Intuitionistic Fuzzy Operators Research Articles

A general approach to modal topological structures illustrated by intuitionistic fuzzy objects

A new, general approach to introducing of the concept of a Modal Topological Structure (MTS) is given. The basic properties of the MTS are studied. The MTSs are illustrated by intuitionistic fuzzy objects - intuitionistic fuzzy sets, operations, relations and operators. So, 38 different intuitionistic fuzzy MTSs are described.

A brief note on intuitionistic fuzzy operators

The research on intuitionistic fuzzy sets gives an extra dimension in mathematics. It has been observed that some operators including the modal operators have very interesting properties in intuitionistic fuzzy sets. More important properties are investigated in this paper and new findings are obtained and proved.

A novel approach employing hesitant intuitionistic fuzzy linguistic Einstein aggregation operators within the EDAS approach for multicriteria group decision making

The Evaluation based on Distance from Average Solution (EDAS) is a multi-criteria decision analysis (MCDA) technique that uses various distances from average values to make decisions. It bears resemblance to other distance-based approaches like SPOTIS, VIKOR or TOPSIS, except that instead of positive and negative ideal solutions, it uses an average solution. For hesitant intuitionistic fuzzy linguistic term sets (HIFLTSs), we first define several operational laws and aggregation operators. As a follow-up, the hesitating intuitionistic fuzzy linguistic Einstein weighted averaging (HIFLEWA) operator is introduced. In this study, the EDAS technique is used to address a multi-criteria group decision making (MCGDM) issue by utilizing the suggested operational laws and aggregation operators for HIFLTSs, aiming to mitigate the uncertainties of decision makers (DMs). A representative numerical example is employed to illustrate the strength and logical soundness of our proposed method in identifying the optimal choice under the given limitations. A comparison examination with the existing TOPSIS approach is also performed to ensure that the results generated with EDAS are accurate.

Two-sided matching decision method and application based on subject differences in interval intuitionistic fuzzy environment

In this paper, a two-sided matching decision model based on interval-valued intuitionistic fuzzy environment is proposed to maximize the demand of individual differences. Firstly, the attribute feature table and weight matrix of both agents are constructed, and a formula for calculating the comprehensive advantage in the interval-valued intuitionistic fuzzy environment is given, namely the interval-valued intuitionistic fuzzy comprehensive advantage aggregation operator (IIFCAAO); Secondly, the interval-valued intuitionistic fuzzy decision matrix of both agents is calculated by using the comprehensive advantage aggregation operator, and the interval-valued intuitionistic fuzzy decision matrix is transformed into a score function matrix by using a score function formula; Thirdly, the two-sided matching model is established to maximize the score; Finally, the scientificity and practicability of the model are verified by an example of college students changing their majors.

Modified Intuitionistic Quantum Fuzzy Operators for Binary Optimization Problems

To facilitate the realization of this groundbreaking concept, this paper presents an original approach to represent intuitionistic fuzzy sets and operators through quadratic optimization problems. This approach aims to enable the deployment of fuzzy inference mechnism on a specific category of quantum computers referred to as quantum annealers.

Archimedean Heronian mean operators based on complex intuitionistic fuzzy sets and their applications in decision-making problems

In this article, we derive the Archimedean aggregation operators for complex intuitionistic fuzzy sets, for this, first, we evaluate some Archimedean operational laws based on complex intuitionistic fuzzy values and then we discuss their special cases because the Archimedean norms are the general form of all existing norms, for instance, algebraic, Einstein, Hamacher, and Frank operational laws. Furthermore, we present the complex intuitionistic fuzzy Archimedean Heronian aggregation operator and complex intuitionistic fuzzy weighted Archimedean Heronian aggregation operator. Several special cases and the basic properties of the above-proposed operators are also diagnosed, because proposing the Heronian mean operators based on Archimedean norms are very challenging and complicated tasks, because of their features and structure. Additionally, a decision-making process is developed under the identified operators by using complex intuitionistic fuzzy information. Finally, we illustrate several examples to show the multi-attribute decision-making technique is more flexible than the prevailing works with the help of sensitive analysis between explored and certain prevailing works.

Intuitionistic Fuzzy Modal Multi-Topological Structures and Intuitionistic Fuzzy Multi-Modal Multi-Topological Structures

On the basis of K. Kuratowski’s definitions of a topological structure with a closure or interior operator, the concept of a modal topological structure (MTS) with one of these operators was introduced by the author. This new structure was illustrated with examples with intuitionistic fuzzy topological operators from both examples, and for this reason, these structures were named intuitionistic fuzzy MTSs (IFMTSs). In a series of papers, the author introduced some modifications and extensions to the IFMTSs, e.g., intuitionistic fuzzy temporal topological structures, intuitionistic fuzzy level topological structures and others, and intuitionistic fuzzy multi modal topological structures and others. In the present paper, four new examples of intuitionistic fuzzy multi modal topological structures are given. On their base, the concepts of a modal multi-topological structure and of a multi-modal multi-topological structure are introduced and illustrated with examples from the area of the intuitionistic fuzzy sets—intuitionistic fuzzy modal multi-topological structure with a closure or an interior operator; and intuitionistic fuzzy multi-modal multi-topological structure with one of these operators. Two intuitionistic fuzzy topological operators are defined. Their basic properties are studied and they are used in the new structures.

Some properties of intuitionistic fuzzy n-binormal operator on IFH-space

The Intuitionistic Fuzzy n-binormal operator on Hilbert space H (IFn – BN) is introduced in this paper. We demonstrate that the addition and multiplication of two IFn – BN operators is the IFn – BN operator. We research some of its characteristics.

Multi-attribute group decision-making algorithm based on intuitionistic fuzzy rough Schweizer-Sklar aggregation operators

Multi-attribute group decision-making algorithm based on intuitionistic fuzzy rough Schweizer-Sklar aggregation operators

Intuitionistic fuzzy operations and operators: Some observations

Since its inception, the concept of intuitionistic fuzzy sets is getting popularity day by day. In addition to several operations, so many operators are there to excel the development of this thought. Few of such operators have been focused here. The key objective of this paper is to study those operators over intuitionistic fuzzy sets and to explore some major properties on it.

Intuitionistic fuzzy level operators related to degree of uncertainty

Two new intuitionistic fuzzy operators of level type are introduced and some of their properties are studied. They are related to the degree of uncertainty of a given intuitionistic fuzzy set. Geometrical interpretations onto the intuitionistic fuzzy interpretation triangle are provided.

Four new intuitionistic fuzzy bimodal topological structures

Two intuitionistic fuzzy modal operators from a second type are used for introducing of new intuitionistic fuzzy modal topological structures. After this, these structures, extended with the two standard intuitionistic fuzzy modal operators, generate four new intuitionistic fuzzy bimodal topological structures. They are illustrated with examples.

Some new results on intuitionistic fuzzy operators

The concept of intuitionistic fuzzy sets is becoming very popular day by day among mathematicians and researchers from other areas of science. It has been noticed that some operators have very interesting properties in Intuitionistic fuzzy sets. That is why these properties are investigated in this study. New findings on equality are obtained and proved.

Novel intuitionistic fuzzy Aczel Alsina Hamy mean operators and their applications in the assessment of construction material

Aggregation operators (AOs) are utilized to overcome the effects of attributes under some specific degree of weight in the decision-making (DM) process. The AOs have a large capacity to deal with uncertain and unpredictable information in multi-attribute decision-making (MADM) problems. The Hamy mean (HM) aggregation tools are well-known aggregation models, which are utilized to define correlation among different input arguments adequately. The intuitionistic fuzzy (IF) sets (IFS) can express unpredictable and vague information. The Aczel Alsina aggregation expressions are extensions of triangular norms. Recently, Aczel Alsina aggregation tools attained a lot of attentions from numerous research scholars. By inspiring the robustness and reliability of Aczel Alsina aggregation tools, we expose some appropriate operations of Aczel Alsina expressions under consideration of IF information. In this manuscript, we developed an intuitionistic fuzzy Aczel Alsina HM (IFAAHM) and an intuitionistic fuzzy Aczel Alsina weighted HM (IFAAWHM) operator. We also expressed the theory of Dual HM (DHM) tools and established a series of new approaches including intuitionistic fuzzy Aczel Alsina Dual HM (IFAADHM) and intuitionistic fuzzy Aczel Alsina weighted Dual HM (IFAAWDHM) operators. Some reliable characteristics and special cases of our derived approaches are also presented. The authors solved an application of a MADM technique under consideration of our derived approaches. To check the reliability and dependency of our derived mythologies, we gave an experimental case study to evaluate a desirable construction material based on some specific criteria of different Alternatives. To see the advantages and compatibility of our derived approaches, by comparing the results of existing approaches with the results of currently discussed AOs.

Multi-attribute group decision-making based on intuitionistic fuzzy aggregation operators defined by weighted geometric means

AbstractThis paper proposes a multi-attribute group decision-making methodology that takes advantage of a new weighted geometric mean aggregation operator on intuitionistic fuzzy numbers (IFNs). To this purpose, first, we define the intuitionistic fuzzy direct weighted geometric operator on IFNs, then we prove that it is a representable intuitionistic aggregation operator, and afterwards, we compare it with other aggregation operators motivated by the geometric mean. We use two proxies for the quantitative comparison of performances, namely the average of the Euclidean distances to the IFNs and the sum of squared error inspired by the k-means clustering algorithm.

Intuitionistic fuzzy bimodal topological structures

Two new intuitionistic fuzzy operators from a modal type are defined. Some properties of these operators are studied. Based on them, four new intuitionistic fuzzy modal topological structures are introduced and after this, four intuitionistic fuzzy bimodal topological structures are constructed. All they are examples of modal and bimodal topological structures.

An approach to multi-attribute decision making based on intuitionistic fuzzy rough Aczel-Alsina aggregation operators

A concept of intuitionistic fuzzy rough set based on approximations plays a vital role in coping with uncertainty. Aczel-Alsina t-norm and t-conorm are the most flexible operational laws based on the parameter for fuzzy frameworks. In multi-attribute group decision-making (MAGDM), the aim of this article is to develop some tools based on norm operations for the information fusion. In this article, intuitionistic fuzzy rough Aczel-Alsina weighted geometric operators are developed and studied their properties. Based on these operators, MAGDM algorithm is presented. The developed aggregation operators (AOs) are compared with some existing AOs, and their significance is discussed.

Generalized Similarity Operator for Intuitionistic Fuzzy Sets and its Applications Based on Recognition Principle and Multiple Criteria Decision Making Technique

Many complex real-world problems have been resolved based on similarity operators under intuitionistic fuzzy sets (IFSs). Numerous authors have developed intuitionistic fuzzy similarity operators (IFSOs) but with some setbacks, which include imprecise results, omission of hesitation information, misleading interpretations, and outright violations of metric axioms of similarity operator. To this end, this article presents a newly developed similarity operator under IFSs to ameliorate the itemized setbacks noticed with the hitherto similarity operators. To buttress the validity of the new similarity operator, we discuss its properties in alliance with the truisms of similarity. In addition, we discuss some complex decision-making situations involving car purchase selection process, pattern recognition, and emergency management using the new similarity operator based on multiple criteria decision making (MCDM) technique and recognition principle, respectively. Finally, comparative studies are presented to argue the justification of the new similarity operator. In short, the novelty of this work includes the evaluation of the existing IFSOs to isolate their fault lines, development of a new IFSO technique with the capacity to resolve the fault lines in the existing techniques, elaboration of some properties of the newly developed IFSO, and its applications in the solution of disaster control, pattern recognition, and the process of car selection for purchasing purpose based on the recognition principle and MCDM.

TOPSIS approach for MCGDM based on intuitionistic fuzzy rough Dombi aggregation operations

Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts’ attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model.

On Two Intuitionistic Fuzzy Modal Topological Structures

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) was introduced previously, and some of its properties were studied. So far, there are two different IFMTSs based on the classical intuitionistic fuzzy operations: “union” (∪) and “intersection” (∩). In the present paper, two new IFMTSs are developed. They are based on new intuitionistic fuzzy topological operators from closure and interior types, introduced here for the first time, and on the two standard intuitionistic fuzzy modal operators □ and ◊. Some basic properties of the new IFMTSs are discussed. The newly presented IFMTSs could be considered as a basis for the next research on the IFMTSs. Some ideas for the future development of the IFMTS theory and open problems are formulated, related to the existence of other intuitionistic fuzzy operations that can generate new intuitionistic fuzzy topological operators and, respectively, new IFMTSs.