Intuitionistic Fuzzy Operators Research Articles

On two new intuitionistic fuzzy topological operators and four new intuitionistic fuzzy feeble modal topological structures

In the intuitionistic fuzzy sets theory there are some intuitionistic fuzzy topological operators. Here, two new operators are defined, some of their properties are shown and on their basis, four new intuitionistic fuzzy feeble modal topological structures are introduced and some of their properties are discussed.

On Intuitionistic Fuzzy Temporal Topological Structures

In the present paper, four different intuitionistic fuzzy temporal topological structures are introduced, and some of their properties are discussed. These topological structures are based on the intuitionistic fuzzy topological operators and on the temporal intuitionistic fuzzy topological operators, which exist in intuitionistic fuzzy sets theory. The new structures are direct extensions of the IFTSs and will be the basis for introducing of a new type of topological structures.

Analysis and Prioritization of the Factors of the Robotic Industry With the Assistance of EDAS Technique Based on Intuitionistic Fuzzy Rough Yager Aggregation Operators

The focus of the interdisciplinary and scientific discipline of robotics is to design, maintain and use mechanical robotics. There exist many issues faced by the robotic industry but there are some factors that can cover these complexities effectively. Handling vague and imprecise data is a difficult task nowadays. So there is a need to define such kind of effective and valuable tool that can handle complex and vague data more dominantly. The evaluation based on distance from average solution (EDAS) method is a very useful tool that can handle complex data more effectively. The best alternative can be chosen based on distance from the average solution. The EDAS method is relatively simple to use and provide a quick evaluation of alternative based on multiple criteria. Yager t-norm and t-conorm are two fuzzy logic operators proposed by Yager. So based on the importance of Yager t-norm and t-conorm, initially, in this article, we have proposed the basic operative laws for intuitionistic fuzzy rough numbers. Based on these developed operational laws, we have developed some new intuitionistic fuzzy rough aggregation operators called intuitionistic fuzzy rough Yager average (weighted, ordered weighted, hybrid) aggregation operators and intuitionistic fuzzy rough Yager geometric (weighted, ordered weighted, hybrid) aggregation operators. Moreover, we have proposed the EDAS technique based on intuitionistic fuzzy rough Yager aggregation operators and used these notions for the selection of suitable factors that play a vital role in the robotic industry. Also, to show the effective use of these introduced notions, we have proposed an algorithm for the EDAS method based on intuitionistic fuzzy rough Yager aggregation operators along with a descriptive example. To show the superiority of the introduced work we have developed a comparative analysis.

Intuitionistic fuzzy credibility Dombi aggregation operators and their application of railway train selection in Pakistan

<abstract><p>The degree of credibility of the fuzzy assessment value demonstrates its significance and necessity in the fuzzy decision making problem. The fuzzy assessment values should be closely related to their credibility measures in order to increase the credibility levels and degrees of fuzzy assessment values. This will increase the abundance and the credibility of the assessment information. As a new extension of the intuitionistic fuzzy concept, this study suggests the idea of an intuitionistic fuzzy credibility number (IFCN). So, based on Dombi norms, we proposed some new operational laws for intuitionistic fuzzy credibility numbers. Different intuitionistic fuzzy credibility aggregation operators are defined using Dombi t-norm and t-conorm operations. i.e., intuitionistic fuzzy credibility Dombi weighted averaging (IFCDWA), intuitionistic fuzzy credibility Dombi ordered weighted averaging (IFCDOWA), intuitionistic fuzzy credibility Dombi hybrid weighted averaging (IFCDHWA) operators. Next, we defined multiple criteria group decisions (MCGDM) approach. To ensure that their results are reliable and applicable, we also gave an example of railway train selection and discussed comparative result analysis.</p></abstract>

Analytical Studies of the Application Aspects of Fuzzy Intuitionistic and Fuzzy Type 2 Set

The main aim of this paper is to introduce the definition of intuitionistic fuzzy set and operations on it that will prove fruitful to conclude to a solution on problems of real life and how fuzzy logic and Graphics Processing unit can be used together to solve different domain problems for faster responses. Various comprehensive survey of Type-2 fuzzy set and the intuitionistic fuzzy set theories have been described here. IFS is nothing but a simple extension of the fuzzy set defined in the domain of discourse. Graphics Processing Unit (GPU) has been used to enhance the speed of execution. The intuitionistic fuzzy set is utilized as a proper element for representing the degree of hesitation concerning both the non-membership and membership degrees of an element of a set. Recent trends show how GPU is used for various computational applications that are run parallel to reduce overall execution time. Both the fuzzy domains seek application in tackling of the situation of vagueness with their respective characteristic feature sets to the fields concerned to different engineering domains of interdisciplines. This paper highlights the overview of the two eminent fuzzy categories like Fuzzy type 2 and intuitionistic fuzzy theory along with their application on greater scale.

Intuitionistic Fuzzy Rough Aczel-Alsina Average Aggregation Operators and Their Applications in Medical Diagnoses

Managing ambiguous and asymmetric types of information is a very challenging task under the consideration of classical data. Furthermore, Aczel-Alsina aggregation operators are the new developments in fuzzy sets theory. However, when decision-makers need to use these structures in fuzzy rough structures, these operators fail to deal with such types of values, as fuzzy rough structures use lower and upper approximation spaces. Thus, an encasement of an intuitionistic fuzzy set has a chance of data loss, whereas an intuitionistic fuzzy rough set can resolve the problem of data loss. Motivated by the notion of intuitionistic fuzzy rough sets and new aggregation operators i.e., intuitionistic fuzzy Aczel-Alsina operators, this paper firstly initiates some basic Aczel-Alsina operational rules for intuitionistic fuzzy rough numbers. Secondly, based on these newly defined operational rules, we have developed some new aggregation operators, such as intuitionistic fuzzy rough Aczel-Alsina weighted average (IFRAAWA), intuitionistic fuzzy rough Aczel-Alsina ordered weighted average (IFRAAOWA), and intuitionistic fuzzy rough Aczel-Alsina hybrid average (IFRAAHA) aggregation operators. Moreover, the properties of these aggregation operators have been initiated. These operators can help in evaluating awkward and asymmetric information in real-life problems. The use of aggregation operators in medical diagnosis and MADM is an efficient method that can help in healthcare and decision-making applications. To present an effective use of these developed operators in medical diagnosis and the selection of the best next-generation firewall, we have established an algorithm along with a numerical example to provide authenticity and clarity to the established work. Furthermore, a comparative analysis of the introduced work shows the superiority of the introduced approach.

Power Muirhead mean operators of interval-valued intuitionistic fuzzy values in the framework of Dempster–Shafer theory for multiple criteria decision-making

Multiple criteria decision-making (MCDM) based on interval intuitionistic fuzzy value (IVIFV) is a process of aggregating decision criteria represented by multiple interval-valued intuitionistic fuzzy numbers to select the optimal alternative. Among them, an aggregation operator is an indispensable tool, and the properties of an aggregation operator directly affect the decision results. Existing aggregation operators based on IVIFV have satisfactory results in eliminating the correlation between criteria and removing the influence of outliers on the results. However, there are some unreasonable results due to some undesired properties of IVIFVs. In this paper, IVIFV operation under the Dempster-Shafer theory (DST) framework is applied to combine the power average and Muirhead mean operators and interval intuitionistic fuzzy power Muirhead mean operators under DST framework are presented. Then a method based on the presented operators for MCDM problems is proposed. Finally, a set of numerical experiments are conducted to demonstrate the proposed method. The experimental results suggest that the proposed method not only retains the robustness of the power average operator and the capability of the Muirhead mean operator, but also eliminates a shortcoming that existing interval intuitionistic fuzzy operators cannot handle the case where the weights are in IVIFVs.

A Study on Intuitionistic Fuzzy Critical Path Problems Through Centroid Based Ranking Method

In this study the intuitionistic fuzzy version of the critical path method has been proposed to solve networking problems with uncertain activity durations. Intuitionistic fuzzy set [1] is an extension of fuzzy set theory [2] unlike fuzzy set, it focuses on degree of belonging, the degree of nonbelonging or non-membership function and the degree of hesitancy which helps the decision maker to adopt the best among the worst cases. Trapezoidal and the triangular intuitionistic fuzzy numbers are utilized to describe the uncertain activity or task durations of the project network. Here trapezoidal and triangular intuitionistic fuzzy numbers are converted into their corresponding parametric form and applying the proposed intuitionistic fuzzy arithmetic operations and a new method of ranking based on the parametric form of intuitionistic fuzzy numbers, the intuitionistic fuzzy critical path with vagueness reduced intuitionistic fuzzy completion duration of the project has been obtained. The authentication of the proposed method can be checked by comparing the obtained results with the results available in pieces of literature.

Intuitionistic Fuzzy Modal Topological Structure

The concept of an Intuitionistic Fuzzy Modal Topological Structure (IFMTS) or for brevity, Intuitionistic Fuzzy Modal Topology (IFMT), is introduced. It is proved that the two standard intuitionistic fuzzy topological operators C and I, and the two standard intuitionistic fuzzy modal operators ☐ and ♢ generate two different IFMTs. Some basic properties of both IFMTs are discussed. Some important properties of the intuitionistic fuzzy modal and topological operators are discussed. These properties will be a basis of next research on the IFMTSs. Ideas for future development of the IFMT theory are formulated.

On the intuitionistic fuzzy modal feeble topological structures

In the paper, for the first time, ideas for intuitionistic fuzzy modal feeble topological structures (of two types) are introduced, and some of their properties are discussed. These topologies are based on the intuitionistic fuzzy operation @, intuitionistic fuzzy operator W, on the two intuitionistic fuzzy modal operators □, ◊ and of simplest intuitionistic fuzzy extended Dα.

Enhanced intuitionistic fuzzy similarity operators with applications in emergency management and pattern recognition

Enhanced intuitionistic fuzzy similarity operators with applications in emergency management and pattern recognition

Several significant equalities on intuitionistic fuzzy operators

There are various operators and operations in intuitionistic fuzzy set theory. The roles of these operators and operations are very significant as they show a deeper interconnection between the two ordinary modal logic operators. It can be well noted that modal operators can change intuitionistic fuzzy sets into fuzzy sets easily. Considering all of these, we establish several equalities on intuitionistic fuzzy sets.

Modified Szmidt and Kacprzyk’s Intuitionistic Fuzzy Distances and their Applications in Decision-making

Intuitionistic fuzzy models are significant in resolving decision-making. Distance measures under intuitionistic fuzzy environment are reliable techniques deployed to express the application of IFSs. Some approaches of estimating distances between IFSs have been explored by Szmidt and Kacprzyk, where the complete parameters of IFSs are considered. Albeit, the distance operators lack reliability because of certain setbacks. In this paper, we modified Szmidt and Kacprzyk's distance operators between IFSs to enhance reliability in terms of applications. Some theorems are given to substantiate the validity of the modified intuitionistic fuzzy distance operators. Futhermore, decision-making cases of pattern recognition and disease identification are discussed using the Szmidt and Kacprzyk's distances and their improved versions where information are represented in intuitionistic fuzzy pairs. From the study, it is observed that the modified Szmidt and Kacprzyk's distance operators between IFSs yield better results compare to the Szmidt and Kacprzyk's distance operators between IFSs.

Covering-based compound mean operators arising from Heronian and Bonferroni mean operators in fuzzy and intuitionistic fuzzy environments

Both Heronian mean (HM) operators and Bonferroni mean (BM) operators can capture the interrelationship between input arguments and have been a hot research topic as a useful aggregation technique in fuzzy and intuitionistic fuzzy environments. In this paper, associated with the common characters of these operators we propose the covering-based compound mean operators in fuzzy environments to capture various interrelationships between input arguments, some desirable properties and special cases of the proposed mean operators are provided. Then, conditions under which these covering-based compound mean operators can be directly used to aggregate the membership degrees and nonmembership degrees of intuitionistic fuzzy information, are provided. In particular, novel intuitionistic fuzzy HM operators and intuitionistic fuzzy BM operators are directly derived from the classical ones. We list the detailed steps of multiple attribute decision making with the developed aggregation operators, and give a comparison of the new extensions of BM operators by this paper with the corresponding existing ones to prove the rationality and effectiveness of the proposed method.

A new type of intuitionistic fuzzy modal operators over intuitionistic fuzzy pairs

In the paper, two intuitionistic fuzzy modal operators from a new type are introduced over intuitionistic fuzzy pairs. Some of the basic properties of the new operators are formulated and checked.

Humanitarian Rescue Scheme Selection under the Covid-19 Crisis in China: Based on Group Decision-Making Method

Humanitarian rescue has become an important part of government emergency management in China. In order to select the optimal humanitarian rescue scheme accurately and in a timely manner in an emergency, reduce the harm of disasters to human life and health, and improve the government’s emergency management ability, a multi-attribute emergency group decision-making method is proposed. First, interval-valued intuitionistic fuzzy sets are used to express the preferences of decision-makers, and interval-valued intuitionistic fuzzy entropy is used to calculate attribute weights. Then, based on the technique for order preference by similarity to an ideal solution (TOPSIS) method, the weight of the decision-maker is calculated. Then, the relevant interval intuitionistic fuzzy operators are used to summarize the preferences of decision-makers in group decision-making. Finally, we will use the closeness ranking method to choose the optimal scheme, and the feasibility and practicability of the proposed method are demonstrated by an example. The example shows that the model is more scientific, objective, and comprehensive in solving the problem of multi-attribute group decision-making than the traditional scheme selection, which only depends on the subjective discussion of decision-makers.

The α, β-Cut Intervals and Weakest t-Norm Based Importance Measure for Criticality Analysis in Intuitionisitic Fuzzy Fault Tree Analysis of LNG-ESD System

Different importance measures have been developed and widely utilized in system reliability analysis to measure the importance of system components. During operation period of a complex system, it becomes more difficult to collect exact failure data of system components i.e. the collected failure data may have some sort of uncertainties due to various reasons. Generally, triangular shaped fuzzy numbers or intuitionistic fuzzy numbers (IFNs) are used to quantify the various types of uncertainty in failure data of the system’s components and fuzzy arithmetic operations are utilized which computes each reliability index with wide range of prediction due to accumulating phenomenon of fuzziness. In this paper, different types of intuitionistic fuzzy number (IFN) are used to quantify the failure data uncertainty of the system’s components while α, β-cut intervals and weakest t-norm (Tw)-based arithmetic operations are employed to reduce the range of prediction for each reliability index. The objective of the present study is to develop Tw-based importance measure for criticality analysis in intuitionistic fuzzy fault tree analysis (IF-FTA) of a system, when different types of uncertainties in crisp failure data of basic events are quantified by different types of membership and non-membership functions. The developed importance measure applies system fault tree, α-cut and β-cut intervals, different types of intuitionistic fuzzy number (IFN) and weakest t-norm (Tw) based intuitionistic fuzzy arithmetic operations. To demonstrate the applicability of the proposed measure, a case study of liquefied natural gas terminal emergency shutdown system (LNG-ESD system) is performed. The IF-FTA of LNG-ESD system is presented to evaluate the fault intervals of the system at different levels using Tw-based arithmetic operations on different types of IFNs. The developed importance measure is applied to identify and rank the critical basic events in IF-FTA of LNG-ESD system. The proposed measure is also compared with some existing importance measures.

Generalized intuitionistic fuzzy aggregation operators based on confidence levels for group decision making

The focus of our this paper is to develop a series of Einstein hybrid aggregation operators using confidence level, such as confidence intuitionistic fuzzy Einstein hybrid averaging operator, confidence intuitionistic fuzzy Einstein hybrid geometric operator, generalized confidence intuitionistic fuzzy Einstein hybrid averaging operator and generalized confidence intuitionistic fuzzy Einstein hybrid geometric operator. The main advantage of the new operators is that these operators not only provide information to the experts of the problems, but these methods also consider the degrees of the experts of the problems that they are familiar with the selection option. The new approaches provide more general, more accurate and precise results as compared to the existing methods. Finally, the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach.

Intuitionistic Fuzzy Normal Operator on IFH - Space

In this article, we define Intuitionistic Fuzzy Normal Operator operating on an IFH-Space. An operator 𝓢 is an intuitionistic fuzzy normal operator if 𝓢𝓢∗=𝓢∗𝓢 i.e. 𝓢 commutes with its intuitionistic fuzzy adjoint.

The induced generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric aggregation operator and their application to group decision-making

The induced generalized interval-valued intuitionistic fuzzy Einstein hybrid geometric aggregation operator and their application to group decision-making