only extends the existing notions such as the expectation score function, but also overcomes the difficulty that Hamming (or Euclidean) distance-based score functions cannot distinguish those intuitionistic fuzzy values with identical expectation score (or ideal positive degree). We examine several critical properties of the Minkowski score function of q-rung orthopair membership grades. By taking advantage of the q-rung orthopair fuzzy weighted averaging (or geometric) operator and the Minkowski score function, a flexible approach is developed to support multiple attribute decision making with generalized orthopair fuzzy soft information. Finally, a benchmark problem is used for comparison with several existing methods to verify the cogency and feasibility of the proposed method.

A hybrid decision-making model under q-rung orthopair fuzzy Yager aggregation operators

Abstract: Aggregation operators perform a significant role in many decision-making problems. The purpose of this paper is to analyze the aggregation operators under the q-rung orthopair fuzzy environment with Yager norm operations. The q-rung orthopair fuzzy set is an extension of intuitionistic fuzzy set and Pythagorean fuzzy set in which sum of qth power of membership and non-membership degrees is bounded by 1. By applying the Yager norm operations to q-rung orthopair fuzzy set, we developed six families of aggregation operators, namely q-rung orthopair fuzzy Yager weighted arithmetic operator, q-rung orthopair fuzzy Yager ordered weighted arithmetic operator, q-rung orthopair fuzzy Yager hybrid weighted arithmetic operator, q-rung orthopair fuzzy Yager weighted geometric operator, q-rung orthopair fuzzy Yager ordered weighted geometric operator and q-rung orthopair fuzzy Yager hybrid weighted geometric operator. To prove the validity and feasibility of proposed work, we discuss two multi-attribute decision-making problems. Moreover, we investigate the influence of some values of parameter on decision-making results. Finally, we give a comparison with existing operators.

Set-theoretic models of three-way decision

Abstract: The theory of three-way decision is about a philosophy of thinking in threes, a methodology of working with threes, and a mechanism of processing in threes. We approach a whole through three parts, in terms of three units, or from three perspectives. A trisecting–acting–outcome (TAO) model of three-way decision involves trisecting a whole into three parts and acting on the three parts, in order to produce an optimal outcome. In this paper, we further explore the TAO model in a set-theoretic setting and make three new contributions. The first contribution is an examination of three-way decision with nonstandard sets for representing concepts under the two kinds of objective/ontic and subjective/epistemic uncertainty. The second contribution is an introduction of an evaluation-based framework of three-way decision. We present a classification of trisections and investigate the notion of an evaluation space. The third contribution is, within the proposed framework, a systematical study of three-way decision with rough sets, interval sets, fuzzy sets, shadowed sets, rough fuzzy sets, interval fuzzy sets (or equivalently, vague sets, interval-valued fuzzy sets, intuitionistic fuzzy sets), and soft sets.

Intuitionistic fuzzy time series functions approach for time series forecasting

Abstract: Fuzzy inference systems have been commonly used for time series forecasting in the literature. Adaptive network fuzzy inference system, fuzzy time series approaches and fuzzy regression functions approaches are popular among fuzzy inference systems. In recent years, intuitionistic fuzzy sets have been preferred in the fuzzy modeling and new fuzzy inference systems have been proposed based on intuitionistic fuzzy sets. In this paper, a new intuitionistic fuzzy regression functions approach is proposed based on intuitionistic fuzzy sets for forecasting purpose. This new inference system is called an intuitionistic fuzzy time series functions approach. The contribution of the paper is proposing a new intuitionistic fuzzy inference system. To evaluate the performance of intuitionistic fuzzy time series functions, twenty-three real-world time series data sets are analyzed. The results obtained from the intuitionistic fuzzy time series functions approach are compared with some other methods according to a root mean square error and mean absolute percentage error criteria. The proposed method has superior forecasting performance among all methods.

Extension of Einstein geometric operators to multi-attribute decision making under q -rung orthopair fuzzy information

Abstract: Aggregation operators are mathematical functions and essential tools of unifying the several inputs into single valuable output. The purpose of this paper is to analyze the aggregation operators (AOs) under the q-rung orthopair fuzzy environment with the help of Einstein norms operations. This paper presents AOs, namely, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG), q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG), generalized q-rung orthopair fuzzy Einstein weighted geometric (Gq-ROFEWG), generalized q-rung orthopair fuzzy Einstein ordered weighted geometric (Gq-ROFEOWG) operators. Some properties of these operators are explained. An algorithmic model to deal with multi-attribute decision making problems in q-rung orthopair fuzzy(q-ROF) environment using generalized q-ROF Einstein weighted geometric operator is established. These operators can remunerate for the possible asymmetric roles of the attributes that represent the problem. At the end, to prove the validity and feasibility of the proposed model, we give applications for the selection of location of thermal power station and selection of best cardiac surgeon. The comparison analysis with other existing operators shows the reliability of our work.

Novel distance measures for Pythagorean fuzzy sets with applications to pattern recognition problems

Abstract: Pythagorean fuzzy set (PFS) is a concept that generalizes intuitionistic fuzzy sets. The notion of PFSs is very much applicable in decision science because of its unique nature of indeterminacy. The main feature of PFSs is that it is characterized by membership degree, non-membership degree, and indeterminate degree in such a way that the sum of the square of each of the parameters is one. In this paper, we propose some novel distance measures for PFSs by incorporating the conventional parameters that describe PFSs. We provide a numerical example to illustrate the validity and applicability of the distance measures for PFSs. While analyzing the reliability of the proposed distance measures in comparison with similar distance measures for PFSs in the literature, we discover that the proposed distance measures, especially, $$d_5$$ yields the most reasonable measure. Finally, some applications of $$d_5$$ to pattern recognition problems are explicated. These novel distance measures for Pythagorean fuzzy sets could be applied in decision making of real-life problems embedded with uncertainty.

Hexagonal fuzzy number and its distinctive representation, ranking, defuzzification technique and application in production inventory management problem

Abstract: In this article, we envisage the hexagonal number from various distinct rational perspectives and viewpoints to give it a look of a conundrum. Hexagonal fuzzy number is used as an authoritative logic to ease understanding of vagueness information. This article portrays an impression of different representation, ranking, defuzzification and application of hexagonal fuzzy number. Additionally, disjunctive types of linear and nonlinear hexagonal fuzzy numbers both with symmetry and asymmetry are addressed here along with its graphical representation. Further, a new ranking method is established and two different kinds of approaches to computing the defuzzification of hexagonal fuzzy number are fabricated in this research arena. Finally, one production inventory management problem has been analyzed and solved in the hexagonal fuzzy environment along with the numerical sensitivity analysis tables. This real-life problem plays a crucial role to demonstrate the effectiveness of this method compared to the usual results in crisps environment. This noble thought will help us to solve a plethora of daily-life problems in uncertainty arena.

Generalized triparametric correlation coefficient for Pythagorean fuzzy sets with application to MCDM problems

Abstract: Pythagorean fuzzy set (PFS) is an advanced version of intuitionistic fuzzy set which generalizes fuzzy set. Consequently, PFS has a better applicative expression in real-life decision-making (RLDM) or multicriteria decision-making (MCDM) problems due to its capacity to curb uncertainties embedded in decision making. Correlation coefficient is a significant measuring tool applicable to solving RLDM/MCDM problems via Pythagorean fuzzy environment approach. The main aim of this paper is to reexamine Garg’s correlation coefficient for PFSs and generalize it for a better output in resolving MCDM problems. The axiomatic description of correlation coefficient for PFSs is proposed, and the generalized triparametric correlation coefficient for PFSs is characterized with some number of results. Numerical verification of the proposed correlation coefficient is given to validate the preeminence of the generalized correlation coefficient for PFSs over Garg’s approach. Lastly, some MCDM problems such as pattern recognition problem (e.g., classification of mineral fields) and diagnostic medicine in the framework of Pythagorean fuzzy pairs are discussed with the aid of the novel correlation coefficient. This proposed measuring tool could be exploited in other MCDM problems via object-oriented approach.

Training simple recurrent deep artificial neural network for forecasting using particle swarm optimization

Abstract: Deep artificial neural networks have been popular for time series forecasting literature in recent years. The recurrent neural networks present more suitable architectures for forecasting problems than other deep neural network types. The simplest deep recurrent neural network type is simple recurrent neural networks according to the number of employed parameters. These neural networks can be preferred to solve forecasting problems because of their simple structure if they are trained well. Unfortunately, the training of simple recurrent neural networks is problematic because of exploding or vanishing gradient problems. The contribution of this study is proposing a new training algorithm based on particle swarm optimization. The algorithm does not use gradients so it has not vanished or exploding gradient problem. The performance of the new training algorithm is compared with long short-term memory trained by the Adam algorithm and Pi-Sigma artificial neural network. In the applications, ten-time series are used to compare the performance of the methods. The ten-time series is consisting of daily observations of the Dow-Jones and Nikkei stock exchange opening prices between the years 2014 and 2018. At the end of the analysis processes, the proposed method produces more accurate forecast results than established benchmarks.

Arithmetic operations on normal semi elliptic intuitionistic fuzzy numbers and their application in decision-making

Abstract: Decision-making problems are more often tainted with uncertainty. Fuzzy numbers play utmost important role to band uncertainty, more especially intuitionistic fuzzy number (IFN) which is the extension of fuzzy number (FN). Different types of IFNs such as normal and generalized trapezoidal, triangular and symmetric hexagonal IFNs are explored. However, based on nature of the data, semi-elliptic type of IFN may exists in real world decision-making problems. In this paper, a maiden attempt has been made to study normal semi elliptic intuitionistic fuzzy number (NSEIFN). Our emphasis has been on arithmetic operations of NSEIFNs and comparing with the other existing IFNs. Also rank of NSEIFNs has been proposed based on mean and value. Apart from that inverse, exponential, logarithm, square root and nth root of NSEIFNs are derived. Finally, the proposed ranking method is applied to the decision making problem where criteria and rating of alternatives are represented in terms of NSEIFN. It is observed that the proposed model produces better results and overcome the drawbacks of existing approaches.

Multi-attribute decision-making with q -rung picture fuzzy information

Abstract: q-rung picture fuzzy sets can handle complex fuzzy and impression information by changing a parameter q based on the different hesitation degree and yield a flexible framework that captures imprecise information involving different views (typically but not exclusively: yes, abstention, no, and rejection). The Einstein operators perform well for the aggregation of data in various other frameworks of uncertain information. By combining these concepts, in this article we expand the field of application of the Einstein operators to the q-rung picture fuzzy environment. Thus, we develop novel concepts of q-rung picture fuzzy aggregation operators under Einstein operators and discuss their application in multi-attribute decision-making. First, we propose Einstein operational laws for q-rung picture fuzzy numbers. We then introduce the q-rung picture fuzzy Einstein weighted averaging, q-rung picture fuzzy Einstein ordered weighted averaging, generalized q-rung picture fuzzy Einstein weighted averaging and generalized q-rung picture fuzzy Einstein ordered weighted averaging operators. We develop an algorithm to solve complex decision-making problems using these operators. Finally, to show the practicality and effectiveness of the proposed method, we discuss two multi-attribute decision-making problems (1) selection of a suitable business location (2) selection of a supplier. To demonstrate the superiority and advantage of our proposed method, a comparison with existing methods is presented.

Rough approximation models via graphs based on neighborhood systems

Abstract: Neighborhood systems are used to approximate graphs as finite topological structures. Throughout this article, we construct new types of eight neighborhoods for vertices of an arbitrary graph, say, j-adhesion neighborhoods. Both notions of Allam et al. and Yao will be extended via j-adhesion neighborhoods. We investigate new types of j-lower approximations and j-upper approximations for any subgraph of a given graph. Then, the accuracy of these approximations will be calculated. Moreover, a comparison between accuracy measures and boundary regions for different kinds of approximations will be discussed. To generate j-adhesion neighborhoods and rough sets on graphs, some algorithms will be introduced. Finally, a sample of a chemical example for Walczak will be introduced to illustrate our proposed methods.

Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making

Abstract: The focus of our this paper is to develop a series of Einstein hybrid aggregation operators using confidence level, such as confidence intuitionistic fuzzy Einstein hybrid averaging operator, confidence intuitionistic fuzzy Einstein hybrid geometric operator, generalized confidence intuitionistic fuzzy Einstein hybrid averaging operator and generalized confidence intuitionistic fuzzy Einstein hybrid geometric operator. The main advantage of the new operators is that these operators not only provide information to the experts of the problems, but these methods also consider the degrees of the experts of the problems that they are familiar with the selection option. The new approaches provide more general, more accurate and precise results as compared to the existing methods. Finally, the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach.

Particle swarm optimization and intuitionistic fuzzy set-based novel method for fuzzy time series forecasting

Abstract: Many fuzzy time series (FTS) methods have been developed by the researchers without including non-determinacy caused using single function for both membership and non-membership grades. Optimum length of intervals and inclusion of non-determinacy have been two important key issues for the researchers for long time. In this paper, we propose a novel hybrid FTS forecasting method using particle swarm optimization (PSO) and intuitionistic fuzzy set (IFS). PSO determines optimum length and IFS includes non-determinacy during fuzzification of time series data. To show the applicability and suitability of proposed forecasting method, it is implemented on three time series data of the University of Alabama, State bank of India (SBI) share price at Bombay Stock Exchange (BSE), India and car sells in Quebec. Performance of proposed method is measured using mean square error (MSE). Reduced amount of MSE confirms outperformance of proposed FTS forecasting method over various existing fuzzy set, IFS, hesitant and probabilistic hesitant fuzzy set-based FTS forecasting methods in forecasting the University of Alabama enrollments, SBI share price and car sells in Quebec. Validity of the proposed FTS forecasting method is also verified using tracking signal.

Multiattribute decision-making under Fermatean fuzzy bipolar soft framework

Abstract: Fermatean fuzzy set theory is emerging as a novel mathematical tool to handle uncertainties in different domains of real world. Fermatean fuzzy sets were presented in order that uncertain information from quite general real-world decision-making situations could be mathematically tractable. To that purpose, these sets are more flexible and reliable than intuitionistic and Pythagorean fuzzy sets. This paper presents a novel hybrid model, namely, the Fermatean fuzzy bipolar soft set (FFBSS, in short) model as a general extension of two powerful existing models, that is, fuzzy bipolar soft set and Pythagorean fuzzy bipolar soft set models. Some fundamental properties of the proposed FFBSS model, namely, subset-hood, equal FFBSSs, relative null and relative absolute FFBSSs, restricted intersection and union, extended intersection and union, AND operation and OR operation are investigated along with numerical examples. In addition, certain basic operations, including Fermatean fuzzy weighted average and score function of FFBSSs are proposed. Furthermore, two applications of FFBSS are explored to deal with different multiattribute decision-making situations, that is, selection of best surgeon robot and analysis of most affected country due to COVID-19 (‘CO’ stands for corona, ‘VI’ for virus, ‘D’ for disease, and ‘19’ stands for its year of emergence, that is, 2019). The proposed methodology is supported by an algorithm. At the end, a comparison analysis of the proposed hybrid model with some existing models, including Pythagorean fuzzy bipolar soft sets is provided.

Pythagorean fuzzy Schweizer and Sklar power aggregation operators for solving multi-attribute decision-making problems

Abstract: The objective of this paper is to develop Pythagorean fuzzy (PF) aggregation operators, utilizing the concept of power aggregation operators through Schweizer and Sklar (SS) operations. A series of aggregation operators, viz., PF SS power average operator, PF SS power weighted average operator, PF SS power geometric operator, and PF SS power weighted geometric operator under PF environment is proposed in this paper. The developed operators possess the capacity to make information aggregation technique more flexible than other existing operators due to the presence of SS t-norms and t-conorms in PF environment. Also, for the appearance of power aggregation operator, the developed operators contain the capability to eliminate effects of unreasonable data from biased decision makers by considering interrelationships among the fused arguments. Several properties of the proposed operators are studied and a method for solving multi-attribute decision-making problems under PF context is developed. To illustrate the proposed method and to show its efficiency, an example, studied previously, is solved and compared with existing methods.

Picture fuzzy Choquet integral-based VIKOR for multicriteria group decision-making problems

Abstract: Choquet integral operator has been proved more ideal than traditional aggregation operators in the modeling of interaction phenomena among the criteria in multicriteria group decision-making (MCGDM) problems. In this paper, we mention the limiting behavior of Choquet integral operator for intuitionistic fuzzy set (IFS) and propose Choquet integral for picture fuzzy set (PFS). This limitation is due to the incapability of IFS to model information that may be available in the form of refusal and abstain. We define Choquet averaging and Choquet geometric mean operators for PFS along with their few properties. We have also proposed picture fuzzy Choquet integral-based VIKOR (VlseKriterijumska Optimizacija I Kompromisno Resenje) for MCGDM problems. Proposed picture fuzzy Choquet integral-based VIKOR method includes benefits of PFS and addresses issue of interdependency among noncommensurable criteria in MCGDM problems. An example of supplier selection problem is included to show suitability and applicability of proposed picture fuzzy Choquet integral-based VIKOR method.

Intuitionistic fuzzy scale-invariant entropy with correlation coefficients-based VIKOR approach for multi-criteria decision-making

Abstract: In this paper, a parametric generalization of Shannon entropy, i.e., Logarithmic $$\beta$$ -Norm entropy measure has been discussed. We have also derived the desired entropy characteristics of new generalized entropy measure including its positivity, expandability, extensivity and additivity and in addition, provided the much desired scale invariance property. This striking property is satisfied neither by Shannon entropy nor by its existing generalization like Renyi’s and Tsallis entropies, etc. Then we define the scale-invariant entropy measure in intuitionistic fuzzy set and discuss its several mathematical properties and validity. Thereafter, we suggested a new multi-criteria decision-making (MCDM) method using weighted correlation coefficient-based VIKOR approach for finding the ranking and measuring the uncertainity in place of distance measure. The proposed decision-making technique is well described through the numerical example based on supplier selection with the help of two approaches. In first approach we considered the case of partially known criteria weights, whereas unknown criteria weights are discussed in second approach. The comparative results show the flexibility and effectiveness of the proposed approach to solve problems in real life.

Some modified Pythagorean fuzzy correlation measures with application in determining some selected decision-making problems

Abstract: Pythagorean fuzzy set (PFS) is an advanced version of generalized fuzzy sets. It has a better applicative expression in decision-making because of its capability in curbing fuzziness embedded in decision science. Correlation coefficient is a reliable measuring operator for the applicability of generalized fuzzy sets in decision-making. Some approaches of estimating correlation of PFSs have been explored, albeit with certain setbacks. This paper introduces some methods of calculating the correlation coefficient of PFSs which resolve the setbacks in the existing methods. Some numerical examples are supplied to confirm the superiority of the novel methods over the existing correlation coefficient measures. In addition, certain decision-making problems such as marital choice-making, classification of building materials, and electioneering process represented in Pythagorean fuzzy values are resolved using the proposed correlation measure. Specifically, the objectives of this work are to (1) introduce some new triparametric methods of computing correlation coefficient of PFSs, (2) characterize their theoretic properties, (3) ascertain their advantages over the existing methods, and (4) explore the application of the proposed methods in certain decision-making problems. From the study, it is observed that the new Pythagorean fuzzy correlation coefficients give reliable outputs compared to the existing ones and, hence, can suitably handle multiple criteria decision-making effectively.

Q-rung orthopair fuzzy Frank aggregation operators and its application in multiple attribute decision-making with unknown attribute weights

Abstract: In decision-making problems, q-rung orthopair fuzzy sets are considered as a more effective tool than intuitionistic fuzzy sets and Pythagorean fuzzy sets. This article develops some aggregation operators based on Frank t-norm and t-conorm for fusing q-rung orthopair fuzzy (q-ROF) information. Then a multiple attribute decision-making (MADM) approach is introduced based on the proposed operators. The Frank operations of t-norm and t-conorm can have the advantage of good flexibility with the operational parameter. From that point of view, in this paper, we extend the ideas of Frank t-norm and t-conorm to the q-ROF environment and introduce some aggregation operators. Moreover, we illustrate the compatible properties of the proposed operators. Generally, the attribute weights are unknown in the MADM problems. The analytical hierarchy process and entropy methods are efficient tools to handle such MADM problems with unknown attribute weights. So, we present an MADM approach with unknown attribute weights under q-ROF environment using proposed operators. Then to elaborate the flexibility and validity of the proposed model, we discuss and solve a numerical problem concerned with a government project of choosing the best way of industrialization. Next, we show how the involvement of the parameters in our proposed model affects the decision-making results. Finally, to exhibit the superiority of our proposed methodology, the obtained results are compared with the existing ones.

Recurrent fuzzy time series functions approaches for forecasting

Abstract: The recurrent fuzzy time series function method can be obtained in two ways. First is using a similar model to the autoregressive moving average to obtain fuzzy functions and the second one is using recurrent connections in the combining equation. The recurrent structure provides less number of inputs and more accurate forecasts. The contribution of the paper is proposing a recurrent fuzzy time series function method and its bootstrapped version. The recurrent models are used to obtain fuzzy functions in the proposed method. The classical bootstrap method is applied and bootstrap samples are generated from learning samples. The bootstrap method provides lower forecast error variance for the proposed method. The performance of new methods is compared with some fuzzy function methods and classical approaches. First, Turkey electrical consumption data time series are analyzed. Second, the Australian beer consumption time series are analyzed. As a result of applications, new methods have good forecasting performance if compare to established benchmarks.

Intuitionistic interval-valued hesitant fuzzy matrix games with a new aggregation operator for solving management problem

Abstract: In our daily life, we encounter many problems with uncertainty and vagueness in nature. Mathematical formulations and solutions of these problems are not easy and appear to be a challenging task to the researchers. Crisp sets and fuzzy sets suffer to deal with these. Hesitant fuzzy set—a protracted version of fuzzy set—comes into the fore to bridge over the gap. The set of all possible values of membership of hesitant fuzzy set might be considered as a set of possible intervals. Non-membership functions are also added therein to get intuitionistic interval-valued hesitant fuzzy numbered sets. In the literature, several aggregation operators exist, and here we consider a new one which is easy to apply in our formulated problems. Here, a matrix game whose payoffs are intuitionistic interval-valued hesitant fuzzy numbers is solved using our proposed aggregation operator. A tangible management problem with numerical values is demonstrated here to verify the applicability of the new aggregation operator over the matrix game.

Complex Pythagorean Dombi fuzzy graphs for decision making

Abstract: A complex Pythagorean fuzzy set (CPFS) is the generalization of Pythagorean fuzzy set (PFS) in which the range of degrees is extended from [0, 1] to complex plane with unit disk. The averaging operators play a significant role to transform the information into a single value. The flexibility of Dombi operators with operational parameters is outstanding, and the Dombi operators are very efficient in decision-making problems. In this research article, we present a new graph called, complex Pythagorean Dombi fuzzy graph (CPDFG) as the Dombi operators are not yet applied on CPFSs. We employ graph terminology on CPFSs using Dombi operators. We define regular, totally regular, strongly regular and biregular graphs with appropriate elaboration, and their pivotal properties are discussed. Moreover, edge regularity of CPDFG is also explained with significant characteristics. We introduce two operators, namely complex Pythagorean Dombi fuzzy arithmetic averaging (CPDFAA) and complex Pythagorean Dombi fuzzy geometric averaging (CPDFGA) operators, which are capable to aggregate the complex Pythagorean fuzzy information. We utilize CPDFAA and CPDFGA operators in solving a decision-making numerical example, which is related to the selection of suitable place to build a bus terminal in a city. In order to examine the superiority of our propose operators, we provide a comparative analysis with the existing operators.

Knowledge measure and entropy: a complementary concept in fuzzy theory

Abstract: The knowledge measure can be considered as a dual measure of entropy for fuzzy sets. In the present work, a new entropy-based knowledge measure is proposed for FSs, which complies with the extended idea of De Luca and Termini axioms. Besides this, some of its major properties are also discussed. Comparison of the proposed measure with various existing fuzzy measures indicates that the proposed knowledge measure has a greater ability in discrimination of various FSs. Moreover, a fuzzy inaccuracy measure is introduced based on the proposed measure and investigated some properties. Considering the significance of integrated weights, a new multiple attribute decision-making (MADM) model is introduced under fuzzy set environment. The proposed knowledge measure is utilized to calculate the weights vector, when weights are partially known and other when weights are completely unknown. Finally, an example is employed to illustrate the effectiveness and consistency of the new MADM method.

Complex fuzzy ordered weighted quadratic averaging operators

Abstract: A complex fuzzy set, the generalization of fuzzy set provides a powerful mathematical framework whose membership degrees are in the form of complex numbers in the unit disc. The averaging operators consisting of the properties of both t-norm and t-conorm are of great importance in complex fuzzy environment. In this paper, we present certain quadratic averaging operators, including complex fuzzy weighted quadratic averaging, complex fuzzy ordered weighted quadratic averaging, complex fuzzy Einstein weighted quadratic averaging and complex fuzzy Einstein ordered weighted quadratic averaging operators. These operators are used to study many different issues of periodic nature. We apply these models to the multi-attribute decision-making problems and wireless detection of target location. Conclusively, we can choose the best opinion by the ranking of the aggregated outputs and detect the position and direction of a target. Moreover, we describe these models through numerical examples to check their validity and importance in real life problems. To explain the consistency and authenticity of our model, we examine a comparative analysis with existing aggregation techniques.

Multi-criteria decision-making based on bi-parametric exponential fuzzy information measures and weighted correlation coefficients

Abstract: This paper proposes a new bi-parametric exponential fuzzy information measure. In addition to the validation of proposed fuzzy information measure, some of its major properties are also studied. Besides, the performance of proposed fuzzy information measure is demonstrated using two numerical examples. Further, based on the concept of TOPSIS (Technique for Order Preference by Similarity to Ideal Solutions) method, a new improved TOPSIS method based on weighted correlation coefficients has been introduced. Considering the importance of criteria weights in the solution of Multi-Criteria Decision-Making (MCDM) problems, two methods have been discussed for the evaluation of criteria weights. In first method, criteria weight evaluation from the partial information provided by experts is discussed. Second method proposes the criteria weight evaluation in case they are completely unknown or incompletely known. The proposed MCDM method is explained through a numerical example based on fault detection in an ill-functioning machine.

A deep learning approach for financial market prediction: utilization of Google trends and keywords

Abstract: This study used the amount of Internet search on Google Trend and analyzed the correlation between the search volume on Google Trend and Taiwan Weighted Stock Index. The keyword search volume provided by Google Trend was used in the correlation test and the unit root test. Then, the keywords obtained were analyzed in two experiments—first, machine learning, and second, search trend. After empirical analysis, it was found that neural network in experiment one performed better than support vector machine and decision trees. Therefore, neural network was selected to compare with the search trend in the second experiment. Through comparative analysis of calculation of return values, it was found that the return value in search trend is higher than that of the neural network. Therefore, this paper revealed that there was a correlation between using company names of Taiwan 50 Index as search keywords and the rise and fall of TAIEX index.

Failure prioritization and control using the neutrosophic best and worst method

Abstract: Failure prioritization process is described by identifying potential failures and its effects, quantifying their priorities and determining appropriate ways to mitigate or control. In the literature, many approaches are suggested to prioritize failures and associated effects quantitatively. Multicriteria decision-making (MCDM) approaches are forefront that they can express the failures verbally based on decision-makers’ judgments. They explain different types of uncertainties, which are generally modeled by fuzzy sets. However, fuzzy sets focus only on one membership value in decision-making. At this point, neutrosophic sets are more suitable than classical fuzzy sets by proposing three membership values named truth-membership, indeterminacy-membership and falsity-membership. Therefore, in this study, a novel approach based on the neutrosophic best and worst method (NBWM) is proposed and a case study is also performed in the implant production. The best and worst method (BWM) is merged with neutrosophic sets since it has fewer pairwise comparisons while determining the importance weights of failures. To show the applicability of the approach, a case study in an implant manufacturing plant that produces many products, including implants in different shapes and sizes in Turkey is carried out. Besides the case study, a comparative study is performed to test the validity of the proposed NBWM approach. This approach can make the decision-making process more dynamic in real-world problems with indeterminate and inconsistent information, considering the benefits of BWM and neutrosophic sets either individually or in integration. The present study contributes to the knowledge both methodologically and in an application by proposing NBWM for failure assessment problems for the first time in the literature and creating an adaptive model for manufacturing and other industries.