Fuzzy c-means (FCM) is a time-honored method for its simplicity of calculation and ease of understanding. However, the previous image segmentation work exploiting FCM could not achieve the ideal effect in image edge recognition of the fuzzy information or antinoise of the pixel. This paper exploits the spatial T-spherical fuzzy c-means model with bias correction ( E M- s T S F C M p q ) to improves the effect of antinoise and image edge recognition. First, the image is transformed into a T-spherical fuzzy set by a novel T-spherical fuzzification technology with the processing of the bias fields. Second, the membership degree of the image is updated through the proposed T-spherical FCM algorithm. Third, a novel calculation method of weighted combination is exploited to integrate spatial information to overcome the noise. The proposed method is applied to three-dimensional MR image segmentation and the Berkeley segmentation datasets to illustrate the accuracy and efficiency.

Probabilistic linguistic term sets (PLTSs) have many applications in the field of group decision making (GDM) because it includes both linguistic evaluation and probabilistic distribution when expressing preference information. However, the difference of information credibility in PLTSs is ignored, resulting in an inaccurate representation of decision information and unreasonable probability calculation. In this paper, we first consider the credibility of the information and propose the concept of Z-uncertain probabilistic linguistic variables (Z-UPLVs). Subsequently, the operational rules, normalization, distance and similarity measures, and comparison method of Z-UPLVs are introduced. Then, a probability calculation method based on credibility, an extended TOPSIS method, and some operators are proposed, which can be applied to emergency decision making in the Z-uncertain probabilistic linguistic (Z-UPL) environment. Finally, an emergency decision-making case of COVID-19 patients and comparative analysis illustrate the necessity and effectiveness of this method.

The reliable evaluation of financial performance of universities plays an important role in sustainable development of universities, and it could be regarded as a multicriteria group decision making problem. Based on this, in this paper, with respect to the attribute evaluation values are expressed by interval 2-tuple Pythagorean fuzzy linguistic variables, we develop an extended MULTIMOORA method. First, we propose the interval 2-tuple Pythagorean fuzzy linguistic set based on Pythagorean fuzzy set and interval-valued 2-tuple linguistic variables, and further introduce the score and accuracy functions and Hamming distance of it. Then, considering that there are some deficiencies in the traditional MULTIMOORA method, such as exist the case of circular reasoning, and so forth. We improve it by proposing a comprehensive integration approach, which can not only consider both the utility values and sort results, but also reflect the preference attitude of decision makings simultaneously. Based on these research findings, an interval 2-tuple Pythagorean fuzzy linguistic MULTIMOORA method is presented and the calculation process of this method is described in detail. Finally, we give the numerical example concerning the evaluation of financial management performance in universities to illustrate practicability and reliability of the proposed approach and compare the proposed method with different methods to perform its flexibility.

Nowadays the emergency decision has become a hot topic in the field of decision-making with interval-valued Pythagorean fuzzy linguistic (IVPFL) information. Moreover, with the increase of attributes and decision makers, the complexity of the operation is a great challenge for making decision. How to overcome multicollinearity is a crucial link in the emergency decision modeling process. In this paper, we treat the attributes and DMs as IVPFL variables and construct the IVPFL principal component analysis (IVPFL-PCA) model to overcome the multicollinearity. Then, a novel TODIM (abbreviation for interactive and multicriterial decision-making in Portuguese) method is proposed to tackle the IVPFL information under several new variables that are independent of each other (i.e., the PCs) and the reasonable weights of PCs obtained based on the IVPFL-PCA model. Finally, a case study on earthquake emergency decision is presented to show the applicability of the proposed approach and some comparisons are presented to illustrate its superiorities.

To solve the problems of making decision with uncertain and imprecise information, Zadeh proposed the concept of Z-number as an ordered pair, the first component of which is a restriction of variable, and the second one is a measure of reliability of the first component. But the decision-makers’ confidence in decision-making was neglected. In this paper, firstly, we present a new method to evaluate and rank -numbers based on the operations of trapezoidal Type 2 fuzzy numbers and generalized trapezoidal fuzzy numbers. Then, linguistic-induced ordered weighted averaging operator and linguistic combined weighted averaging aggregation operator are developed to solve multiple attribute group decision-making problems. And we analyze the main properties of them by utilizing some operational laws of fuzzy linguistic variables. Finally, a numerical example is provided to illustrate the rationality of the proposed method.

Multiple attribute linguistic group decision making (MALGDM) is one of the important research topics in decision-making theory. The material supplier grading involves multiple attributes and forms a typical MALGDM problem. In this paper, based on interval-valued Pythagorean uncertain linguistic Euclidean distance (IVPUL-Euclidean distance) and IVPUL aggregation operators, we develop a new outranking sorting approach, which can cope with MALGDM problems in IVPUL environment. The proposed IVPUL-Euclidean distance defines a novel outranking relation, and it introduces three parameters that can adjust outranking sorting result according to various decision-making situations. Meanwhile, the IVPUL aggregation operators are introduced to aggregate the IVPUL information. Eventually, we give a numerical example concerning the comprehensive assessment of material supplier to illustrate validity and applicability of the proposed approach and compare the proposed method with different generalized aggregation operators to perform its flexibility.

Preference relations (PRs) as useful and efficient information description tools have been widely applied in practical multiple-attribute group decision-making (MAGDM) problems. Due to fuzziness and complexity of problems, the limitations of the experts’ professional knowledge and experience, the provided PRs are usually inconsistent, will lead to unreasonable conclusion. Consequently, we define the concept of trapezoidal Pythagorean fuzzy linguistic PRs (TrPFLPRs), a method for confirm the consistent of PRs and repair inconsistent PFs in this paper. Meanwhile, we propose trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted Minkowski distance operator to aggregate the TrPFLPRs information. Finally, a numerical example is given to illustrate the practicality and effectiveness of the proposed operator.

In the multiple attribute linguistic group decision making analysis with interval-valued intuitionistic fuzzy linguistic information, seeking highly efficient aggregation method and order relation play a crucial role. In this paper, we redefine an interval-valued intuitionistic fuzzy linguistic variable that considers principal component and propose generalized interval-valued intuitionistic fuzzy linguistic induced hybrid aggregation (GIVIFLIHA) operator with entropic order-inducing variable and interval-valued intuitionistic fuzzy linguistic technique for order preference by similarity to an ideal solution (TOPSIS) order relation based on interval-valued intuitionistic fuzzy linguistic distance measure. Then, some primary properties of the GIVIFLIHA operator are discussed, and a linguistic group decision-making approach based on GIVIFLIHA operator and interval-valued intuitionistic fuzzy linguistic TOPSIS order relation is proposed. Finally, a numerical example concerning the investment strategy is given to illustrate the validity and applicability of the proposed method, and then the method is compared with the existing method to further illustrate its flexibility.

Recently some new models based on Pythagorean fuzzy sets (PFSs) have been proposed to deal with the uncertainty in multiple attribute group decision making (MAGDM) problems. In this paper, considering linguistic variables and entropic, we propose a new trapezoidal Pythagorean fuzzy linguistic entropic combined ordered weighted averaging operator to solve MAGDM problems. Next, we study some main properties by utilizing some operational laws of the trapezoidal Pythagorean fuzzy linguistic variables. Finally, a numerical example concerning the enterprise location is given to illustrate the practicality and effectiveness of the proposed operator.

Multicriteria decision making (MCDM) has been attracting attention in recent years. There are two essential directions in the research territory, one direction is the research of representation of evaluation information and another is the construction of ranking function. In this paper, we consider some nonstandard fuzzy sets, intuitionistic, and interval-valued fuzzy sets. Especially, the Pythagorean membership grade and Pythagorean fuzzy set receive much attention. Then, to reflect the importance of principal value, we shall propose the principal-value Pythagorean fuzzy number (p-PFN) and principal-value Pythagorean fuzzy set. Furthermore, a novel ranking function is constructed to select the ideal alternative(s) based on p-PFNs in MCDM. Finally, an investment strategy decision-making problem is proposed to reveal the availability and practicability of the function under the new environment.

Entropy, a basic concept of measuring the amount of information and the degree of confusion, has been applied in many weighted averaging operators in the linguistic group decision making. In the paper, we construct an intuitionistic fuzzy linguistic entropy based on the intuitionistic fuzzy entropy and the intuitionistic fuzzy linguistic variable. Then, inspired by operations of concentration and dilation (De SK, Biswas R, and Roy AR, Fuzzy Sets Syst. 2000;114(3):477ȓ484), we extend the intuitionistic fuzzy linguistic entropy to the intuitionistic fuzzy interval-valued linguistic entropy. After that, the intuitionistic fuzzy interval-valued linguistic entropic combined weighted averaging (IFIVLECWA) operator is proposed for multiple attribute linguistic group decision making. Finally, a numerical example about the selection of optimal alternative(s) is presented to illustrate the applicability and effectiveness of the proposed method.

The linguistic aggregation operator is an important decision-making model that is proving effective for dealing with the input data that takes the form of uncertain information. In this paper, considering the principal component of the intuitionistic fuzzy linguistic variables, we develop a new intuitionistic fuzzy linguistic hybrid aggregation (NIFLHA) operator to solve group decision-making problems under the situation with intuitionistic fuzzy linguistic information. Then, we study some of its main properties by utilizing some operational laws of intuitionistic fuzzy linguistic variables and the different families of the NIFLHA operator. Moreover, the multiperson NIFLHA (MP-NIFLHA) operator is introduced to evaluate the opinions of experts. Finally, an illustrative example about a multiperson decision-making problem is developed to reveal the applicability and the availability of the raised operator.

In the paper, we develop the novel intuitionistic fuzzy induced ordered weighted Euclidean distance (NIFIOWED) operator based on the generalized intuitionistic fuzzy distance for multiple attribute group decision making problems. The NIFIOWED operator's attribute values take the form of Atanassov's intuitionistic fuzzy numbers(A-IFNs), and the principal component x of A-IFN is taken into account first. The prime properties of the NIFIOWED operator are investigated. Finally, a new method and a numerical example are provided to reveal the availability and practicability of the NIFIOWED operator.

In the paper, we develop a new method for multiple attribute group decision making) for fuzzy numbers. The fuzzy entropic weighted averaging (FEOWA) operator is an extension of the entropic ordered weighted averaging operator, which unifies the fuzzy entropy and the ordered weighted averaging operator in the same formulation. Then, some of its main properties by utilizing some operational laws of fuzzy numbers are studied. We also present the generalized entropic ordered weighted averaging operator and the fuzzy generalized entropic ordered weighted averaging operator. Moreover, a method based on the FEOWA operator for decision making is presented. Finally, a numerical example illustrates the applicability and effectiveness of the proposed method.

With respect to multiple attribute group decision making problems, in which the attribute values take the form of fuzzy linguistic scale variables, some decision analysis approaches are proposed. In this paper, we introduce the fuzzy linguistic induce generalized ordered weighted averaging operator and study some of its main properties by utilizing some operational laws of fuzzy linguistic scale variables. We end the paper with a numerical example of the new approach in a fuzzy linguistic decision making.

In this paper, we develop a new method for group linguistic decision making, in which the attribute values take the form of fuzzy linguistic information, namely the fuzzy linguistic induced Euclidean ordered weighted averaging distance (FLIEOWAD) operator. This operator is an extension of the IOWA operator that utilizes induce OWA operator, Euclidean distance measures, and uncertain information represented as fuzzy linguistic variables. Then, some of its main properties by utilizing some operational laws of fuzzy linguistic variables are studied. Thus, a method based on the FLIEOWAD operator for decision making is presented. Finally, a numerical example is used to illustrate the applicability and effectiveness of the proposed method.