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In this paper, we propose a new entropy measure of Pythagorean fuzzy sets (PFSs). The proposed entropy measure of PFSs can conquer the shortcomings of the existing entropy measure of PFSs. We also propose the Pythagorean fuzzy weighted arithmetic mean (PFWAM) aggregation operator (AO) of Pythagorean fuzzy numbers (PFNs). The proposed PFWAM AO of PFNs can conquer the shortcomings of the existing sine trignometry Pythagorean fuzzy weighted averaging (ST-PFWA) AO and the existing sine trignometry Pythagorean fuzzy weighted geometric (ST-PFWG) AO of PFNs. Based on the proposed entropy measure of PFSs and the proposed PFWAM AO of PFNs, we propose a new group decision making (GDM) approach in the environment of PFNs. The proposed GDM approach can conquer the shortcomings of existing GDM approaches, where they cannot distinguish the ranking orders (ROs) of alternatives in some conditions. It offers us a very useful approach to deal with GDM problems in the environment of PFNs. [ABSTRACT FROM AUTHOR]

This paper proposes a new group decision making (GDM) approach in the environments of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs, where the proposed score function of IVIFVs can overcome the drawbacks of the existing score function of IVIFVs. The properties of the proposed score function of IVIFVs are also presented. Then, we propose the advanced interval-valued intuitionist fuzzy averaging (AIVIFA) aggregation operator of IVIFVs. We also provide the proofs of the properties of the proposed AIVIFA aggregation operator. Then, we propose the advanced interval-valued intuitionist fuzzy weighted averaging (AIVIFWA) aggregation operator of IVIFVs. Then, we propose a new GDM approach based on the proposed AIVIFWA aggregation operator of IVIFVs and the proposed score function of IVIFVs. Finally, we apply the proposed GDM approach to deal with a real-world application of cloud service selection. The proposed GDM approach can overcome the drawbacks of the existing GDM approach, which is unable to distinguish the ranking orders of alternatives in some situations. The proposed GDM approach gives us a very useful way to deal with GDM problems in the environments of IVIFVs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new score function of Fermatean fuzzy numbers (FFNs). The proposed score function of FFNs can conquer the drawbacks of the existing score function of FFNs. We develop a new multicriteria decision making (MCDM) method based on the proposed score function of FFNs, the criteria importance through intercriteria correlation (CRITIC) method and the gained and lost dominance score (GLDS) method with Fermatean fuzzy information. The developed MCDM method can conquer the shortcomings of the existing MCDM methods for MCDM in the environments of FFNs. It provides us a very useful way for MCDM in the context of FFNs. [ABSTRACT FROM AUTHOR]

This paper focuses on optimal strategies and the profit allocation of the three-echelon food supply chain (FSC) formed by a farmer, a food processor and two retailers. By comparing optimal strategies in the decentralized and the centralized scenarios, we find that the centralized scenario generates the largest profit. On this basis, considering the supply chain link cycle structure and the coalition restriction caused by the technology, the division of the labor, the politics and the history reasons, this paper adopts the average tree solution to distribute the profit. To illustrate the superiority of the new distribution scheme, a numerical example is given to compare the new scheme with five previous allocation mechanisms. The results show that the new scheme is more practical and more reasonable than the previous ones. This paper proposes the first method using the cooperative game theory with the communication structure to allocate the profits of FSC with a link cycle. [ABSTRACT FROM AUTHOR]

Linguistic intuitionistic fuzzy numbers (LIFNs) are useful to express the uncertainty of qualitative aspects of information, which have received many attentions in recent years. In this paper, we propose the distance measure of linguistic intuitionistic fuzzy sets (LIFSs), where the membership grade and the non-membership grade of each element in the universe of discourse belonging to a LIFS are represented by LIFNs. We also provide the proofs of the validity and some desirable properties of the proposed distance measure of LIFSs. Moreover, we also propose the weighted distance measure of LIFSs. Based on the proposed weighted distance measure of LIFSs and the "Technique for Order Preference by Similarity to Ideal Solution" (TOPSIS) method, we propose a new group decision making (GDM) approach in the environments of LIFNs. We also use some examples to illustrate the practicability and the feasibility of the proposed GDM approach. The proposed GDM approach can overcome the drawbacks of the existing GDM approaches, where they have the drawbacks that they cannot distinguish the ranking orders of the alternatives in some situations. It provides us a very useful method for dealing with GDM problems in the environments of LIFNs. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel multiattribute decision making (MADM) approach based on Fermatean hesitant fuzzy sets (FHFSs) and the modified VIKOR method. Firstly, we propose the definition of distance measures of FHFSs and present its properties. Further, taking the effectiveness of FHFSs for dealing with ambiguous and imprecise data in MADM problems, this paper proposes the remoteness index-based Fermatean hesitant fuzzy-VIKOR (FHF-VIKOR) MADM method. The generalized distance measure for FHFSs is subsequently employed to establish the notions of remoteness indices with the positive ideal and the negative ideal remoteness indices. The objective weighting procedure is developed using the maximum deviation principle and the generalized distance measure to obtain the attributes' weights. Some examples are discussed to reveal the performance of the proposed MADM method. Finally, the advantages of the proposed MADM method in terms of the robustness and the flexibility are shown by a comparative study. The proposed MADM method based on FHFSs and the modified VIKOR method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiattribute decision making (MADM) method using the nonlinear programming (NLP) methodology and the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a new score function of IVIFVs to conquer the drawbacks of the existing score functions of IVIFVs. Then, we construct the converted matrix based on the proposed score function of IVIFVs by calculating the score value of each IVIFV in the decision matrix (DM) offered by the decision maker (DMK). Then, we construct the NLP model via the obtained converted matrix and the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute given by the DMK. Then, we solve the NLP model to obtain the optimal weight for each attribute. Then, based on the obtained converted matrix and the obtained optimal weight of each attribute, we calculate the weighted score of each alternative. Finally, the alternatives are ranked on the basis of the obtained weighted scores of the alternatives. The larger the weighted score of an alternative, the better the preference order of the alternative. The proposed MADM method can overcome the drawbacks of the existing MADM methods. It offers us a very useful approach for MADM in IVIF settings. [ABSTRACT FROM AUTHOR]

In this paper, we develop an improved linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (ILIVAIFWA) aggregation operator (AO) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs). The ILIVAIFWA AO of LIVAIFNs presented in this paper can conquer the drawbacks of the linguistic interval-valued Atanassov intuitionistic fuzzy weighted averaging (LIVAIFWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted averaging (LIVAIFOWA) AO, the linguistic interval-valued Atanassov intuitionistic fuzzy weighted geometric (LIVAIFWG) AO and the linguistic interval-valued Atanassov intuitionistic fuzzy ordered weighted geometric (LIVAIFOWG) AO of LIVAIFNs. We also develop a novel group decision making (GDM) method on the basis of the proposed ILIVAIFWA AO of LIVAIFNs. The GDM method presented in this paper can oconquer the drawbacks of the existing GDM methods in the context of LIVAIFNs. [ABSTRACT FROM AUTHOR]

In this paper, we propose the advanced intuitionistic fuzzy Heronian mean (AIFHM) aggregation operator (AO) and the advanced intuitionistic fuzzy weighted Heronian mean (AIFWHM) AO of intuitonistic fuzzy values (IFVs). The proposed AIFHM AO and the proposed AIFWHM AO of IFVs have the advantage of condidering interrelationships among aggregating inputs. We also explore some properties of the proposed AIFHM AO and the proposed AIFWHM AO of IFVs. Furthermore, based on the proposed AIFWHM AO of IFVs, we propose a new group decision making (GDM) method. We also provide some examples to illustrate that the proposed GDM method can overcome the drawbacks of the existing GDM methods. The proposed GDM method offers us a very useful approach to deal with GDM problems in intuitionistic fuzzy environments. [ABSTRACT FROM AUTHOR]

Pythagorean fuzzy sets (PFSs) become a useful tool to describe the complex cognition of decision makers (DMs). In this paper, Pythagorean fuzzy preference relations (PFPRs) whose elements are PFSs are used for group decision making (GDM). First, a novel multiplicative consistency of PFPRs is proposed. Then, a programming model is constructed to derive the priority weight vector of PFPRs. Then, an inconsistency-repairing method of PFPRs is designed. Moreover, a group consensus index to calculate the degrees of similarity among PFPRs is proposed and an iterative consensus reaching procedure with PFPRs is developed. By maximizing the group consensus level of PFPRs, a model is built to determine DMs' weights. Furthermore, a new GDM method based on PFPRs is proposed. Finally, we offer an example to illustrate the proposed GDM method and complete a comparative analysis. The proposed GDM method outperforms the existing GDM methods for GDM in Pythagorean fuzzy environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a noval addition operation (AOP) and a novel scalar multiplication operation (SMOP) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs) based on Yager's t -conorm and t -norm. The proposed AOP and the proposed SMOP of LIVAIFNs can conquer the shortcomings of the existing AOP and the existing SMOP of LIVAIFNs. Based on the proposed AOP and the proposed SMOP of LIVAIFNs, we propose the linguistic interval-valued Atanassov intuitionistic fuzzy Yager weighted arithmetic (LIVAIYFWA) aggregation operator (AO) of LIVAIFNs. We also prove some properties of the proposed LIVAIFYWA AO of LIVAIFNs. Moreover, by using the proposed LIVAIFYWA AO of LIVAIFNs, we propose a noval group decision making (GDM) method. The proposed GDM method can conquer the drawbacks of the existing GDM methods in the context of LIVAIFNs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new distance measure between picture fuzzy sets (PFSs) to overcome the drawbacks of the existing distance measures between PFSs. We also propose a weight-determination method to determine attributes' weights using the proposed distance measure between PFSs. We also propose a novel multi-attribute decision-making (MADM) method on the basis of the proposed distance measure between PFSs and the modified combined compromise solution (CoCoSo) method. The proposed MADM method can overcome the drawbacks of the existing MADM methods based on PFSs. It gives us a very useful way for MADM in picture fuzzy environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose the q -rung orthopair fuzzy weighted averaging (q -ROFWA) aggregation operator (AO) of q -rung orthopair fuzzy numbers (q -ROFNs). The proposed q -ROFWA AO of q -ROFNs can overcome the drawbacks of the q -rung orthopair fuzzy interaction weighted Hamy mean (q -ROFIWHM) AO and the q -rung orthopair fuzzy power weighted Maclaurian symmetric mean (q -ROFPWMSM) AO of q -ROFNs. Moreover, we propose a new group decision making (GDM) method based on the proposed q -ROFWA AO of q -ROFNs. The proposed GDM method can overcome the drawbacks of the existing GDM methods. It provides us a very useful approach to deal with GDM problems in q -rung orthopair fuzzy environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiple attribute group decision making (MAGDM) method based on the proposed advanced linguistic intuitionistic fuzzy weighted averaging (ALIFWA) aggregation operator of linguistic intuitionistic fuzzy numbers (LIFNs). The proposed ALIFWA aggregation operator of LIFNs can overcome the shortcomings of the linguistic intuitionistic fuzzy weighted averaging (LIFWA) aggregation operator, the improved LIFWA (ILIFWA) aggregation operator, and the linguistic intuitionistic fuzzy Einstein weighted averaging (LIFEWA) aggregation operator of LIFNs, which have the shortcomings that the membership degrees and the non-membership degrees of their obtained aggregated LIFNs are indeterminated in some situations. Based on the proposed ALIFWA aggregation operator of LIFNs, we propose a new MAGDM method in linguistic intuitionistic fuzzy environments. The proposed MAGDM method can overcome the drawbacks of the existing MAGDM methods. It offers us a very useful way for handling MAGDM problems in linguistic intuitionistic fuzzy environments. [ABSTRACT FROM AUTHOR]

In this paper, we systematically study the algebraic structures of the spaces L ([ 0 , 1 ]) , encompassing all closed subintervals of [ 0 , 1 ] , under the generated admissible orders. We first prove that the admissible order on L ([ 0 , 1 ]) generated by a non-degenerate matrix must be the form of two weighted averaging operators. As a corollary, we deduce that each admissible order on L ([ 0 , 1 ]) generated by a non-degenerate matrix and the standard order ≤ on [ 0 , 1 ] are not isomorphic. Furthermore, we show that each admissible order on L ([ 0 , 1 ]) derived from two continuous mappings and the standard order ≤ on [ 0 , 1 ] are not isomorphic, partially answering a conjecture proposed by Santana et al. (2020) [38]. Besides, we prove that L ([ 0 , 1 ]) is a complete lattice under the admissible order generated by two continuous mappings. This is the first result regarding the completeness of L ([ 0 , 1 ]). Finally, we apply the admissible orders to solve a minimal path problem within the context of interval-valued fuzzy weighted graph. The above results theoretically refine the study of the classification, non-isomorphism, and completeness of admissible orders, while expanding the scope of interval-valued fuzzy sets in practical applications. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new similarity measure (SM) between picture fuzzy sets (PFSs). The proposed SM between PFSs can overcome the drawbacks of the existing SMs between PFSs. We also propose a weight-determination approach based on the proposed SM between PFSs to determine attributes' weights in picture fuzzy environments. We also propose a new multi-attribute decision-making (MADM) approach based on the proposed SM between PFSs and the Measurement of Alternatives and Ranking according to Compromise Solution (MARCOS) method for MADM with picture fuzzy information. The proposed MADM approach can overcome the shortcomings of the existing MADM approaches based on PFSs. It provides us a very useful approach for MADM in picture fuzzy settings. [ABSTRACT FROM AUTHOR]

This paper proposes a new approach for multiattribute decision making (MADM) using the proposed q -rung orthopair fuzzy Yager prioritized weighted arithmetic (q -ROFYPWA) aggregation operator (AO) of q -rung orthopair fuzzy numbers (q -ROFNs). Firstly, we propose the q -ROFYPWA AO of q -ROFNs based on Yager's t -conorm and t -norm and the concept of prioritized average AO. The proposed q -ROFYPWA AO consider the prioritized relationship among aggregating q -ROFNs. Moreover, we present several properties of the proposed q -ROFYPWA AO. Then, we propose a new MADM approach based on the proposed q -ROFYPWA AO of q -ROFNs. The propsoed MADM approach considers the prioritization among the attributes to overcome the drawbacks of the existing MADM approaches, where they cannot distinguish the ranking orders of the alternatives in some situations. The proposed MADM approach is very useful for MADM in the environment of q -ROFNs. [ABSTRACT FROM AUTHOR]

• We propose a new score function of interval-valued intuitionistic fuzzy values (IVIFVs). • We propose a new MADM method based on the proposed score functions of IVIFVs. • It is based on the Beta distribution and the expected values of intervals. • It deals with MADM in the interval-valued intuitionistic fuzzy (IVIF) context. • The proposed method provides us with a very useful way for MADM in the IVIF context. In this paper, we propose a new multiple attribute decision making (MADM) method using the Beta distribution of intervals, the expected values of intervals, and the proposed new score function of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, it transformed each IVIFV in the decision matrix (DM) into three intervals to get the transformed matrix (TM). Then, it calculates the expected values of the obtained three intervals for each triplet in the TM, respectively, and then uses the proposed new score function to calculate the score value of each IVIFV in the DM to obtain the score matrix. Then, it transforms the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute into three intervals and calculates the expected values of the obtained three intervals, respectively. Then, it uses the proposed new score function to calculate the score value of the IVIF weight of each attribute to obtain the normalized optimal weight of each attribute. Finally, based on the obtained score matrix and the obtained optimal weight of each attribute, it computes the weighted score of each alternative to get the preference order of alternatives. The proposed MADM method can overcome the drawbacks of the existing MADM methods in IVIF environments. [ABSTRACT FROM AUTHOR]

Trapezoidal fuzzy numbers are efficient to represent the quantitative vagueness and ambiguity of decision makers (DMs). Preference relations are powerful to express pairwise judgments of DMs with respect to alternatives. Combining their advantages, this paper focuses on group decision making (GDM) with multiplicative trapezoidal fuzzy preference relations (MTrFPRs) and proposes a new consistency-consensus based GDM method. To achieve this goal, a new consistency concept for MTrFPRs is proposed by analyzing the drawbacks of the previous ones. By utilizing this concept, optimal models for judging the consistency of MTrFPRs are built. Meanwhile, a consistency index is proposed to measure the consistency level of any given MTrFPR. After that, an algorithm for ranking alternatives from acceptable consistent MTrFPRs is proposed. For GDM, a central-derivation model for determining the fuzzy measure on a set of DMs is proposed. Furthermore, an optimal model for reaching the consensus threshold is constructed. Finally, a GDM method with MTrFPRs is proposed and an application example is utilized to show the efficiency of the proposed GDM method and to compare with the existing GDM methods. The proposed GDM method outperforms the existing GDM methods. It provides us with a very useful way for GDM based on MTrFPRs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs) and the means and the variances of score matrices, where the proposed score function can conquer the shortcomings of the existing score functions. Firstly, it computes the score value of each IVIFV in the decision matrix based on the proposed score function to construct the score matrix. Then, it calculates the mean and the variance of the obtained score matrix. Then, it builds the standard score matrix based on the obtained score matrix. Then, it converts the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute into a crisp weight based on the proposed score function. Finally, based on the obtained standard score matrix and the obtained converted IVIF weights, it calculates the weighted score of each alternative to rank the alternatives. The larger the weighted score of an alternative, the better the preference order (PO) of the alternative. The proposed MADM method can conquer the shortcomings of the existing MADM methods. It offers us a very useful way for MADM in IVIF environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiattribute decision making (MADM) method on the basis of the proposed score function of interval-valued intuitionistic fuzzy values (IVIFVs) and normalized score matrices. Firstly, it calculates the score value of each IVIFV in the decision matrix (DM) based on the proposed score function of IVIFVs to construct the score matrix. Then, it constructs the normalized score matrix based on the obtained score matrix. Then, it computes the optimal weight of the interval-valued intuitionistic fuzzy (IVIF) weight of each attribute. Then, based on the obtained normalized score matrix and the obtained optimal weight of the IVIF weight of each attribute, it constructs the weighted normalized DM. Then, based on the obtained weighted normalized DM, it calculates the weighted score value of each alternative. Finally, it ranks the alternatives based on the weighted score values of the alternatives. The larger the weighted score value of an alternative, the better the preference order (PO) of the alternative. The proposed MADM method overcomes the drawbacks of the existing MADM methods. The proposed MADM method provides a very useful way to us for dealing with MADM problems in IVIF environments. [ABSTRACT FROM AUTHOR]

The q -rung orthopair fuzzy preference relations are useful tools to represent hesitant and uncertain judgments of decision makers. In this paper, we propose a new group decision making method based on multiplicative consistency-and-consensus preference analysis for incomplete q -rung orthopair fuzzy preference relations. First, we provide a novel concept of multiplicative consistency for q -rung orthopair fuzzy preference relations. Then, a multiplicative consistency index is offered, by which we derive the concept of acceptable multiplicative consistency for q -rung orthopair fuzzy preference relations. Following this concept, optimization models for ascertaining unknown values in an incomplete q -rung orthopair fuzzy preference relation are built. Furthermore, optimization models for obtaining acceptable multiplicative q -rung orthopair fuzzy preference relation are proposed. Then, an optimization model for group decision making is proposed to attain an enough consensus. Afterward, a group decision making method with incomplete and unacceptable multiplicative consistent q -rung orthopair fuzzy preference relations is proposed. Finally, we use an application example to show the practicality of the proposed group decision making method. The proposed group decision making method outperforms the existing group decision making methods for group decision making in incomplete q -rung orthopair fuzzy environments. [ABSTRACT FROM AUTHOR]

This paper proposes a new group decision making (GDM) method based on the consistency and the consensus analysis of dual multiplicative linguistic preference relations (DMLPRs). A new type of linguistic variables, called dual multiplicative linguistic variables (DMLVs), is presented, which is defined on the multiplicative linguistic scale. DMLVs are used to represent asymmetrical qualitative hesitancy judgments of decision makers (DMs). A maximum-consistency-based interactive algorithm to derive multiplicative linguistic intuitionistic preference relations (MLIPRs) is presented, by which the consistency concept for DMLPRs is obtained. Then, we define the concept of inconsistent DMLPRs and propose an optimal-model-based method for deriving consistent DMLPRs. Furthermore, incomplete DMLPRs also can be dealt with by the proposed maximum-consistency-based interactive algorithm. For GDM, the weights of DMs are determined by the cosine-based correlation coefficient between individual DMLPRs. Moreover, we propose a consensus measure to calculate the agreement degree of DMLPRs and build an optimal model to increase the consensus level of individual DMLPRs. Finally, a new GDM method (call Algorithm III) is offered and an application example is used to illustrate the proposed GDM method. The proposed GDM method outperforms the former GDM methods for GDM in the environments of DMLPRs. [ABSTRACT FROM AUTHOR]

• We propose an information entropy measure for intuitionistic fuzzy values (IFVs). • We propose the IIFEWA operator for IFVs. • We propose a new multiattribute decision making (MADM) method. • The proposed MADM method is based on the proposed IIFEWA operator of IFVs. • It provides us with a very useful way for MADM in the intuitionistic fuzzy context. This paper proposes the improved intuitionistic fuzzy Einstein weighted averaging (IIFEWA) operator of intuitionistic fuzzy values (IFVs). The proposed IIFEWA operator can overcome the drawbacks of the intuitionistic fuzzy Einstein improved weighted averaging (IFEIWA) operator, the intuitionistic fuzzy Hamacher improved weighted averaging (IFHIWA) operator, the intuitionistic fuzzy Hamacher weighted averaging (IFHWA) operator, the intuitionistic fuzzy Einstein weighted averaging (I F W A ω ε) operator, the intuitionistic fuzzy weighted averaging (IFWA) operator and the intuitionistic fuzzy Hamacher interactive ordered weighted averaging (IFHIOWA) operator of IFVs, where they have the drawbacks that (1) the membership grades and the non-membership grades of their obtained aggregating IFVs are indeterminated in some situations and (2) if there is only one IFV whose membership grade is equal to 1, then the membership grade of the aggregated IFV of n IFVs becomes 1; if there is only one IFV whose non-membership grade is equal to 0, then the non-membership grade of the aggregated IFV of n IFVs becomes 0. Based on the proposed IIFEWA operator, we propose a new multiattribute decision making (MADM) method. The proposed MADM method overcomes the drawbacks of the existing MADM methods, where they cannot distinguish the ranking orders of alternatives in some situations. [ABSTRACT FROM AUTHOR]

In this paper, we propose an optimization-based group decision making (GDM) method using interval-valued intuitionistic fuzzy preference relations (IVIFPRs). First, the concept of consistency of intuitionistic fuzzy preference relations (IFPRs) is provided. Moreover, the consistency index for IFPRs is presented. Subsequently, by splitting an IVIFPR into two IFPRs, an additive consistency is proposed for IVIFPRs. Afterward, a consensus index is presented for GDM. When the consistency and the consensus do not achieve the requirement, we propose several models to reach the requirement. Furthermore, individual IVIFPRs are integrated into a collective IVIFPR. After that, a procedure is offered to obtain the interval-valued intuitionistic fuzzy (IVIF) priority weights of the alternatives. Moreover, a new GDM method with IVIFPRs is offered. Finally, some application examples are offered. The proposed GDM method can conquer the shortcomings of the existing GDM methods. It offers us a useful way for GDM in the IVIF context. [ABSTRACT FROM AUTHOR]

To deal with multicriteria decision making (MCDM) problems with interaction criteria, the Choquet integral (CI) is one of effective tools. This paper first proposes the reverse Choquet integral (RCI), which defines the importance of the ordered elements in an opposite principle to the CI. To show the principle of the RCI, we offer its concrete expression in view of the Möbius representation by which one can clearly see the difference and the relationship between the CI and the RCI. Then, we propose the "bi-direction Choquet integral" (BDCI), which is a convex combination of the CI and the RCI. To get the interactions of ordered coalitions comprehensively, this paper further proposes the generalized Shapley bi-direction Choquet integral (GSBDCI). Furthermore, the hybrid generalized Shapley bi-direction Choquet integral (HGSBDCI) is proposed, which defines the importance of ordered positions and the criteria with interactions simultaneously. With respect to these types of CIs, their exponent forms are also discussed. Finally, we use an application case to show the utilization of the proposed new CIs for MCDM. The proposed new Choquet integrals provide us a very useful way to deal with MCDM problems. [ABSTRACT FROM AUTHOR]

• We propose a new multiattribute decision making (MADM) method. • It deals with MADM in interval-valued intuitionistic fuzzy (IVIF) environments. • It obtains the converted decision matrix (CDMx) from the IVIF decision matrix. • It is based on the CDMx, probability density functions and IVIF values. • The proposed MADM method can conquer the shortcomings of the existing MADM methods. In this paper, we propose a new multiattribute decision making method based on converted decision matrices, probability density functions and interval-valued intuitionist fuzzy values. First, it obtains the converted decision matrix from the interval-valued intuitionistic fuzzy decision matrix given by the decision maker. Then, it computes the standard deviations and the mean values of the intervals appear at each row of the converted decision matrix, respectively, by using probability density functions. Then, by using the mean values and the standard deviations of the alternatives and the converted decision matrix, it gets the z -score decision matrix. Afterwards, the optimal weights of the attributes are calculated from the interval-valued intuitionist fuzzy weights of the attributes. Finally, it computes the value of overall performance of each alternative by using the z -score decision matrix and the optimal weights of the attributes for ranking the alternatives. The proposed method can conquer the shortcomings of the existing methods for interval-valued intuitionistic fuzzy multiattribute decision making. [ABSTRACT FROM AUTHOR]

• We propose a novel score function for connection numbers (CNs). • We propose a new multiattribute decision making (MADM) method. • It is based on the proposed score function of CNs and the set pair analysis theory. • It deals with MADM in the interval-valued intuitionistic fuzzy (IVIF) context. • The proposed method provides us with a very useful way for MADM in the IVIF context. This paper proposes a new multiattribute decision making (MADM) method based on the proposed score function of connection numbers (CNs) and the set pair analysis (SPA) theory in the interval-valued intuitionist fuzzy (IVIF) context. Firstly, we develop a score function for ranking CNs. The various notable characteristics of the proposed score function of CNs are also presented. Then, we propose a new MADM method based on interval-valued intuitionist fuzzy values (IVIFVs), the proposed score function of CNs and the SPA theory, where we convert IVIFVs into CNs and the optimal weights of attributes are calculated from the IVIF weights of attributes. Finally, the proposed MADM method is applied for MADM in the IVIF context, where the preference orders (POs) of the alternatives obtained by the proposed MADM method are compared with the ones obtained by the existing MADM methods. The proposed MADM method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

• We propose a novel score function for connection numbers (CNs). • We propose a new multiattribute decision making (MADM) method. • It is based on the proposed score function of CNs and the set pair analysis theory. • It deals with MADM in the interval-valued intuitionistic fuzzy (IVIF) context. • The proposed method provides us with a very useful way for MADM in the IVIF context. This paper proposes a new multiattribute decision making (MADM) method based on the proposed score function of connection numbers (CNs) and the set pair analysis (SPA) theory in the interval-valued intuitionist fuzzy (IVIF) context. Firstly, we develop a score function for ranking CNs. The various notable characteristics of the proposed score function of CNs are also presented. Then, we propose a new MADM method based on interval-valued intuitionist fuzzy values (IVIFVs), the proposed score function of CNs and the SPA theory, where we convert IVIFVs into CNs and the optimal weights of attributes are calculated from the IVIF weights of attributes. Finally, the proposed MADM method is applied for MADM in the IVIF context, where the preference orders (POs) of the alternatives obtained by the proposed MADM method are compared with the ones obtained by the existing MADM methods. The proposed MADM method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

• We propose an additive consistency definition for q -ROFPRs. • We propose the models for dealing with incomplete and inconsistent q -ROFPRs. • We propose a method to increase the consensus degrees of q -ROFPRs. • We propose a new GDM method in incomplete q -ROFPRs environments. • The proposed GDM method can overcome the drawbacks of the existing GDM methods. In this paper, we propose a novel group decision making (GDM) method in incomplete q -rung orthopair fuzzy preference relations (q -ROFPRs) environments. We propose an additive consistency definition, which is characterized by a q -rung orthopair fuzzy priority vector. The property of the proposed additive consistency definition is offered and a model to obtain missing judgments in incomplete q -ROFPRs is proposed. We present an approach to adjust the inconsistency for q -ROFPRs, propose a model to obtain the priority vector, and propose a method to increase consensus degrees of q -ROFPRs. Finally, we present a GDM method in incomplete q -ROFPRs environments and use two illustrative examples and some comparisons to illustrate that our method outperforms the existing methods for GDM in incomplete q -ROFPRs environments. The proposed GDM method offers us a useful way for GDM in incomplete q -ROFPRs environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method for multiattribute decision making (MADM) using probability density functions and the transformed decision matrix (TDMx) of the decision matrix (DMx) offered by the decision maker (DM) in interval-valued intuitionistic fuzzy (IVIF) environments. First, it gets the TDMx of the DMx given by the DM. Then, it computes the average value of the interval-valued intuitionistic fuzzy values (IVIFVs) appearing at each column of the TDMx. Then, it calculates the variance of each IVIFV in the TDMx. Then, it computes the standard deviation (SD) of the IVIFVs appearing at each column of the TDMx. Then, based on the obtained TDMx, the obtained average value of the IVIFVs appearing at each column of the TDMx, and the obtained SD of the IVIFVs appearing at each column of the TDMx, it gets the z -score DMx. Then, each attribute's IVIF weight is transformed into a crisp weight between zero and one. Finally, each alternative's weighted score is calculated using the z -score DMx and each attribute's transformed crisp weight. The larger the weighted score of an alternative, the better the preference order (PO) of the alternative. It can overcome the shortcomings of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new group decision making (GDM) approaches based on the proposed linguistic intuitionistic fuzzy Yager weighted arithmetic (LIYFWA) aggregation operator (AO) of linguistic intuitionistic fuzzy numbers (LIFNs), where the proposed first GDM considers the situation that experts' weights and attributes' weights are completely known; the proposed second GDM approach considers the situation that experts' weights and attributes' weights are completely unknown. Firstly, we propose new operational laws for LIFNs based on Yager's norm, namely, the addition operation operation and the scalar multiplication operation. The proposed addition operation and the proposed scalar multiplication operation of LIFNs can conquer the drawbacks of the existing addition operation and the existing scalar multiplication operation of LIFNs. Then, based on the proposed addition operation and the proposed scalar multiplication operation of LIFNs, we propose the LIYFWA AO of LIFNs. We also prove some properties of the proposed LIFYWA AO. Finally, based on the proposed LIFYWA AO, we propose two new GDM approaches of LIFNs. The proposed GDM approaches can conquer the drawbacks of existing GDM methods, where they cannot distinguish the ranking orders of alternatives in some situations. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the Gini coefficient, and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs). Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of the existing SFs of IVIFVs. Then, we construct a score matrix (SMX) based on the proposed SF of IVIFVs and the decision matrix given by the decision maker (DMK). Then, we construct a NLP model based on the constructed SMX, the Gini coefficient, and the interval-valued intuitionistic fuzzy (IVIF) weights of the attributes given by the DMK. After solving the constructed NLP model, we obtain the optimal weight (OW) of each attribute. Then, we compute the weighted score (WS) of each alternative based on the constructed SMX and the obtained OWs of the attributes. Finally, we rank the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods in IVIF environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method using the proposed nonlinear programming (NLP) model, the proposed score function (SCF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the standard deviation of the score values appeared in each column of the constructed score matrix (SX). The proposed SCF of IVIFVs can overcome the shortcomings of the existing SCFs of IVIFVs. Firstly, we construct the SX using the decision matrix given by the decision maker and the proposed SCF of IVIFVs. Then, we construct a NLP model using the obtained SX, the standard deviation of the score values appeared in each column of the SX, the interval-valued intuitionistic fuzzy weights of the attributes, the largest ranges of IVIFVs, and the concept of deviation variables. Then, we solve the NLP model to get the optimal weights of the attributes, respectively. Then, based on the constructed SX and the obtained optimal weights of the attributes, we calculate the weighted score of each alternative. Finally, we rank the alternatives according to the obtained weighted scores. The proposed MADM method can overcome the drawbacks of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel multiple attribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the distance between the score values appeared in the constructed score matrix (SCMX), and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), where the NLP model is used to get the optimal weights (OWs) of the attributes. Firstly, we propose a novel SF to conquer the shortcomings of the existing SFs of IVIFVs. Then, we use the proposed SF to construct the SCMX from the decision matrix (DM) given by the decision maker (DK). Then, we propose a NLP model to obtain the OWs of the attributes based on the distance between the score values appeared in the constructed SCMX, the interval-valued intuitionistic fuzzy weights (IVIFWs) of the attributes provided by the DK, the concept of deviation variables, and the largest range of the IVIFW of each attribute. Then, we calculate the weighted score (WS) of each alternative based on the obtained SCMX and the obtained OWs of the attributes. Finally, we rank the alternatives according to the WSs of the alternatives. The proposed MADM method can conquer the shortcomings of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, and the proposed nonlinear programming (NLP) model. The proposed SF of IVIFVs overcomes some shortcomings of the existing SFs of IVIFVs. The proposed MADM method overcomes some shortcomings of the existing MADM methods based on IVIFVs. Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of some existing SFs of IVIFVs. Then, we construct a score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, we build a NLP model based on the cosine similarity measure of IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes. Then, we solve the NLP model to obtain the optimal weights (OWs) of the attributes, respectively. Based on the obtained OWs of the attributes and the constructed score matrix, we compute the weighted scores (WSs) of the alternatives, respectively. Finally, we rank the alternatives based on the obtained WSs. The proposed MADM method provides us a very useful approach for MADM in the interval-valued intuitionistic fuzzy context. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the dispersion degree of the score values appeared in each column of the score matrix (SMX). Firstly, we propose a new SF of IVIFVs to construct the SMX. The proposed SF of IVIFVs can overcome the drawbacks of the existing SFs of IVIFVs. Then, we calculate the dispersion degree of the score values appeared at each column of the SMX. Then, we construct a NLP model to get the optimal weight (OW) of each attribute based on the obtained SMX, the dispersion degree of the score values appeared at each column of the SMX, and the interval-valued intuitionistic fuzzy weights of the attributes given by the decision maker. Then, we calculate the weighted score (WS) of each alternative based on the obtained SMX and the obtained OWs of the attributes. Finally, we get the preference order (PFO) of the alternatives based on the obtained WSs of the alternatives. The proposed MADM method can overcome the drawbacks of some existing MADM methods in an interval-valued intuitionistic fuzzy setting. [ABSTRACT FROM AUTHOR]

This paper proposes a new multiple attribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the score matrix (SMT), and the proposed nonlinear programming model. Firstly, we use the proposed SF of IVIFVs to construct the SMT, where the proposed SF of IVIFVs can overcome the drawbacks of the existing SFs of IVIFVs. Then, we calculate the average value of the values appeared at each column of the SMT. Then, we construct the nonlinear programming model using the obtained SMT, the obtained average value of the values appeared at each column of the SMT, the concept of deviation variables, and the interval-valued intuitionistic fuzzy weight of each attribute offered by the decision maker. Then, we solve the nonlinear programming model to obtain the optimal weight (OW) of each attribute. Then, we calculate the weighted score (WTS) of each alternative using the obtained SMT and the OWs of the attributes. Finally, we rank the alternatives according to the obtained WTSs. The bigger the WTS of an alternative, the better the preference order (PO) of the alternative. Our proposed MADM method can overcome the shortcomings of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new multiple attribute decision making (MADM) approach based on the multi-attribute ideal-real comparative assessment (MAIRCA) method, the standard deviation-based method, and Pythagorean fuzzy sets. We also propose a weight-determining method to determine the weights of attributes using a standard deviation-based approach with Pythagorean fuzzy information. The drawbacks of the existing MADM methods in Pythagorean fuzzy environments are that they cannot distinguish the preference orders of alternatives in some situations. The proposed MADM approach can overcome the drawbacks of the existing MADM approaches in the Pythagorean fuzzy context. The main contributions of this paper include: (1) It proposes a weight-determining method to derive attributes' weights based on the standard deviation-based method with Pythagorean fuzzy information, (2) It proposes a new MADM methodology based on the MAIRCA method, the standard deviation-based method, and PFSs for MADM in the Pythagorean fuzzy setting, and (3) The proposed MADM method can overcome the shortcomings of the existing MADM methods in the Pythagorean fuzzy context. It provides us a flexible and effective method for MADM in Pythagorean fuzzy environments. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new group decision making (GDM) method based on the acceptable multiplicative consistency and consensus of hesitant fuzzy linguistic preference relations (HFLPRs). First, an approach for improving the consistency of HFLPRs is proposed to generate an acceptable multiplicative consistent HFLPR. Then, a consensus index of HFLPRs is defined and an optimization model is presented to meet an acceptable consensus requirement under the premise of the acceptable multiplicative consistency and the smallest information loss, where it yields adjusted HFLPRs with an acceptable consistency and consensus. Then, the weights of decision makers (DMs) are calculated based on the obtained adjusted HFLPRs. Moreover, we propose a new GDM method based on HFLPRs. Finally, the proposed GDM method is illustrated by an application example and comparative analyses are conducted to show the performance and the superiority of the proposed GDM method. [ABSTRACT FROM AUTHOR]

• We propose a new multiattribute decision making (MADM) method. • It is based on the U -quadratic distribution of intervals and the transformed matrix. • It deals with MADM in interval-valued intuitionistic fuzzy (IVIF) environments. • It computes the weighted score of each alternative for ranking alternatives. • The proposed MADM method can overcome the drawbacks of the existing MADM methods. In this paper, we propose a new multiattribute decision making (MADM) method based on the U -quadratic distribution of intervals and the transformed matrix of the decision matrix given by the decision maker in interval-valued intuitionistic fuzzy (IVIF) environments. First, it gets the transformed matrix of the decision matrix. Then, it calculates the variances of the intervals appearing at each element of the obtained transformed matrix, respectively. Then, it calculates the standard deviations of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it calculates the middle points of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it calculates the average values of the intervals appearing in the elements of each column of the obtained transformed matrix, respectively. Then, it builds the z -score matrix. Then, it calculates the transformed weight of the IVIF weight of each attribute. Finally, according to the obtained z -score matrix and the obtained transformed weight of the IVIF weight of each attribute, it computes the weighted score of each alternative for ranking alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop a novel multiple attribute decision making (MADM) method using the improved intuitionistic fuzzy weighted geometric (IIFWG) operator of intuitionistic fuzzy values (IFVs) proposed in this paper. First, we develop the IIFWG operator of IFVs to conquer the weak points of the existing operators of IFVs, where they have the drawbacks that their aggregated values are indeterminate in some situations. Based on the proposed IIFWG operator of IFVs, we present a MADM method to overcome the weak points of the existing MADM methods, which have the shortcomings that they obtain unreasonable ranking orders (ROs) of alternatives or they cannot discriminate the ROs of alternatives in some circumstances. [ABSTRACT FROM AUTHOR]

To represent decision makers' qualitative uncertainty and hesitation judgments, interval linguistic hesitant fuzzy variables (ILHFVs) are efficient tools, which can be regarded as an expansion of interval linguistic variables (ILVs). Taking the merits of ILHFVs and preference relations, this paper focuses on group decision making (GDM) with interval linguistic hesitant fuzzy preference relations (ILHFPRs). By considering the consistency of ILHFPRs, a new definition of acceptable consistency is presented. Using the acceptable consistency index, some models are built to measure whether a given ILHFPR is acceptable consistent. If the consistency is unacceptable, some models are constructed to derive acceptable consistent ILHFPRs by considering the total adjustment and the number of adjusting ILVs. In order to cope with incomplete ILHFPRs, some models for obtaining the values of unknown ILVs are proposed. For GDM with ILHFPRs, an index for measuring the consensus degree of ILHFPRs is proposed. When ILHFPRs do not meet the requirement of the consensus, some models for enhancing the consensus degree are proposed. According to the analysis of acceptable additive consistency and consensus of ILHFPRs, a new method for GDM with ILHFPRs is proposed. In order to show the merits of the proposed GDM method, an application example is used. [ABSTRACT FROM AUTHOR]

This paper deals with group decision making (GDM) with hesitant fuzzy preference relations (HFPRs) based on the acceptable multiplicative consistency and the consensus analysis. We first offer a multiplicative consistency index for fuzzy preference relations (FPRs) and then use the Monte Carlo simulation method to derive the average multiplicative consistency value. After that, a model-based interactive algorithm is offered to test acceptable multiplicative consistency of HFPRs, by which the concept of acceptable multiplicative consistency for HFPRs is obtained. Meanwhile, a model-based interactive algorithm for deriving acceptable multiplicative consistent HFPRs from unacceptable multiplicative consistent ones is provided, where both the total adjustment and the number of adjusted variables are considered. As for incomplete HFPRs, a model-based interactive algorithm for getting the values of missing preferences is provided. Furthermore, the weights of the decision makers are determined by the offered model and an algorithm of model-based adjustment for the consensus level is provided. Finally, a procedure for GDM with acceptable multiplicative consistent HFPRs is given, and a case study about selecting the most suitable project management information systems (PMISs) is provided to show the application of the proposed GDM method and to compare the proposed GDM method with the previous GDM methods. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy variables are powerful tools to denote positive and negative information simultaneously. Considering the situation where decision makers (DMs) may adopt different types of preference relations to express their judgements, this paper studies group decision making (GDM) with heterogeneous intuitionistic fuzzy preference relations (IFPRs), including intuitionistic fuzzy preference relations (IFPRs), multiplicative intuitionistic fuzzy preference relations (MIFPRs), additive linguistic intuitionistic fuzzy preference relations (ALIFPRs) and multiplicative linguistic intuitionistic fuzzy preference relations (MLIFPRs). We first study their consistency. Then, we discuss the transformation relationships among them. Using consistent MLIFPRs, we further offer a formula for ascertaining DMs' weights and investigate the consensus. When the individual consensus level is lower than a predefined threshold, a model for increasing the consensus level is built that ensures the smallest total adjustment and allows the adjusted proportions of different judgements to be different. Moreover, we give a new GDM method with heterogeneous IFPRs. Finally, we use an example to illustrate the application of the proposed GDM method and make a comparison of different GDM methods with heterogeneous preference relations. [ABSTRACT FROM AUTHOR]

• We propose a deep rule ensemble creation approach. • It is driven by iterative expansion of the feature space. • It involves multiple ways of heuristic creation of diversity. • We compare the proposed approach with existing rule learning and ensemble methods. • The proposed approach achieves significant advances in classification accuracy. Rule learning approaches, which essentially aim to gerenate a decision tree or a set of "if-then" rules, have been popularly used in practice for automatically building rule-based models for prediction tasks, e.g., classification and regression. The key strength of rule-based models is their ability to interpret how an output is obtained given an input, in comparison with models trained by other machine learning approaches, e.g., neural networks. Moreover, ensemble learning approaches have been adopted as a popular way for advancing the performance of rule-based prediction through producing multiple rule-based models with diversity. Traditional approaches of ensemble learning are typically designed to train a single ensemble. In recent years, there have been some studies on creation of multiple ensembles towards increasing the diversity among rule-based models and the depth of ensemble learning. In this paper, we propose a feature expansion driven approach for automatic creation of deep rule ensembles, i.e., the dimensionality of the feature space is increased at each iteration by adding features newly created at the previous iteration. The proposed approach is compared with more recent approaches of rule learning and ensemble creation. The experimental results show that the proposed approach achieves improved performance on various data sets. [ABSTRACT FROM AUTHOR]

q -rung orthopair fuzzy sets (q -ROFSs) are prominent ideas to express fuzzy data in decision-making. The q -ROFSs can dynamically adapt the area of evidence by altering the parameter q ≥ 1 based on the fluctuation degree and therefore support more innumerable possibilities. Hence, this set defeats over the existing Atanassov intuitionistic fuzzy sets (AIFSs) and Pythagorean fuzzy sets (PFS). In today's life, there is frequently a setup concerning a neutral attitude towards the evaluation of the decision-makers. To arrange a pleasant decision throughout the method, in this paper, we illustrate innovative operational laws by uniting the features of the membership coefficients sum as well as the interaction between the membership degrees into the study for q -ROFSs. Associated with these laws, we establish some weighted averaging neutral aggregation operators (AOs) to aggregate the q -ROF erudition. Furthermore, we introduce an innovative MAGDM ("multiattribute group decision making") process based on suggested AOs and illustrate with numerous numerical cases to verify it. A contrastive review is also administered to confirm the supremacies of the method. [ABSTRACT FROM AUTHOR]