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Artificial neural networks (ANNs) are the collection of computational techniques or models encouraged by the shape and purpose of natural or organic neural networks. Furthermore, a cubic intuitionistic fuzzy (CIF) set is the modified or extended form of a Fuzzy set (FS). Our goal was to address or compute the model of Aczel-Alsina operational laws under the consideration of the CIF set as well as Aczel-Alsina t-norm (AATN) and Aczel-Alsina t-conorm (AATCN), where the model of Algebraic norms and Drastic norms were the special parts of the Aczel-Alsina norms. Further, using the above invented operational laws, we aimed to develop the model of Aczel-Alsina average/geometric aggregation operators, called CIF Aczel-Alsina weighted averaging (CIFAAWA), CIF Aczel-Alsina ordered weighted averaging (CIFAAOWA), CIF Aczel-Alsina hybrid averaging (CIFAAHA), CIF Aczel-Alsina weighted geometric (CIFAAWG), CIF Aczel-Alsina ordered weighted geometric (CIFAAOWG), and CIF Aczel-Alsina hybrid geometric (CIFAAHG) operators with some well-known and desirable properties. Moreover, a procedure decision-making technique was presented for finding the best type of artificial neural networks with the help of multi-attribute decision-making (MADM) problems based on CIF aggregation information. Finally, we determined a numerical example for showing the rationality and advantages of the developed method by comparing their ranking values with the ranking values of many prevailing tools. [ABSTRACT FROM AUTHOR]

Meta-analysis is a statistical technique used to process an overall summary estimation, and the technique of meta-analysis is mostly used in medicine, social science, and psychology. In this manuscript, we aimed to combine the techniques of the Bonferroni mean (BM) operator based on circular Pythagorean fuzzy (CPF) sets, called the CPF Bonferroni mean (CPFBM) operator, and CPF weighted Bonferroni mean (CPFWBM) operator and described their special cases with the help of two parameters, "s" and "t", and some describable properties of them are also proposed. Further, we present the evaluation technique based on distance from average solution (EDAS) technique and the proposed operators. Moreover, we use some examples to show the flexibility and dominance of the proposed operators by comparing the proposed methods with some existing techniques. [ABSTRACT FROM AUTHOR]

In 1960, Schweizer and Sklar introduced the novel Schweizer-Sklar t-norm and t-conorm which is used in the construction of aggregation operators. Schweizer-Sklar norms are more general than algebraic norms and Einstein norms. Additionally, computing the power operators based on the Schweizer-Sklar norms for complex Atanassov intuitionistic fuzzy (CA-IF) set is very awkward and complicated. In this manuscript, firstly, we propose the Schweizer-Sklar operational laws for CA-IF values, and secondly, we develop the CA-IF Schweizer-Sklar power averaging (CA-IFSSPA) operator, CA-IF Schweizer-Sklar power ordered averaging (CA-IFSSPOA) operator, CA-IF Schweizer-Sklar power geometric (CA-IFSSPG) operator, and CA-IF Schweizer-Sklar power ordered geometric (CA-IFSSPOG) operator. Some suitable and dominant properties for the above operators are also discussed. Furthermore, to simplify the above operators, we develop the procedure of decision-making technique, called multi-attribute decision-making (MADM) methods based on the proposed operators based on CA-IF values. Finally, we compare the proposed methods with some existing methods to describe the efficiency and capability of the discovered approaches by some examples. [ABSTRACT FROM AUTHOR]

Algebraic and Einstein are two different types of norms which are the special cases of the Hamacher norm. These norms are used for evaluating or constructing three different types of aggregation operators, such as averaging/geometric, Einstein averaging/geometric, and Hamacher averaging/geometric aggregation operators. Moreover, complex Atanassov intuitionistic fuzzy (CA-IF) information is a very famous and dominant technique or tool which is used for depicting unreliable and awkward information. In this manuscript, we present the Hamacher operational laws for CA-IF values. Furthermore, we derive the power aggregation operators (PAOs) for CA-IF values, called CA-IF power Hamacher averaging (CA-IFPHA), CA-IF power Hamacher ordered averaging (CA-IFPHOA), CA-IF power Hamacher geometric (CA-IFPHG), and CA-IF power Hamacher ordered geometric (CA-IFPHOG) operators. Some dominant and valuable properties are also stated. Moreover, the multi-attribute decision-making (MADM) methods are developed based on the invented operators for CA-IF information and the detailed decision steps are given. Many prevailing operators are selected as special cases of the invented theory. Finally, the derived technique will offer many choices to the expert to evaluate the best alternatives during comparative analysis. [ABSTRACT FROM AUTHOR]

The complex q-rung orthopair fuzzy (CQ-ROF) set can describe the complex uncertain information. In this manuscript, we develop the Yager operational laws based on the CQ-ROF information and Yager t-norm and t-conorm. Furthermore, in aggregating the CQ-ROF values, the power, averaging, and geometric aggregation operators have played a very essential and critical role in the environment of fuzzy set. Inspired from the discussed operators, we propose the CQ-ROF power Yager averaging (CQ-ROFPYA), CQ-ROF power Yager ordered averaging (CQ-ROFPYOA), CQ-ROF power Yager geometric (CQ-ROFPYG), and CQ-ROF power Yager ordered geometric (CQ-ROFPYOG) operators. These operators are the modified version of the Power, Yager, averaging, geometric, and the combination of these all based on fuzzy set (FS), intuitionistic FS, Pythagorean FS, q-rung orthopair FS, complex FS, complex intuitionistic FS, and complex Pythagorean FS. Moreover, we also discuss the main properties of the proposed operators. Additionally, we develop a multi-attribute decision-making (MADM) method based on the developed operators. To show the supremacy and validity of the proposed method, the comparison between the proposed method and some existing methods is done by some examples, and results show that the proposed method is better than the others in terms of generality and effectiveness. [ABSTRACT FROM AUTHOR]

The MULTIMOORA is a relatively new multi-attribute decision-making (MADM) technique containing three major parts. It has partial and complete aggregation information. The MULTIMOORA procedure contains three major parts: the full multiplicative shape, ratio system, and reference point. Furthermore, the Muirhead mean (MM) operator can easily capture the interaction between any number of preferences. The main feature of this model is to evaluate the novel theory of complex Pythagorean fuzzy uncertain linguistic (CPFUL) settings and utilize their useful properties ("algebraic laws, score value, and accuracy value"). Additionally, we combined the main theory of MM operators with information taken from the theory of CPFUL to diagnose the major idea of the CPFUL Muirhead mean (CPFULMM), CPFUL weighted Muirhead mean (CPFULWMM), CPFUL dual Muirhead mean (CPFULDMM), and CPFUL dual weighted Muirhead mean (CPFULDWMM) operators. We then evaluated their valuable properties ("idempotency, Boundedness, and monotonicity"). Moreover, to enhance the worth and feasibility of the diagnosed approach, we elaborated the extension of the MULTIMOORA method under CPFUL information. We then diagnosed a procedure of the MADM scenario whilst considering the evaluated operators using the CPFUL set theory. Lastly, to compare the diagnosed information with some old operators, we used numerical examples to illustrate the flexibility and feasibility of the presented information. [ABSTRACT FROM AUTHOR]

In an uncertain and complex decision-making environment, limited by the scope of human cognition, traditional utility decision-making has a certain deviation to actual decision-making. The revision of behavioral decision-making (BDM) to traditional rational decision-making theory makes the new model more universal. In light of this point, we reveal a new three-way decision (3WD) model by virtue of prospect theory (PT) on multi-scale information systems (MS-ISs) for persuing multi-attribute decision-making (MADM) problems. By utilizing an expected evaluation, our newly designed value function can not only reflect the relative position of the object but also avoid the drawbacks of the reference point being too subjective. Through the value function, we obtain a more reasonable avail function to replace the loss function in the traditional 3WD model. At the same time, the weighting function of the object in different states can be calculated, by synthesizing avail function and the weighting function under different decision attitudes. The comprehensive prospect value and classification conditions of the object are calculated. Then, through data selected from the UCI database, we verify the effectiveness of the constructed method. Comparative and experimental analyses are also used to illustrate the superiority and stability of our designed method. [ABSTRACT FROM AUTHOR]

With the increasing complexity of real decision-making problems, some experts try to use multi-scale information to express expert opinions in group decision-making problems. Facing the problem of group decision-making with multi-scale information, this paper attempts to explore a multi-scale group decision-making method consisting of two stages to provide theoretical support and methodological basis for establishing a multi-scale decision analysis system. In the first stage, we introduce a newly ranking decision-making approach based on a reflexive fuzzy α-neighborhood operator to deal with single-scale ranking problems with a single expert, which greatly enriches the ranking decision analysis theory. We also use a numerical example and experimental analysis to detect the stability and validity of the method. In the second stage, considering that the decision-making opinions of multiple experts may appear at the same time in the decision-making process, we propose the score labeling approach and the decision fusion approach to obtain the comprehensive decision-making result, which provides a feasible research idea for the comprehensive analysis of group decision-making results. Combining these two stages, a complete multi-scale group decision-making method in a multi-scale environment is described in detail, which can effectively deal with multi-scale group decision-making problems. Moreover, a series of simulation calculations are conducted to test the validity and stability of the proposed group decision-making method. [ABSTRACT FROM AUTHOR]

In the evaluation scenario with undesirable outputs, the SBM-Undesirable model is usually used together with the SuperSBM-Undesirable model to fully differentiate efficient and inefficient decision-making units (DMUs). The existing SuperSBM-Undesirable model has two main forms, but both have problems in implementation. One form may be infeasible under the variable returns to scale (VRS); Another form has an inappropriate definition for undesirable output efficiency. These two problems are seriously ignored in the existing applications. In this paper, we first propose an improved SuperSBM-Undesirable model with strongly efficient projections, which is feasible under the constant returns to scale (CRS) or VRS technology. Then, by integrating the SBM-Undesirable and the improved SuperSBM-Undesirable models, we focus on proposing a concise, precise and practical one-stage model considering undesirable outputs to differentiate all DMUs and determine their strongly efficient projections simultaneously. The proposed one-stage model only contains essential decision variables and constraints, thereby effectively conserving computational time for large-scale practical applications. Further, by introducing the weighting preference of inputs and outputs, we construct the one-stage model with weighting preference to differentiate the importance of different indicators. Finally, through several data experiments, the superiority of our models in computational results and computational scale are verified. [ABSTRACT FROM AUTHOR]

As a more massive feasible and prominent tool than the complex interval-valued Pythagorean fuzzy (CIVPF) set and complex interval-valued intuitionistic fuzzy (CIVIF) set, the complex interval-valued q-rung orthopair fuzzy (CIVQROF) set has been usually used to represent ambiguity and vagueness for real-life decision-making problems. In this paper, we firstly proposed some distance measures, Yager operational laws, and their comparison method. Further, we developed CIVQROF Yager weighted averaging (CIVQROFYWA), CIVQROF Yager ordered weighted averaging (CIVQROFYOWA), CIVQROF Yager weighted geometric (CIVQROFYWG), CIVQROF Yager ordered weighted geometric (CIVQROFYOWG) operators with CIVQROF information, and some certain well-known and feasible properties and outstanding results are explored in detail. Moreover, we proposed a new and valuable technique for handling multi-attribute decision-making problems with CIVQROF information. Lastly, a practical evaluation regarding the high blood pressure diseases of the patient is evaluated to illustrate the feasibility and worth of the proposed approaches. [ABSTRACT FROM AUTHOR]

Complex q-rung orthopair fuzzy (CQROF) set is very feasible to depict the complex uncertain information in real-life problems because it is the modified concept from the complex Pythagorean and complex intuitionistic fuzzy sets. In this manuscript, we concentrate to analyze the improved Einstein operational laws for CQROF information. Then, based on the improved Einstein operational laws, we develop the complex q-rung orthopair fuzzy Einstein interaction weighted geometric (CQROFEIWG) operator, complex q-rung orthopair fuzzy Einstein interaction ordered weighted geometric (CQROFEIOWG) operator, and complex q-rung orthopair fuzzy Einstein interaction hybrid geometric (CQROFEIHG) operator. Furthermore, we analyze their major results and main three properties such as idempotency, boundedness, and monotonicity. Additionally, a decision-making approach with complex q-rung orthopair fuzzy information is developed, in which weights are handled objectively. Finally, some illustrated examples are used to demonstrate the supremacy and feasibility of the proposed approaches by comparing them with some existing ones. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set (PFS), an extended version of intuitionistic fuzzy set (IFS), is verified to be fastest emerging research discipline and is a significant mode to tackle the imprecise and vague information. It provides a broader representation domain than the IFS. Similarity and divergence measures play paramount role in the field of IFSs' doctrine as well as PFSs' doctrine. These measures are integral aspects of utilizing generalized fuzzy sets in real-life problems. In this manuscript, novel similarity and divergence measures for PFSs are developed and compared with extant measures to illustrate their efficiency and reliability. Further, an extended version of multi-objective optimization based on the ratio analysis (MOORA) with the full multiplicative form (MULTIMOORA) approach is introduced by employing developed similarity and divergence measures on PFSs information. To reveal the feasibility and usefulness of the presented approach, a problem of medical equipment supplier selection is discussed from Pythagorean fuzzy perspective. Finally, a comparison with previously developed models is studied to certify the applicability and stability of the introduced MULTIMOORA technique. The outcomes of the work indicate that the present approach is more applicable and efficient than existing techniques under PFSs' context. [ABSTRACT FROM AUTHOR]

As more attention is given to environmental protection, sustainable development has become a hot topic for the international community and the companies are motivated to focus on reverse logistics (RL) in their operations for resource conservation and sustainability. However, many enterprises are limited by their economic strength and resources so that outsourcing RL to third-party reverse logistics provider (3PRLP) is their best choice. Therefore, how to effectively assess and select the 3PRLP has been a crucial issue. Given that the preference and optimism of decision makers (DMs) should be exhibited, in this paper, an improved ELECTRE II method with double attitude parameters under linguistic Z-number (LZN) environment is proposed to deal with such decision problems. Firstly, the LZN is in use to describe experts' assessments as well as the reliability of evaluations qualitatively. Then an improved ELECTRE II model based on ideal point method is presented to rank alternatives accurately, in which the main concept of ideal point method is pressed into service in determining the preference levels of alternatives and identifying the outranking relations. Meanwhile, two attitude parameters are introduced, which can express DMs' preference for risk as well as profit and their optimism for decision making, thereby making the decision process more practical and the ranking more reasonable. Then a numerical example on the selection of 3PRLP is shown to minutely explain procedures of the presented method and a sensitivity analysis on the double attitude parameters is conducted to illustrate effects of the two indexes and verify the robustness of the proposed method. Finally, some comparisons are carried out to prove its effectiveness and meliority. [ABSTRACT FROM AUTHOR]

The existing three-way decision (TWD)-making methods cannot effectively handle incomplete multiattribute decision-making (MADM) problems in real life; it is necessary to explore an effective three-way MADM model in incomplete fuzzy decision systems (IFDSs). First, we consider the preference of decision makers for each alternative and introduce the concept of predecisions, thus an IFDS is obtained. Then, the weighted conditional probabilities are calculated with the aid of the defined similarity relation. Subsequently, we introduce the notion of relative utility functions and then present an approach to determine the relative utility function values. Afterward, we construct a TWD model in IFDSs and apply it to the modeling of incomplete MADM (IMADM) problems. Our study not only enriches TWD and MADM theories but also provides a new perspective for realistic IMADM problems. At last, the results of comparative and experimental analyses demonstrate the validity, stability, and superiority of our proposed model. [ABSTRACT FROM AUTHOR]

The q-rung Orthopair fuzzy set (QROFS) is one of the fuzzy structures which can introduce more fuzzy information than other fuzzy frames proposed by Ronald R. Yager. In this article, the dynamic multiple attribute decision making (DMADM) approach with complex q-rung Orthopair fuzzy (CQROF) information has been introduced. The ideas of CQROF variable and uncertain CQROF variables are defined and introduced new dynamic weighted averaging (DWA) operators called dynamic complex q-rung Orthopair fuzzy weighted average (DCQROFWA) operator and uncertain dynamic complex q-rung Orthopair fuzzy weighted average (UDCQROFWA) operator. For the moment, a procedure has been developed based on DCQROFWA and CQROFWA operator to solve DMADM problems where all attribute information are used in complex q-rung Orthopair fuzzy numbers (CQROFNs) collected at distinct periods, and another procedure is developed based on UDCQROFWA and CIVQROFWA operators to solve uncertain DMADM problems for interval uncertainty in which all attribute information takes in the form of complex interval-valued q-rung Orthopair fuzzy numbers (CIVQROFNs) collected at distinct periods. Finally, a comprehensive comparative analysis has been made for the proposed approach for testing its applicability and efficiency by considering a numerical example. [ABSTRACT FROM AUTHOR]

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

In this study, the neutrosophic cubic graphs are further developed. We discussed and explored the open and the closed neighborhood for any vertex in neutrosophic cubic graphs, regular and totally regular neutrosophic cubic graphs, complete neutrosophic cubic graphs, balanced and strictly balanced neutrosophic cubic graphs, irregular and totally irregular neutrosophic cubic graphs, complement of a neutrosophic cubic graph, neighborly irregular and neighborly totally irregular neutrosophic cubic graphs, and highly irregular neutrosophic cubic graphs. It has been demonstrated that the proposed neutrosophic cubic graphs are associated with specific conditions. The comparison study of the proposed graphs with the existing cubic graphs has been carried out. Eventually, decision-making approaches for handling daily life problems such as effects of different factors on the neighboring countries of Pakistan and selection of a house based on the notions of proposed graphs are presented. [ABSTRACT FROM AUTHOR]

The main aim of the proposed work is to develop the new technique based on decision‐theoretical rough sets (DTRSs) and their applications in three‐way decision‐making problems. This study first develop a fractional fuzzy set (FFS) and their operations, the FFS is a more generalized and accurate tool for describing uncertainty in real‐life data information. A new form of decision technique for dealing with the issue of choice based on DTRSs is included in the three‐way decisions. The loss function of DTRSs is being used in the proposed decision method model. Initially, the idea of fractional fuzzy α‐covering (FF α‐covering), fractional fuzzy α–neighborhood (FF α–neighborhood) was introduced. Under the fractional fuzzy state, we integrated the loss function of DTRSs with covering‐based fractional fuzzy rough sets. Furthermore, we proposed and established performance characteristics for a new fractional fuzzy α‐covering decision‐theoretical rough sets model (FFCDTRSs). Then, according to the level of fractional fuzzy numbers (FFN's) positive and negative membership and related three‐way decision‐making, four methods to solve the expected loss expressed in the form of (FFNs) are described. We have developed a multicriteria decision algorithm (MCDM) based on FFCDTRS. Then an example is used to prove the feasibility of the four methods to solve the MCDM problem. Finally, the results of four distinct decision procedures with various loss functions are compared. The proposed three‐way decision‐making models are more accurate as compared with particular fuzzy sets. [ABSTRACT FROM AUTHOR]

New energy investment assessment has a significant effect on facilitating the new energy industry's development. Reasonable evaluation methods can effectively reduce the risk of new energy investment and push forward the sustainable development of new energy resources. However, there are few research results in this area, especially in the complex decision-making environment. Thus, to make up for that, an integrated multi-attribute group decision-making (MAGDM) framework is developed to assess the new energy investment problems. First, considering the complex decision-making environment of new energy investment, hesitant fuzzy dual linguistic term sets (HFDLTSs) are applied to represent the new energy alternative evaluation values. Due to the cloud models can reflect the fuzziness and uncertainties of linguistic information, an algorithm is proposed to realize the quantitative transformation from HFDLTSs to cloud models. Second, in view of the heterogeneity of decision makers (DMs) regarding to different attributes, a cloud model similarity-based method is proposed to derive the weight information of DMs. Then, an integrated TOPSIS–ORESTE method with cloud model is established to rank the new energy investment alternatives. The proposed method could overcome the information loss due to Besson's ranks. In addition, the global preference score considers the ideal and negative solutions relative to the traditional ORETSE method. Finally, a case study on new energy investment of Shandong province, China is conducted to illustrate the application of the established MAGDM model. The effectiveness and superiority of the introduced method are further demonstrated through the sensitivity analysis of parameters and the comparison with other representative methods. [ABSTRACT FROM AUTHOR]

The use of incomplete probabilistic linguistic term sets (InPLTSs) can enrich the flexibility of qualitative decision-making information expression, especially in decision-making situations with high time pressure and insufficient knowledge. In this article, we develop a method for group decision-making (GDM) with incomplete probabilistic linguistic preference relations (InPLPRs), considering consistency and consensus simultaneously. First, to fully explore the ability of InPLTSs to express uncertain information, InPLTSs are specifically classified. Then, an expected multiplicative consistency of InPLPRs is introduced, which is conducive to estimating the missing information more accurately and effectively. Subsequently, considering the consensus of GDM problems, a consensus index, which considers the principle of majority and minority, is developed to measure the agreement degree among multiple individuals. Because individual InPLPRs may not all meet acceptable consistency after reaching consensus, a consistency- and consensus-improving mathematical programming model considering information distortion is presented. Then, to aggregate all individual preference relations into a collective one, a reliability-induced ordered weighted geometric operator is introduced, whose induced variable reliability is determined by the confidence degree and consistency index of individual preference relations. Furthermore, a multiphase algorithm with InPLPRs is developed to solve GDM problems. Finally, a numerical example of fire emergency decisions is presented to illustrate the applicability of the proposed method, and a detailed validity test and comparative analysis are conducted to highlight the advantages of the proposed method. [ABSTRACT FROM AUTHOR]

A normal wiggly hesitant fuzzy set is a very useful tool to mine the potential uncertain information given by decision makers, which is considered as an extension of hesitant fuzzy set and can improve the effectiveness of decision making. Power average operator can relieve the impact on decision result of unreasonable data, and the generalized Maclaurin symmetric mean operator (GMSM) is an extension of Maclaurin symmetric mean operator with wider range of applications, which can consider the relationship among decision attributes. By integrating the advantages of them, in this paper, we develop the normal wiggly hesitant fuzzy power GMSM (NWHFPGMSM) operator and its weighted form based on the distance measure of two normal wiggly hesitant fuzzy elements, then we further discuss their properties and some special cases. Thus, a new multi-attribute decision making method based on the NWHFPGMSM operator under normal wiggly hesitant fuzzy environment is proposed. Finally, we select some examples to illustrate the effectiveness and superiority of the proposed method in this paper through comparison and analysis with other methods. [ABSTRACT FROM AUTHOR]

With growing hesitation in human perception, hesitant fuzzy set, an important extension of fuzzy set, has gained much attention from the research community. The concept of HFS gives decision makers the ability to provide multiple preferences for the same instance. However, the chance of these preferences occurring is assumed to be equal, which is unreasonable in practice. To circumvent this issue, probabilistic hesitant fuzzy set (PHFS) is adopted in this work, which is an extension of hesitant fuzzy set with associated probability values. Based on the literature review on PHFS, it is evident that (i) occurrence probability of each element was not methodically calculated; (ii) hesitation was not properly captured during criteria weight calculation; (iii) interrelationship among criteria was not captured during aggregation; and (iv) broad/rational ranking of alternatives with compromise solution was lacking. Motivated by these challenges and to alleviate the same, a systematic procedure is proposed in this paper to estimate these probabilities. Additionally, in this procedure, decision makers' preferences are aggregated using the newly proposed probabilistic hesitant fuzzy generalized Maclaurin symmetric mean operator and criteria weights are calculated using the proposed statistical variance method in the context of PHFS. A new ranking method is also proposed that extends a well-known VIKOR method to the PHFS context. Further, the practical use of the proposed decision framework is demonstrated by two examples viz., selecting a suitable coordinator for a research and development project and selection of a doctoral candidate for the supervisor position. Finally, the strength and weakness of the proposed decision framework are realized by comparing it with state-of-the-art methods. [ABSTRACT FROM AUTHOR]

Complex q-rung orthopair fuzzy set (CQROFS) is a proficient technique to describe awkward and complicated information by the truth and falsity grades with a condition that the sum of the q-powers of the real part and imaginary part is in unit interval. Further, Schweizer–Sklar (SS) operations are more flexible to aggregate the information, and the Muirhead mean (MM) operator can examine the interrelationships among the attributes, and it is more proficient and more generalized than many aggregation operators to cope with awkward and inconsistence information in realistic decision issues. The objectives of this manuscript are to explore the SS operators based on CQROFS and to study their score function, accuracy function, and their relationships. Further, based on these operators, some MM operators based on PFS, called complex q-rung orthopair fuzzy MM (CQROFMM) operator, complex q-rung orthopair fuzzy weighted MM (CQROFWMM) operator, and their special cases are presented. Additionally, the multi-criteria decision making (MCDM) approach is developed by using the explored operators based on CQROFS. Finally, the advantages and comparative analysis are also discussed. [ABSTRACT FROM AUTHOR]

In group decision-making problems, decision makers prefer to use several linguistic terms to describe their own perception and knowledge, and give their preference intensity of each possible linguistic terms based on their own understanding and interpretation. Due to the nonlinearity of decision maker's cognition, the gaps between adjacent linguistic terms are unbalanced. The unbalanced probabilistic linguistic term set (UPLTS) is proposed to present such situation. To this phenomenon, a resolution framework is constructed to analyze multiple attribute group decision-making problems under unbalanced probabilistic linguistic environment. Firstly, the integration model based on evidential reasoning theory is proposed to aggregate UPLTSs from different groups in view of incomplete probabilistic distributions in UPLTS. Secondly, the transformation function based on proportional 2 tuple is developed to transform UPLTS into probabilistic linguistic term set, making it easier for subsequent analysis and processing. Thirdly, Based on the multiple types of partitioned structure relationship among attributes, partitioned fuzzy measure is developed to globally capture these interactions among attributes. Then the probabilistic linguistic Choquet integral operator with partitioned fuzzy measure is proposed to obtain the comprehensive performances of alternatives. Lastly, the effectiveness and practicability of the proposed method is demonstrated using three numerical examples and comparing with other methods. [ABSTRACT FROM AUTHOR]

T-spherical fuzzy numbers (FNs), which add an abstinence degree based on membership and non-membership degrees, can express neutral information conveniently and have a considerable large range of information expression. The normal FNs (NFNs) are very available to characterize normal distribution phenomenon widely existing in social life. In this paper, we first define the normal T-SFNs (NT-SFNs) which can combine the advantages of T-SFNs and NFNs. Then, we define their operational laws, score value, and accuracy value. By considering the interrelationship among multi-input parameters, we propose the Maclaurin symmetric mean operator with NT-SFNs (NT-SFMSM) and its weighted form (NT-SFWMSM). Furthermore, we study some characteristics and special cases of them. Based on the NT-SFWMSM operator, we put forward a novel multi-attribute decision-making (MADM) approach. Finally, some numerical examples are conducted to prove that the proposed approach is valid and superior to some other existing methods. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy set (PyFS) is an extension of various fuzzy concepts, such as fuzzy set (FS), intuitionistic FS, and it is enhanced mathematical gizmo to pact with uncertain and vague information. In this article, some drawbacks in the Dombi operational rules for Pythagorean fuzzy numbers (PyFNs) are examined and some improved Dombi operational laws for PyFNs are developed. We also find out that the value aggregated using the existing Dombi aggregation operators (DAOs) is not a PyFN. Furthermore, we developed two new aggregations, improved existing aggregation operators (AOs) for aggregating Pythagorean fuzzy information (PyFI) and are applied to multiple-attribute decision making (MADM). To acquire full advantage of power average (PA) operators proposed by Yager, the Pythagorean fuzzy Dombi power average (PyFDPA) operator, the Pythagorean fuzzy Dombi weighted power average (PyFDWPA) operator, Pythagorean fuzzy Dombi power geometric (PyFDPG) operator, Pythagorean fuzzy Dombi weighted geometric (PyFDPWG) operator, improved the existing AOs and their desirable properties are discussed. The foremost qualities of these developed Dombi power aggregation operators is that they purge the cause of discomfited data and are more supple due to general parameter. Additionally, based on these Dombi power AOs, a novel MADM approach is instituted. Finally, a numerical example is given to show the realism and efficacy of the proposed approach and judgment with the existing approaches is also specified. [ABSTRACT FROM AUTHOR]

In regard to multicriteria decision making (MCDM) problems where the values of the criteria are expressed by 2-D uncertain linguistic variables (2DULVs), where the criteria are interactive and the criteria weights are incompletely known, two novel MCDM methods are proposed in this paper. First, we offer some novel operational laws of 2DULVs, which can avoid the operational results exceeding the boundary of linguistic term sets. Then, we propose four operators to capture the interactions over the criteria, namely, the 2-D uncertain linguistic Choquet averaging (2DULCA) operator, the 2-D uncertain linguistic Choquet geometric (2DULCG) operator, the Shapley 2DULCA (S2DULCA) operator, and the Shapley 2DULCG (S2DULCG) operator. In addition, we establish the models based on the maximization deviation approach and the Shapley function to get the criteria weights. Finally, we propose two novel MCDM methods under 2-D uncertain linguistic environments, where four examples are used to explain the created MCDM methods. Comparative experimental results are presented to highlight the superiorities of the created approaches. [ABSTRACT FROM AUTHOR]

The recently proposed q-rung orthopair fuzzy set, which is characterized by a membership degree and a non-membership degree, is effective for handling uncertainty and vagueness. This paper proposes the concept of complex q-rung orthopair fuzzy sets (Cq-ROFS) and their operational laws. A multi-attribute decision making (MADM) method with complex q-rung orthopair fuzzy information is investigated. To aggregate complex q-rung orthopair fuzzy numbers, we extend the Einstein operations to Cq-ROFSs and propose a family of complex q-rung orthopair fuzzy Einstein averaging operators, such as the complex q-rung orthopair fuzzy Einstein weighted averaging operator, the complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator, the generalized complex q-rung orthopair fuzzy Einstein weighted averaging operator, and the generalized complex q-rung orthopair fuzzy Einstein ordered weighted averaging operator. Desirable properties and special cases of the introduced operators are discussed. Further, we develop a novel MADM approach based on the proposed operators in a complex q-rung orthopair fuzzy context. Numerical examples are provided to demonstrate the effectiveness and superiority of the proposed method through a detailed comparison with existing methods. [ABSTRACT FROM AUTHOR]

This article puts forward an innovative notion of complex picture fuzzy set (CPFS) which is particularly an extension and a generalization of picture fuzzy sets (PFSs) by the addition of phase term in the description of PFSs. The uniqueness of CPFS lies in the capability to manage the uncertainty and periodicity, simultaneously, due to the presence of phase term which broadens the range of CPFS from a real plane to the complex plane of unit disk. We describe and verify the fundamental operations and properties of CPFSs. We introduce the aggregation operators, namely; complex picture fuzzy power averaging and complex picture fuzzy power geometric operators in CPFSs environment, based on weighted and ordered weighted averaging and geometric operators. We construct multi-criteria decision making (MCDM) problem, using these operators and describe a numerical example to illustrate the validity and competence of this article. Finally, we discuss the advantages of this generalized concept of aggregation technique and analyze a comparative study to demonstrate the superiority and consistency of our model. [ABSTRACT FROM AUTHOR]

The dual generalized Bonferroni mean operator is a further extension of the generalized Bonferroni mean operator which can take the interrelationship of different numbers of attributes into account by changing the embedded parameter. The 2-dimensional uncertain linguistic variable (2DULV) adds a second dimensional uncertain linguistic variable (ULV) to express the reliability of the assessment information in first dimensional information, which is more rational and accurate than the ULV. In this paper, for combining the advantages of them, we propose the dual generalized weighted Bonferroni mean operator for 2DULVs (2DULDGWBM) and the dual generalized weighted Bonferroni geometric mean operator for 2DULVs (2DULDGWBGM). In addition, we explore several particular cases and some rational characters of them. Further, a new approach is introduced to handle multi-attribute decision making problems in the environment of 2DULVs by the proposed operators. Finally, we utilize several illustrative examples to testify the validity and superiority of this new method by comparing with several other methods. [ABSTRACT FROM AUTHOR]

As the development and extension of hesitant fuzzy linguistic term sets (HFLTSs), free double hierarchy hesitant fuzzy linguistic term sets (FDHHFLTSs) can describe the evaluation information in more detail. In addition, in practical multiple attribute decision-making (MADM) problems, priority relations and interaction relations usually exist among attributes, and the prioritized interactive Choquet (PIC) operator based on generalized prioritized measure-guided aggregation (GPMGA) operator and Choquet integral (CI) operator is an effective tool for dealing with decision-making problems with priority relations and interaction relations. Under the above contexts, we improve the PIC operator and propose the FDHHFLPIC operator which can aggregate the evaluation information under free double hesitant fuzzy linguistic environment and take both priority and interaction relations into account. Furthermore, we propose an approach based on the FDHHFLPIC operators to address the real MADM problem, and the proposed method considering the different relations between attributes in decision-making process. Finally, two numerical examples are given to demonstrate the effectiveness and advantages of the proposed method which can consider priority relations and interaction relations under the FDHHFLTSs. [ABSTRACT FROM AUTHOR]

Normal wiggly hesitant fuzzy set (NWHFS) is a new fuzzy information form to help decision makers (DMs) express their evaluations, which can further dig the potential uncertain information hidden in the original data given by the DMs. Firstly, we define a new distance measure and new operational laws of NWHFSs. Then, for the situation where attribute weights are completely unknown, we propose an extended CCSD method to produce them objectively, which comprehensively uses standard deviation (SD) and correlation coefficient (CC). What's more, we introduce the MABAC (multiattributive border approximation area comparison) method, which takes the distance between alternatives and the border approximation area (BAA) into consideration for handling the complex and uncertain decision‐making problems. Meanwhile, we combine the MABAC method with prospect theory (PT), which considers DMs' psychological behavior, and propose a new NWHF‐CCSD‐PT‐MABAC method to cope with the multi‐attribute decision making problems under normal wiggly hesitant fuzzy environment. Lastly, we illustrate the validity and advantages of the proposed method through an example of college book supplier selection. [ABSTRACT FROM AUTHOR]

The complex q-rung orthopair fuzzy set (Cq-ROFS), an efficient generalization of complex intuitionistic fuzzy set (CIFS) and complex Pythagorean fuzzy set (CPFS), is potent tool to handle the two-dimensional information and has larger ability to translate the more uncertainty of human judgment then CPFS as it relaxes the constrains of CPFS and thus the space of allowable orthopair increases. To solve the multi-criteria decision making (MCDM) problem by considering that criteria are at the same priority level may affect the results because in realistic situations the priority level of criteria is different. In this manuscript, we propose some useful prioritized AOs under Cq-ROF environment by considering the prioritization among attributes. We develop two prioritized AOs, namely complex q-rung orthropair fuzzy prioritized weighted averaging (C-qROFPWA) operator and complex q-rung orthropair fuzzy prioritized weighted geometric (Cq-ROFPWG) operator. We also consider their desirable properties and two special cases with their detailed proofs. Moreover, we investigate a new technique to solve the MCDM problem by initiating an algorithm along with flowchart on the bases of proposed operators. Further, we solve a practical example to reveal the importance of proposed AOs. Finally, we apply the existing operators on the same data to compare our computed result to check the superiority and validity of our proposed operators. [ABSTRACT FROM AUTHOR]

To be able to describe more complex fuzzy uncertainty information effectively, the concept of q-rung orthopair fuzzy sets (q -ROFSs) was first proposed by Yager. The q-ROFSs can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree from the decision-makers, where q ≥ 1, so they outperform the traditional intuitionistic fuzzy sets and Pythagorean fuzzy sets. In real decision-making problems, there is often an interaction phenomenon between attributes. For aggregating these complex fuzzy information, the Maclaurin symmetric mean (MSM) operator is more superior by considering interrelationships among attributes. In addition, the power average (PA) operator can reduce the effects of extreme evaluating data from some experts with prejudice. In this paper, we introduce the PA operator and the MSM operator based on q-rung orthopair fuzzy numbers (q-ROFNs). Then, we put forward the q-rung orthopair fuzzy power MSM (q-ROFPMSM) operator and the q-rung orthopair fuzzy power weighed MSM (q-ROFPWMSM) operator of q-ROFNs and present some of their properties. Finally, we present a novel multiple-attribute group decision-making (MAGDM) method based on the q-ROFPWA and the q-ROFPWMSM operators. The experimental results show that the novel MAGDM method outperforms the existing MAGDM methods for dealing with MAGDM problems. [ABSTRACT FROM AUTHOR]

The unbalanced linguistic terms set (ULTS) is a special linguistic term set which can describe the vagueness assessment that is non-uniform and non-symmetrical distributed. So, it is effective to describe the uncertainty information existed in some special real decision making problems by ULTS. As a special prioritized operator, the scaled prioritized (SP) operator has the advantage of taking the priority among different criteria into account by detailed priority labels in known case and unknown case. In this paper, we combine the merits of SP operators and ULTS for dealing with some special multi-criteria decision making (MCDM) problems where there is a priority relationship between criteria under ULTS evaluation information. We present the unbalanced 2-tuple linguistic scaled prioritized averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric averaging operator, which can handle the issues of the detailed priority relationship among different categories of MCDM problems in knowable case. Further, we propose the unbalanced 2-tuple linguistic scaled prioritized weighted averaging operator and the unbalanced 2-tuple linguistic scaled prioritized geometric weighted averaging operator, which can deal with the case when the detailed priority relationship among different categories of different criteria is unknowable. Then, we discussed several characteristics of the proposed operators, such as boundedness, monotonicity, and idempotency. Besides, we presented an approach for the MCDM problems according to the proposed operators. In the last, we provide an example to explain the calculating steps and effectiveness of these methods. [ABSTRACT FROM AUTHOR]

The information measures (IMs) of complex fuzzy information are very useful tools in the areas of machine learning and decision making. In some multi-attribute group decision making (MAGDM) problems, the decision makers can make a decision mostly according to IMs such as similarity measures (SMs), distance measures (DIMs), entropy measures (EMs) and cross-entropy measures (C-EMs) in order to choose the best one. However, the relation between C-EMs and DIMs in the environment of complex fuzzy sets (CFSs) has not been developed and verified. In this manuscript, the notions of DIMs and C-EMs in the environment of CFSs are investigated and the relation between DIMs and EMs in the environment of CFSs is also discussed. The complex fuzzy discrimination measures (CFDMs), the complex fuzzy cross-entropy measures (CFC-EMs), and the symmetry complex fuzzy cross-entropy measures (SCFC-EMs) are proposed. We also examined that the C-EMs satisfied all the conditions of DIMs, and finally proved that C-EMs including CFC-EMs were also a DIMs. In last, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

Probability multi-valued neutrosophic set (PMVNS) is a preferable tool to capture the preference and hesitancy of decision makers (DMs) and to depict inconsistent and ambiguous information. In this paper, we improve the multi-attributive border approximation area comparison (MABAC) method under the PMVNS environment and establish a three-phase multi-attribute group decision-making (MAGDM) method. Firstly, some concepts of PMVNS, traditional MABAC method and regret theory (RT) are reviewed. Then, the similarity measure for PMVNSs is defined and utilized to derive the important degree of DMs, and the likelihood of preference relations expressed by the probability multi-valued neutrosophic numbers (PMVNNs) is first presented and employed to replace the distance deviation in traditional MABAC method. Furthermore, a novel MAGDM method where the performance of alternatives is expressed by the PMVNN is established by combining the likelihood-based MABAC method and RT which considered given DMs' behavior psychology. Finally, a case study is implemented to demonstrate the feasibility and applicability of our proposed approach. [ABSTRACT FROM AUTHOR]

A normal wiggly hesitant fuzzy set (NWHFS) is a powerful and useful tool to dig the potential indeterminacy of decision makers (DMs) in the process of expressing their preferences, which can be considered as an extended form of the traditional hesitant fuzzy set (HFS). The NWHFSs can not only retain the original hesitant fuzzy information completely, but also explore potential uncertainty of theses information. TODIM is an effective method to capture the psychological behavior based on prospect theory. Considering the advantages of NWHFS and TODIM method, in this paper, we define the distance measure of any two normal wiggly hesitant fuzzy elements (NWHFEs), and put forward an extended normal wiggly hesitant fuzzy TODIM (NWHF-TODIM) approach to handle multiple attribute decision making (MADM) problems with normal wiggly hesitant fuzzy (NWHF) information. Then we use the extended NWHF-TODIM method to rank alternatives and select an ideal one. Lastly, we compare it with two existing approaches to verify the rationality and validity of the proposed approach. [ABSTRACT FROM AUTHOR]

The intuitionistic linguistic (IL) variable (ILV) can express the vague and uncertain information in a better way, and the partitioned Heronian mean (PHM) operator can group attributes that have relationships with each other into one zone and the independent attributes are in different zones, so in this paper, we will propose some new PHM operators for IL information (ILI) and then apply them to multiple attribute group decision-making (MAGDM). Firstly, the some improved operational rules for ILVs are developed, which can provide a more accurate result and avoid the loss of information, then we extend the PHM operator to the IL environment and propose the intuitionistic linguistic partitioned Heronian mean (ILPHM) operator and the intuitionistic linguistic weighted partitioned Heronian mean (ILWPHM) operator, which can fully consider the advantages of the ILI and the PHM operator. Meanwhile, we discuss some desirable properties and special cases of the two operators. Further, we develop the MAGDM approach with ILI based on the developed operators. Lastly, a numerical instance is given to verify the feasibility and the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

The basic idea underneath the generalized picture fuzzy soft set is very constructive in decision-making, since it considers, how to exploit an extra picture fuzzy input from the director to make up for any distortion in the information provided by the evaluation experts, which is defined by Khan et al. In this paper, we introduce a method to solve decision-making problems using adjustable weighted soft discernibility matrix in a generalized picture fuzzy soft set. We define the threshold functions like mid threshold, top-bottom-bottom threshold, bottom-bottom-bottom threshold, top-top-top threshold, med threshold functions and their level soft sets for generalized picture fuzzy soft sets. After, we propose two algorithms based on threshold functions, weighted soft discernibility matrix, and generalized picture fuzzy soft set. To show the supremacy of the given method we illustrate a descriptive example using weighted soft discernibility matrix in the generalized picture fuzzy soft set. Results indicate that the proposed method is more effective and generalized overall existing methods of the fuzzy soft set. [ABSTRACT FROM AUTHOR]

The linguistic D numbers (LDNs) can express the fuzzy evaluation information more easily and precisely by combining the advantages of linguistic terms (LTs) and D numbers (DNs). Existing researches on the fuzzy entropy of LDNs are rare, and most of the definitions of fuzzy entropy for LDNs are unreasonable. In view of this research gap, this paper improves the definition of fuzzy entropy of LDNs, which simultaneously considers the effects of confidence degrees and LTs on the value of fuzzy entropy in LDNs. Then, the weights of attributes can be calculated by the improved fuzzy entropy. Further, a new combination rule for LDNs is also presented in this paper. Based on these studies, we extend the traditional Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method to the LDNs and develop the LD-VIKOR method. The proposed LD-VIKOR method is convenient to handle MADM problems with unknown attributes weights under the environment of LDNs. Finally, we verify the validity and reliability of the proposed method by an illustrative example, and analyze the advantages of the proposed method by comparing it with other existing MADM methods. [ABSTRACT FROM AUTHOR]