The site selection acts a pivotal role in determining the success of a construction project. Since the site selection needs to gather the wisdom of a group of decision makers (DMs) and involves many factors, it can be regarded as a multi-attribute group decision making (MAGDM) problem in artificial intelligence. The assessments of alternatives on attributes are expressed by probabilistic linguistic term sets (PLTSs). A new two-stage normalization method is proposed for PLTSs considering the psychological states of decision makers. A new score function for PLTS is defined. The best and worst method is extended for fuzzy preference relation. The individual objective attribute weights are determined via information entropy. The individual subjective attribute weights are derived through the extended best and worst method. The individual comprehensive attribute weights are derived by minimum relative entropy principle. The weights of DMs are acquired through an optimization model. It minimizes the deviation between the opinions of all DMs and the deviation between the individual and collective comprehensive attribute weight vectors, simultaneously, which effectively overcomes the drawback of only minimizing single deviation. A new method is presented for MAGDM with PLTSs. A hotel site selection example is demonstrated and comparative analyses are executed to verify the validity and advantages of the proposed method. The test statistic Z values of Spearman's rank-correlation test are all smaller than 1.645, which shows that the ranking order obtained by the proposed method is statistically sharply distinct from that produced by other methods and thus further validates the proposed method.

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.

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.

Being a pair of dual concepts, the normalized distance and similarity measures are important tools for decision-making and pattern recognition under the intuitionistic fuzzy set framework. In this paper, we first construct some counterexamples to illustrate that two existing similarity measures do not meet the axiomatic definition of intuitionistic fuzzy similarity measures. We then show that (1) these two measures cannot effectively distinguish some intuitionistic fuzzy values (IFVs); (2) except for the endpoints, there exist infinitely many pairs of IFVs, where the maximum distance “1” can be achieved under these two distances, leading to counter-intuitive results. To overcome these drawbacks, we introduce the concept of strict intuitionistic fuzzy distance measure (SIFDisM) and strict intuitionistic fuzzy similarity measure (SIFSimM), and propose an improved intuitionistic fuzzy distance measure based on Jensen-Shannon divergence. Moreover, we prove that (1) it is a SIFDisM; (2) its dual similarity measure is a SIFSimM; (3) its induced entropy is an intuitionistic fuzzy entropy. Comparative analysis and numerical examples demonstrate that our proposed distance measure is superior to the existing ones. In particular, our proposed distance measure can better distinguish and rank intuitionistic fuzzy sets.

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.

This paper proposes a new intuitionistic fuzzy best-worst method (IFBWM) for group decision making (GDM) with intuitionistic fuzzy (IF) preference relations (IFPRs). IF values (IFVs) are used to express reference comparisons of criteria. Based on the additive consistency of IFPRs, this paper proposes the definition of additive consistency of IF reference comparisons (IFRCs). Based on the deviation minimization, a linear goal programming model is established to calculate the optimal IF priority weights. By the additive consistency, the consistency index in the closed form is computed by the score function of IFVs. A new approach is devised to enhance the additive consistency of IFRCs. Thus, an IFBWM with the additive consistency of IFRCs is proposed. For GDM with IFPRs, the best criterion and the worst criterion are identified for each decision maker by constructing the score matrix of the IFPR. The individual ranking order of the criteria is obtained by using the proposed IFBWM. Then, the collective ranking order of the criteria is obtained via building a 0–1 integer programming model. Therefore, a GDM method based on the developed IFBWM with IFPRs is proposed. Four examples are analyzed to demonstrate the effectiveness and the advantages of the proposed IFBWM for GDM.

This paper proposes an interactive forest algorithm for planning single-tuned harmonic filters for electric power distribution systems. The planning of harmonic filters is a complex problem that must consider multiple objectives, including minimizing the total cost of installed filters and the individual and total harmonic distortion while adhering to operational constraints, such as the voltage drop, the current loading and the harmonic limits. Moreover, system perturbations must be considered, such as frequency variations. This paper proposes a new method for multi-objective optimization of planning single-tuned harmonic filters utilizing the proposed interactive forest algorithm with a non-differentiable multi-objective function involving continuous and discrete variables. A multi-objective optimization technique based on the proposed interactive forest algorithm is proposed. In the interactive approach, planners set expectations for each objective and use the forest algorithm to figure out the optimization problems. The results of the Pareto Front are analyzed and the answers are searched through the interactive process to identify a solution that meets the planner’s expectations, allowing for practical compromise or satisfactory solutions. A case study is reported to show the superiority of the proposed method.

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.

This paper proposes a new multiple attribute decision making (MADM) method in the environments of q-rung orthopair fuzzy numbers (q-ROFNs) based on the proposed score function of q-connection numbers (q-CNs), the proposed q-connection number power weighted geometric (q-CNPWG) aggregation operator (AO) of q-CNs, and the set pair analysis (SPA) theory. Firstly, we propose a score function of q-CNs based on the SPA theory, where we also present some properties of the proposed score function of q-CNs. Then, we propose the q-CNPWG AO for aggregating q-CNs, where we also present some properties of the proposed q-CNPWG AO of q-CNs. Finally, we propose a new MADM method in the environments of q-ROFNs based on the proposed score function of q-CNs, the proposed q-CNPWG AO of q-CNs, and the SPA theory. The proposed MADM method can overcome the drawbacks of existing MADM methods in the environments of q-ROFNs, where they cannot distinguish preference orders of alternatives in some situations. The proposed MADM method is very useful for MADM in the environments of q-ROFNs.

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.

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.

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.

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.

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.

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.

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.

We propose an expanded single-valued neutrosophic (SVN) EDAS model for multiple attribute decision-making (MADM) in this study. Firstly, we present an integrated method for deriving attribute weights relying on the entropy measurement and best-worst method (BWM) under the environment of single-valued neutrosophic sets (SVNSs). Then, combining the integrated weight model, we propose the computing steps of the SVN-EDAS evaluation framework. Furthermore, we explore the usefulness of the presented framework in innovation capability evaluation. Finally, a numerical example related to the innovation capability evaluation of energy enterprises is carried out.

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 ob-tained 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.

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.