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ELECTRE III is a well-established outranking relation model used to address the ranking of alternatives in multi-criteria and multi-actor decision-making problems. It has been extensively studied across various scientific fields. Due to the complexity of decision-making under uncertainty, some higher-order fuzzy sets have been proposed to effectively model this issue. Circular Intuitionistic Fuzzy Set (CIFS) is one such set recently introduced to handle uncertain IF values. In CIFS, each element of the set is characterized by a circular area with a radius, r and membership/non-membership degrees as the centre. This paper introduces CIF-ELECTRE III, an extension of ELECTRE III within the CIFS framework, for group decision analysis. To achieve this, we define extensions for the group decision matrix and group weighting vector based on CIFS conditions, particularly focusing on optimistic and pessimistic attitudes. These attitudinal characters of the group of actors are constructed using conditional rules to ensure that each element of the set falls within the circular area. Parameterized by α ∈ [ 0 , 1 ] for the net score degree, we conduct an extensive analysis of group decision-making between optimistic and pessimistic attitudes. To illustrate the applicability of the proposed model, we provide a numerical example of the stock-picking process. Additionally, we conduct a comparative analysis with existing sets and perform sensitivity analyses to validate the results of the proposed model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of circular Pythagorean fuzzy set (value) (C-PFS(V)) as a new generalization of both circular intuitionistic fuzzy sets (C-IFSs) proposed by Atannassov and Pythagorean fuzzy sets (PFSs) proposed by Yager. A circular Pythagorean fuzzy set is represented by a circle that represents the membership degree and the non-membership degree and whose centre consists of non-negative real numbers μ and ν with the condition μ 2 + ν 2 ⩽ 1. A C-PFS models the fuzziness of the uncertain information more properly thanks to its structure that allows modelling the information with points of a circle of a certain centre and a radius. Therefore, a C-PFS lets decision makers to evaluate objects in a larger and more flexible region and thus more sensitive decisions can be made. After defining the concept of C-PFS we define some fundamental set operations between C-PFSs and propose some algebraic operations between C-PFVs via general triangular norms and triangular conorms. By utilizing these algebraic operations, we introduce some weighted aggregation operators to transform input values represented by C-PFVs to a single output value. Then to determine the degree of similarity between C-PFVs we define a cosine similarity measure based on radius. Furthermore, we develop a method to transform a collection of Pythagorean fuzzy values to a C-PFS. Finally, a method is given to solve multi-criteria decision making problems in circular Pythagorean fuzzy environment and the proposed method is practiced to a problem about selecting the best photovoltaic cell from the literature. We also study the comparison analysis and time complexity of the proposed method. [ABSTRACT FROM AUTHOR]

Consensus creation is a complex challenge in decision making for conflicting or quasi-conflicting evaluator groups. The problem is even more difficult to solve, if one or more respondents are non-expert and provide uncertain or hesitant responses in a survey. This paper presents a methodological approach, the Interval-valued Spherical Fuzzy Analytic Hierarchy Process, with the objective to handle both types of problems simultaneously; considering hesitant scoring and synthesizing different stakeholder group opinions by a mathematical procedure. Interval-valued spherical fuzzy sets are superior to the other extensions with a more flexible characterization of membership function. Interval-valued spherical fuzzy sets are employed for incorporating decision makers' judgements about the membership functions of a fuzzy set into the model with an interval instead of a single point. In the paper, Interval-valued spherical fuzzy AHP method has been applied to public transportation problem. Public transport development is an appropriate case study to introduce the new model and analyse the results due to the involvement of three classically conflicting stakeholder groups: passengers, non-passenger citizens and the representatives of the local municipality. Data from a real-world survey conducted recently in the Turkish big city, Mersin, help in understanding the new concept. As comparison, all likenesses and differences of the outputs have been pointed out in the reflection with the picture fuzzy AHP computation of the same data. The results are demonstrated and analysed in detail and the step-by-step description of the procedure might foment other applications of the model. [ABSTRACT FROM AUTHOR]

Policy-makers are often hesitant to invest in unproven solutions because of a lack of the decision-making framework for managing innovations as a portfolio of investments that balances risk and return, especially in the field of developing new technologies. This study provides a new portfolio matrix for decision making of policy-makers to identify IoT applications in the agriculture sector for future investment based on two dimensions of sustainable development as a return and IoT challenge as a risk using a novel MADM approach. To this end, the identified applications of IoT in the agriculture sector fall into eight areas using the meta-synthesis method. The authors extracted a set of criteria from the literature. Later, the fuzzy Delphi method helped finalise it. The authors extended the SWARA method with interval-valued triangular fuzzy numbers (IVTFN SWARA) and used it to the weighting of the characteristics. Then, the alternatives were rated using the Additive Ratio Assessment (ARAS) method based on interval-valued triangular fuzzy numbers (IVTFN ARAS). Finally, decision-makers evaluated the results of ratings based on two dimensions of sustainability and IoT challenge by developing a framework for decision-making. Results of this paper show that policy-makers can manage IOT innovations in a disciplined way that balances risk and return by a portfolio approach, simultaneously the proposed framework can be used to determine and prioritise the areas of IoT application in the agriculture sector. [ABSTRACT FROM AUTHOR]

In this paper, we develop a new flexible method for interval-valued intuitionistic fuzzy decision-making problems with cosine similarity measure. We first introduce the interval-valued intuitionistic fuzzy cosine similarity measure based on the notion of the weighted reduced intuitionistic fuzzy sets. With this cosine similarity measure, we are able to accommodate the attitudinal character of decision-makers in the similarity measuring process. We study some of its essential properties and propose the weighted interval-valued intuitionistic fuzzy cosine similarity measure. Further, the work uses the idea of GOWA operator to develop the ordered weighted interval-valued intuitionistic fuzzy cosine similarity (OWIVIFCS) measure based on the weighted reduced intuitionistic fuzzy sets. The main advantage of the OWIVIFCS measure is that it provides a parameterized family of cosine similarity measures for interval-valued intuitionistic fuzzy sets and considers different scenarios depending on the attitude of the decision-makers. The measure is demonstrated to satisfy some essential properties, which prepare the ground for applications in different areas. In addition, we define the quasi-ordered weighted interval-valued intuitionistic fuzzy cosine similarity (quasi-OWIVIFCS) measure. It includes a wide range of particular cases such as OWIVIFCS measure, trigonometric-OWIVIFCS measure, exponential-OWIVIFCS measure, radical-OWIVIFCS measure. Finally, the study uses the OWIVIFCS measure to develop a new decision-making method to solve real-world decision problems with interval-valued intuitionistic fuzzy information. A real-life numerical example of contractor selection is also given to demonstrate the effectiveness of the developed approach in solving real-life problems. [ABSTRACT FROM AUTHOR]

Public-private partnership (PPP) is regarded as an innovative way to the procurement of public projects. Models vary with PPP projects due to their differences. The evaluation criteria are usually complex and the judgments offered by decision makers (DMs) show the characteristics of fuzziness and uncertainty. Considering these cases, this paper first analyses the risk factors for PPP models and then proposes a new method for selecting them in the setting of single-valued neutrosophic hesitant fuzzy environment. To achieve these purposes, two single-valued neutrosophic hesitant fuzzy correlation coefficients are defined to measure evaluated PPP models. Considering the weights of the risk factors and their interactions, two single-valued neutrosophic hesitant fuzzy 2-additive Shapley weighted correlation coefficients are defined. When the 2-additive measure on the risk factor set is not exactly known, several distance measure-based programming models are constructed to determine it. Based on these results, an algorithm for evaluating PPP models with single-valued neutrosophic hesitant fuzzy information is developed. Finally, a practical numerical example is provided to verify the validity and feasibility of the new method. [ABSTRACT FROM AUTHOR]

Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) is a very common and useful method for solving multi-criteria decision making problems in certain and uncertain environments. Single valued neutrosophic hesitant fuzzy set (SVNHFS) and interval neutrosophic hesitant fuzzy set (INHFS) are developed on the integration of neutrosophic set and hesitant fuzzy set. In this paper, we extend TOPSIS method for multi-attribute decision making based on single valued neutrosophic hesitant fuzzy set and interval neutrosophic hesitant fuzzy set. Furthermore, we assume that the attribute weights are known, incompletely known or completely unknown. We establish two optimization models for SVNHFS and INHFS with the help of maximum deviation method. Finally, we provide two numerical examples to validate the proposed approach. [ABSTRACT FROM AUTHOR]

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Intuitionistic uncertain linguistic variables (IULVs) are useful to express the qualitative and quantitative recognitions of decision makers. However, after reviewing the previous operational laws on IULVs, we find there are some limitations. To address these issues, we define several new operations on IULVs and give a new ranking method. To improve the utilization of IULVs, this paper defines two Choquet operators: the intuitionistic uncertain linguistic symmetrical Choquet averaging (IULSCA) operator and the intuitionistic uncertain linguistic symmetrical Choquet geometric mean (IULSCGM) operator, which can address the internal correlations among elements. To globally reflect the interactive characteristics of the importance of elements, two generalized Shapley intuitionistic uncertain linguistic symmetrical Choquet operators are presented. Subsequently, a new distance measure is defined, which is then used to build models to ascertain fuzzy measures on decision maker and criteria sets to address the case where the weighting information is partly known. After that, a new procedure to intuitionistic uncertain linguistic group decision making is developed. Finally, a specific example is offered to illustrate the practicality of the new procedure, and the comparison analysis is also made. [ABSTRACT FROM AUTHOR]

Interval-valued intuitionistic hesitant fuzzy sets (IVIHFSs) are useful to denote the decision makers' interval preferred, interval non-preferred and hesitant opinions simultaneously. Considering the application of IVIHFSs, this paper introduces a new decision-making method with interval-valued intuitionistic hesitant fuzzy information that extends the application scopes. To do this, the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted averaging (IVIHFHSWA) operator and the interval-valued intuitionistic hesitant fuzzy hybrid Shapley weighted geometric (IVIHFHSWG) operator are defined to aggregate the collective attribute values of alternatives. To reflect the interactions and reduce the complexity of calculating the weights, the 2-additive measures are used to define these two hybrid Shapley weighted operators. To derive the exact weight information of attributes and ordered positions, the associated programming models for determining the optimal 2-additive measures are constructed that are based on the defined Hamming distance measure. To show the feasibility and efficiency of the new method, a practical decision-making problem is offered, which is also used to compare with the previous methods. [ABSTRACT FROM AUTHOR]

In this paper, we presented another form of eight similarity measures between PFSs based on the cosine function between PFSs by considering the degree of positive membership, degree of neutral membership, degree of negative membership and degree of refusal membership in PFSs. Then, we applied these weighted cosine function similarity measures between PFSs to strategic decision making. Finally, an illustrative example for selecting the optimal production strategy is given to demonstrate the efficiency of the similarity measures for strategic decision making problem. [ABSTRACT FROM AUTHOR]

This paper proposes an extension of the ARAS method which, due to the use of intervalvalued fuzzy numbers, can be more appropriate for solving real-world problems. In order to overcome the complexity of real-world decision-making problems, the proposed extension also includes the use of linguistic variables and a group decision making approach. In order to highlight the proposed methodology an example of a faculty websites evaluation is considered. [ABSTRACT FROM AUTHOR]

The quality of the input data is amongst the decisive factors affecting the speed and effectiveness of recurrent neural network (RNN) learning. We present here a novel methodology to select optimal training data (those with the highest learning capacity) by approaching the problem from a decision making point of view. The key idea, which underpins the design of the mathematical structure that supports the selection, is to define first a binary relation that gives preference to inputs with higher estimator abilities. The Von Newman Morgenstern theorem (VNM), a cornerstone of decision theory, is then applied to determine the level of efficiency of the training dataset based on the probability of success derived from a purpose-designed framework based on Markov networks. To the best of the author's knowledge, this is the first time that this result has been applied to data selection tasks. Hence, it is shown that Markov Networks, mainly known as generative models, can successfully participate in discriminative tasks when used in conjunction with the VNM theorem. The simplicity of our design allows the selection to be carried out alongside the training. Hence, since learning progresses with only the optimal inputs, the data noise gradually disappears: the result is an improvement in the performance while minimising the likelihood of overfitting. [ABSTRACT FROM AUTHOR]

For this article, we shall expand the TODIMmodel to the MADM with the picture fuzzy numbers (PFNs). Firstly, the concept, comparative method and distance of PFNs are introduced and the traditional TODIMmodel is presented. Then, the expanded TODIMmodel is developed to solve MADMproblems with PFNs. Finally, a numerical example is given to verify the proposed approach. [ABSTRACT FROM AUTHOR]

Quantitative and qualitative fuzzy information measures have been proposed to solve multi-attribute decision making (MADM) problems with interval-valued hesitant fuzzy information fromdifferent points.We analyse the existing fuzzy information measures of the interval-valued hesitant fuzzy sets (IVHFSs) in detail and classify them into two categories. One is based on the closeness of the data, such as the distance, and the other is based on the linear relationship or variation tendency, such as the correlation coefficient. These two kinds of information measures are actually partial measures which pay attention to only one factor of the data. Therefore, we construct a novel synthetic grey relational degree by considering both the closeness and the variation tendency factors of the data to improve the existing information measures and enhance the grey relational analysis (GRA) theory for IVHFSs. However, the notion of the synthetic grey relational degree is not only restricted to the IVHFSs but can be extended to other sets. Furthermore, we employ two practical MADM examples about emergency management evaluation and pattern recognition to validate and compare the proposed synthetic grey relational degree with other information measures, which demonstrate its superiorities in discrimination and accuracy. [ABSTRACT FROM AUTHOR]

Linguistic hesitant fuzzy sets (LHFSs) permit the decision maker to apply several linguistic terms with each having several membership degrees to denote his/her preference of one thing. This type of fuzzy sets can well address the qualitative and quantitative cognitions of the decision maker as well as reflect his/her hesitancy, uncertainty and inconsistency. This paper introduces a distance measure between any two LHFSs and then defines a correlation coefficient of LHFSs. Considering the application of LHFSs, the weighted distance measure and the weighted correlation coefficient of LHFSs are defined. To address the interactions between elements in a set, the Shapley weighted distance measure and the Shapley weighted correlation coefficient are presented. It is worth noting that when the elements are independent, they degenerate to the associated weighted distance measure and the weighted correlation coefficient, respectively. After that, their application to pattern recognition is studied. Furthermore, an approach to multi-attribute decision making under linguistic hesitant fuzzy environment is developed. Meanwhile, numerical examples are offered to show the concrete application of the developed procedure. [ABSTRACT FROM AUTHOR]

From the perspective of multiple attribute decision analysis, the evaluation of decision alternatives should be based on the performance scores determined with respect to more than one attribute. Fuzzy logic concepts can equip the evaluation process with different scales of linguistic terms to let the decision-makers point out their ideas and preferences. A more recent one of fuzzy sets is the picture fuzzy set which covers three separately allocable elements: positive, neutral, and negative membership degrees. The novel and distinctive element included by a picture fuzzy set is the refusal degree which is equal to the difference between 1 and the sum of the other three. In this study, we aim to contribute to the literature of the picture fuzzy sets by (i) proposing two novel entropy measures that can be used in objective attribute weighting and (ii) developing a novel picture fuzzy version of CODAS (COmbinative Distance-based ASsessment) method which is empowered with entropy-based attribute weighting. The applicability of the method is shown in a green supplier selection problem. To clarify the differences of the proposed method, a comparative analysis is provided by considering traditional CODAS, spherical fuzzy CODAS, and spherical fuzzy TOPSIS with different entropy-based scenarios. [ABSTRACT FROM AUTHOR]

A p-rung orthopair fuzzy set (p-ROFS) describes a generalization of intuitionistic fuzzy set and Pythagorean fuzzy set in the case where we face a larger representation space of acceptable membership grades, and moreover, it gives a decision maker more flexibility in expressing his/her real preferences. Under the p-rung orthopair fuzzy environment, we are going to propose a novel and parametrized score function of p-ROFSs by incorporating the idea of weighted average of the degree of membership and non-membership functions. In view of this fact, this study is further undertaken to investigate and present different properties of the proposed score function for p-ROFSs. Moreover, we indicate that this ranking technique reduces some of the drawbacks of the existing ones. Eventually, we develop an approach based on the above-mentioned ranking technique to deal with multiple criteria decision making problems with p-rung orthopair fuzzy information. [ABSTRACT FROM AUTHOR]

As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making. [ABSTRACT FROM AUTHOR]

Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness. [ABSTRACT FROM AUTHOR]

Multi-attribute analysis is a useful tool in many economical, managerial, constructional, etc. problems. The accuracy of performance measures in COPRAS (The multi-attribute COmplex PRoportional ASsessment of alternatives) method is usually assumed to be accurate. This method assumes direct and proportional dependence of the weight and utility degree of investigated versions on a system of attributes adequately describing the alternatives and on values and weights of the attributes. However, there is usually some uncertainty involved in all multi-attribute model inputs. The objective of this research is to demonstrate how simulation can be used to reflect fuzzy inputs, which allows more complete interpretation of model results. A case study is used to demonstrate the concept of general contractor choice of on the basis of multiple attributes of efficiency with fuzzy inputs applying COPRAS-G method. The research has concluded that the COPRAS-G method is appropriate to use. [ABSTRACT FROM AUTHOR]

When handling engineering problems associated with optimal alternative selection a researcher often deals with not sufficiently accurate data. The alternatives are usually assessed by applying several different criteria. A method takes advantage of the relationship between fuzzy sets and matrix game theories can be offered for multicriteria decision‐making. Practical investigations have already been discussed for selecting the variants water supply systems. [ABSTRACT FROM AUTHOR]