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Evaluating the teaching quality of traditional decorative patterns in colleges and universities is critical, especially when human judgment and subjective opinions are involved. This paper aims to analyze this assessment process using an enhanced framework of circular intuitionistic fuzzy sets (C-IFS) and the Dombi triangular norm. The aim of this research is to apply the Dombi t-norm (DTN) and t-conorm (DTCN) for aggregating the information within the circular intuitionistic fuzzy (C-IF) framework to evaluate the teaching quality of traditional decorative patterns. Another important feature of the proposed study is that prioritization is used in decision-making preferences by using a priority-based weight vector. To serve this purpose, we mainly proposed the Circular Intuitionistic Fuzzy Dombi Prioritized weighted averaging (C-IFDPWA) and Circular Intuitionistic Fuzzy Dombi Prioritized geometric (C-IFDPWG) operators. Moreover, the special cases of proposed aggregation operators (AOs) and their validity are discussed. An intelligent algorithm is provided involving prioritization of attributes and experts based on proposed AOs to evaluate the multi-criteria group decision-making (MCGDM) problem, particularly in assessing teaching quality. A numerical example is included to demonstrate the effectiveness and flexibility of the proposed work, and to validate its application, a comparison analysis has been conducted. The superiority of this model lies in the fact that general structure, less time complexity, and prioritization of factors make it real. The suggested framework prioritizes decision criteria and manages ambiguity well, making it a reliable tool for assessing the quality of instruction. A case study demonstrates its practical relevance and highlights the advantages of applying fuzzy logic to assess the teaching quality of traditional decorative patterns in colleges and universities.

The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from $ [0, 1] $ to $ [0, \sqrt{2}] $. However, the operations on the radius domain are limited to $ min $ and $ max $. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and non-membership degrees as well as radius domains. First, we proposed new radius operations on CIFS with a domain $ [0, \psi] $, where $ \psi \in [1, \sqrt{2}] $, called a radius algebraic product (RAP) and radius algebraic sum (RAS). Second, we developed basic operators for generalized union and intersection operations on CIFS based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of CIFS, providing valuable insights into its potential applications, particularly in decision-making theory.

The circular intuitionistic fuzzy set (CIFS) extends the concept of IFS, representing each set element with a circular area on the IFS interpretation triangle (IFIT). Each element in CIFS is characterized not only by membership and non-membership degrees but also by a radius, indicating the imprecise areas of these degrees. While some basic operations have been defined for CIFS, not all have been thoroughly explored and generalized. The radius domain has been extended from [0, 1] to [0, √2]. However, the operations on the radius domain are limited to min and max. We aimed to address these limitations and further explore the theory of CIFS, focusing on operations for membership and nonmembership degrees as well as radius domains. First, we proposed new radius operations on CIFS with a domain [0, ψ], where ψ ∈ [1, √2], called a radius algebraic product (RAP) and radius algebraic sum (RAS). Second, we developed basic operators for generalized union and intersection operations on CIFS based on triangular norms and conorms, investigating their algebraic properties. Finally, we explored negation and modal operators based on proposed radius conditions and examined their characteristics. This research contributes to a more explicit understanding of the properties and capabilities of CIFS, providing valuable insights into its potential applications, particularly in decision-making theory. [ABSTRACT FROM AUTHOR]

This article presents a higher-order circular intuitionistic fuzzy time series forecasting method for predicting the stock change index, which is shown to be an improvement over traditional time series forecasting methods. The method is based on the principles of circular intuitionistic fuzzy set theory. It uses both positive and negative membership values and a circular radius to handle uncertainty and imprecision in the data. The circularity of the time series is also taken into consideration, leading to more accurate and robust forecasts. The higher-order forecasting capability of this method provides more comprehensive predictions compared to previous methods. One of the key challenges we face when using the amount featured as a case study in our article to project the future value of ratings is the influence of the stock market index. Through rigorous experiments and comparison with traditional time series forecasting methods, the results of the study demonstrate that the proposed higher-order circular intuitionistic fuzzy time series forecasting method is a superior approach for predicting the stock change index.

In this study, it is aimed to integrate CODAS method with circular intuitionistic fuzzy sets as a new solution method for MCDM problems. Containing a radius notation with degrees of central membership and non-membership degrees is the main advantage of circular intuitionistic fuzzy in decision making. On the other side, Combinative Distance-based Assessment (CODAS) method contains many advantages such as basing on two types of distance calculations (Euclidean and Taxicab distances) comparing with other MCDM methods. When the advantages of circular intuitionistic fuzzy sets and CODAS method are considered, proposed circular intuitionistic fuzzy CODAS method (CIFS-CODAS) presents many superiorities compared to other MCDM techniques. By this way, an application for green logistics park location selection will be handled by using CIFS-CODAS to show the validity of the methodology. After, a comparative analysis with intuitionistic fuzzy CODAS (IFS-CODAS), intuitionistic fuzzy TOPSIS (IFS-TOPSIS) and intuitionistic fuzzy EDAS (IFS-EDAS) methods will be performed for green logistics park location selection problem to confirm the robustness of presented method. Green logistics and Green Deal are also emphasized considering environmental factors as a scope of the article. Finally, the results will be evaluated in the context of the logistics sector and green logistics. [ABSTRACT FROM AUTHOR]

Circular intuitionistic fuzzy sets (CIFS) are a recent extension of intuitionistic fuzzy sets (IFS) that can handle imprecise membership values effectively. However, its representation is limited to the space under the intuitionistic fuzzy interpretation triangle (IFIT). To address this, a new generalization of CIFS called circular q-rung orthopair fuzzy sets (Cq-ROFS) is proposed, extending the IFIT to cover a larger space of imprecision. Several relations and operations, including algebraic operations for Cq-ROFS are proposed. In addition, modal operators and their properties are then investigated. [ABSTRACT FROM AUTHOR]

A circular intuitionistic fuzzy set (CIFS) recently introduced by Atanassov as a new extension of intuitionistic fuzzy sets is represented by a circle whose radius is r and whose center is composed of membership and non-membership degrees. The idea is similar to type-2 fuzzy sets, which are based on the fuzziness of membership functions with a third dimension. CIFSs help us define membership functions more flexibly, taking into account the vagueness in membership and non-membership degrees. In this study, TOPSIS, which is a multi-criteria decision-making (MCDM) method, is developed under circular intuitionistic fuzzy environment. The proposed CIF-TOPSIS method is applied to determine the most appropriate pandemic hospital location selection problem. Then, a sensitivity analysis based on criteria weights and the weight of the decision maker's optimistic and pessimistic attitudes are conducted to check the robustness of the decisions given by the proposed approach. A comparative analysis with the single-valued intuitionistic fuzzy TOPSIS, Pythagorean fuzzy TOPSIS, picture fuzzy TOPSIS methods is also performed to verify the developed approach and to demonstrate its effectiveness. [ABSTRACT FROM AUTHOR]

VIKOR method being one of the frequently used Multi-Criteria Decision Making (MCDM) methods, is based on the distances of alternatives to positive and negative ideal solutions, and presents compromising solutions. AHP is another MCDM method dividing the big problem into small and manageable problems through pairwise comparisons of criteria and alternatives. In these methods, linguistic assessments are generally preferred since exact numerical assignments of criteria values are really difficult and experts can not reflect the thoughts in their minds with crisp numbers. The fuzzy set theory captures the vagueness and impreciseness in these linguistic assessments successfully thorough fuzzy numbers. Circular intuitionistic fuzzy sets (C-IFS) are the latest extension of ordinary fuzzy sets, which was introduced by Atanassov [1]. C-IFS help experts to define membership (belongingness) and nonmembership (unbelongingness) degrees by incorporating the uncertainty of these degrees. In this paper, an integrated C-IF AHP & CIF VIKOR methodology is developed and applied to a multi-expert supplier evaluation problem. The results obtained from the proposed methodology are compared with other methods, and a sensitivity analysis is performed as well. [ABSTRACT FROM AUTHOR]

Circular intuitionistic fuzzy set (C-IFS) is introduced by Atanassov in 2020 as an extension of intuitionistic fuzzy sets. It is represented by a circle with a radius (r) of each element consist of degrees of membership and non-membership. Several MCDM methods based on distance measures of C-IFS are already proposed in the literature. The primary objective of this study is the development, with the use of the C-IFS, of a new formulation of functions to form a novel C-IFS multi-criteria decision making (MCDM) method. In addition to the existing literature, this study contributes to circular intuitionistic fuzzy sets by proposing some formulations on radius calculation and a new defuzzification function for C-IFS. The optimistic and pessimistic points are also defined on the set to identify a novel score function and an accuracy function with decision-makers attitude (λ). When the perspective of the decision-maker (λ) approaches 1, it means that C-IFS is defuzzified close to its optimistic point, and when the perspective (λ) approaches 0, it is defuzzified close to the pessimistic point of C-IFS. With the use of these functions, a novel C-IFS MCDM method is presented based on criteria weighting and alternative ranking algorithms. This technique is applied to a supplier selection problem for a seamless supply chain network. A sensitivity analysis is also performed to test the effect of parameter changes on the final results. The findings of the study are compared with the results of a classical IFS-MCDM model. Since C-IFS is an extension of IFS, in addition to similar rankings, more precise results are obtained by considering the optimistic and pessimistic points by including the decision-maker attitude in the functions proposed for C-IFS. The study is a pioneer in the C-IFS literature by presenting C-IFS defuzzification function and a new C-IFS MCDM procedure. [ABSTRACT FROM AUTHOR]