Interval-valued Intuitionistic Fuzzy Soft Sets Research Articles

Extension of Interaction Geometric Aggregation Operator for Material Selection Using Interval-Valued Intuitionistic Fuzzy Hypersoft Set

A recently emerged area of research named intuitionistic fuzzy hypersoft set (IFHSS) attempts to describe the internal limitations of intuitionistic fuzzy soft sets on multiparameter functions. A computation of such a type connects a power set of the universe with a tuple of sub-parameters. The strategy shows the allocation of attributes to their respective sub-attribute values in distinct groupings. The above features make it a unique methodical tool for handling obstacles of hesitation. The aggregation operators have an important role in the assessment of both types of potential and in identifying problems from their assessment. This research extends the use of the interaction aggregation operator to the interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS), which is an entirely new structure generated through the interval-valued intuitionistic fuzzy soft set (IVIFSS). The IVIFHSS significantly condenses information that is inaccurate and imprecise compared to the frequently utilized IFSS and IVIFSS. Fuzzy reasoning is recognized as the prevalent strategy for improving imperfect data in decision-making processes. The core objective of the research is to develop operational rules for interval-valued intuitionistic fuzzy hypersoft numbers (IVIFHSNs), which promote interactions. This research is designed to broaden the utilization of the interaction geometric aggregation operator in the framework of IVIFHSS. In particular, we propose a novel operator known as the Interval-Valued Intuitionistic Fuzzy Hypersoft Interactive Weighted Geometric (IVIFHSIWG) operator. The aggregation operator indicates industry professional support for the implementation of a robust MCGDM material selection technique in order to address this need. The practical application of the intended MCGDM technique has been introduced in selecting materials (MS) for cryogenic storage containers. The influence advocates that the anticipated model is more operational and stable in demonstrating anxious facts based on IVIFHSS.

From Ambiguity to Clarity: Unraveling the Power of Similarity Measures in Multi-Polar Interval-Valued Intuitionistic Fuzzy Soft Sets

The utilization of similarity measures in the context of multi-polar interval-valued intuitionistic fuzzy soft sets (mPIVIFSS) is a significant theoretical approach that offers a valuable structure for tackling intricate situations that are characterized by imprecise information and uncertainty. Nevertheless, these issues frequently entail conditions that are not limited in scope and exhibit a considerable level of uncertainty in scenarios involving multiple dimensions, hence presenting substantial difficulties. The objective of this research study is to provide a comprehensive understanding of similarity measures in the context of mPIVIFSS. Additionally, we will examine several operations, such as complement, subset, union, intersection, AND, OR, and De-Morgan’s Laws, as they relate to mPIVIFSS. This study not only includes theoretical debates but also explores practical applications. These efforts contribute to the improvement of decision-making, pattern recognition, and data analysis in settings characterized by ambiguous and uncertain information, hence emphasizing the importance of similarity measures in efficiently addressing multi-dimensional problems.

Extension of correlation coefficient based TOPSIS technique for interval-valued Pythagorean fuzzy soft set: A case study in extract, transform, and load techniques.

Correlation is an essential statistical concept for analyzing two dissimilar variables' relationships. Although the correlation coefficient is a well-known indicator, it has not been applied to interval-valued Pythagorean fuzzy soft sets (IVPFSS) data. IVPFSS is a generalized form of interval-valued intuitionistic fuzzy soft sets and a refined extension of Pythagorean fuzzy soft sets. In this study, we propose the correlation coefficient (CC) and weighted correlation coefficient (WCC) for IVPFSS and examine their necessary properties. Based on the proposed correlation measures, we develop a prioritization technique for order preference by similarity to the ideal solution (TOPSIS). We use the Extract, Transform, and Load (ETL) software selection as an example to demonstrate the application of these measures and construct a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) model. The method investigates the challenge of optimizing ETL software selection for business intelligence (BI). This study offers to illuminate the significance of using correlation measures to make decisions in uncertain and complex settings. The multi-attribute decision-making (MADM) approach is a powerful instrument with many applications. This expansion is predicted to conclude in a more reliable decision-making structure. Using a sensitivity analysis, we contributed empirical studies to determine the most significant decision processes. The proposed algorithm's productivity is more consistent than prevalent models in controlling the adequate conformations of the anticipated study. Therefore, this research is expected to contribute significantly to statistics and decision-making.

Prioritization of Thermal Energy Storage Techniques Using TOPSIS Method Based on Correlation Coefficient for Interval-Valued Intuitionistic Fuzzy Hypersoft Set

The correlation between two disparate variables conquers a significant habitation in statistics. The concept of correlation coefficient (CC) is one of the well-known indicators, but it is not used in interval-valued intuitionistic fuzzy hypersoft set (IVIFHSS) information. It is a generalization of interval-valued intuitionistic fuzzy soft sets and a refined extension of intuitionistic fuzzy hypersoft sets. However, using the CC and weighted correlation coefficient (WCC) has not yet been explored for IVIFHSS information. The core objective of this research is to present the correlation coefficient (CC) and weighted correlation coefficient (WCC) for interval-valued intuitionistic fuzzy hypersoft sets (IVIFHSS) and their mandatory properties. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) is developed based on proposed correlation measures. To ensure the symmetry of the developed scheme, we consider mathematical clarifications of correlation contractions. Based on assessments, it conceded vibrant multi-attribute decision-making (MADM) methodology with the most substantial significance. In addition, a statistical illustration is designated to regulate the operative usage of a decision-making configuration in thermal energy storage techniques. The productivity of the advocated algorithm is more reliable than existing replicas to control the favorable configurations of the premeditated study.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets (PFHSS) in their investigations to resolve the indeterminate and imprecise information in the decision-making process. Aggregation operators (AOs) perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception. In this paper, we extend the concept of PFHSS to interval-valued PFHSS (IVPFHSS), which is the generalized form of interval-valued intuitionistic fuzzy soft set. The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set. It is the most potent method for amplifying fuzzy data in the decision-making (DM) practice. Some operational laws for IVPFHSS have been proposed. Based on offered operational laws, two inventive AOs have been established: interval-valued Pythagorean fuzzy hypersoft weighted average (IVPFHSWA) and interval-valued Pythagorean fuzzy hypersoft weighted geometric (IVPFHSWG) operators with their essential properties. Multi-criteria group decision-making (MCGDM) shows an active part in contracts with the difficulties in industrial enterprise for material selection. But, the prevalent MCGDM approaches consistently carry irreconcilable consequences. Based on the anticipated AOs, a robust MCGDM technique is deliberate for material selection in industrial enterprises to accommodate this shortcoming. A real-world application of the projected MCGDM method for material selection (MS) of cryogenic storing vessels is presented. The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

Utilization of interval-valued intuitionistic fuzzy soft set in the health sector

The soft set theory plays a key role for dealing with uncertainty, fuzziness and vagueness. The concept of fuzzy soft set which can be seen as a new mathematical approach to vagueness is used in many applications including reliability evaluation, multi criteria decision making and medical diagnosis problems. Later, it is generalized to an interval-valued intuitionistic fuzzy soft set. In this attempt we present the definition and operations of an interval-valued intuitionistic fuzzy soft set. Furthermore, based on the analysis of several operations on interval-valued intuitionistic fuzzy soft set in the study, we provide some notions such as the restricted intersection and restricted union of two interval-valued intuitionistic fuzzy soft sets for selection of appropriate hospital for patient affected by specific dieses.

Novel distance, similarity and entropy measures for interval valued intuitionistic fuzzy soft set

Soft and fuzzy sets are generic tools to deal with uncertainty. Both contemporary sets are not suitable to deal with all type of uncertain parameters. In this paper the hybridization of soft with extended fuzzy set information measures are derived. Interval-valued intuitionistic fuzzy soft set theory is a powerful tool for dealing with uncertainty of knowledge in information systems. In this paper, firstly some distance and similarity measures for interval-valued intuitionistic fuzzy soft sets were proposed. Further, some new entropy measures are also introduced by using the similarity measures. The validity of these measures is also proved. Applications of the distance measures is also used in the field of multi attribute decision making and medical diagnosis. The proposed measures are also compared with an existing measure to prove its significance.

Application of lattice ordered interval valued intutitionistic fuzzy soft sets in decision-making

Motivated by intuitionistic fuzzy sets and soft sets, a novel concept of lattice ordered interval-valued intuitionistic fuzzy soft sets (LOIVIFSSs) is introduced in this article. Operational rules like union, intersection, complement and some properties of LOIVIFSSs are demonstrated with examples. In this regard, an algorithm is developed to solve the multiple criteria decision-making (MCDM) problems based on LOIVIFSSs. Further, a benchmark problem concerning medical diagnosis have been investigated and a comparative analysis with existing technique is furnished to strengthen our approach.

Interval-Valued Intuitionistic Fuzzy Soft Rough Approximation Operators and Their Applications in Decision Making Problem.

It has been found that fuzzy sets, rough sets and soft sets are closely related concepts. Many complicated problems in economics, engineering, social sciences, medical science and many other fields involve uncertain data. These problems, which one comes in real life, cannot be solved using classical mathematical methods. There are several well-known theories to describe uncertainty, for instance, fuzzy set theory, rough set theory, and other mathematical tools. But all of these theories have their inherit difficulties as pointed out by D. Molodtsov. In 1999, D. Molodtsov introduced the concept of soft sets, which can be seen as a new mathematical tool for dealing with uncertainties. The concept of rough sets, proposed by Z. Pawlak as a framework for the construction of approximations of concepts. It is a formal tool for modeling and processing insufficient and incomplete information. Zhou and Wu first proposed the concept of intuitionistic fuzzy rough sets (IFrough sets). The aim of this paper is to introduce the concept of interval-valued intuitionistic fuzzy soft rough sets (IVIFS rough sets). We also investigate some properties of IVIFS rough approximation operators. Some basic operations and properties are studied. Lastly applications have been shown in decision making problems.

TOPSIS Method Based on the Correlation Coefficient of Interval-Valued Intuitionistic Fuzzy Soft Sets and Aggregation Operators with Their Application in Decision-Making

The correlation coefficient between the two parameters plays a significant part in statistics. Furthermore, the exactness of the assessment of correlation depends upon information from the set of discourses. The data collected for various statistical studies are full of ambiguities. The idea of interval-valued intuitionistic fuzzy soft sets is an extension of intuitionistic fuzzy soft sets that is used to express insufficient evaluation, uncertainty, and anxiety in decision-making. Intuitionistic fuzzy soft sets consider two different types of information, such as membership degree and nonmembership degree. In this paper, the concepts and properties of the correlation coefficient and the weighted correlation coefficient of interval-valued intuitionistic fuzzy soft sets are proposed. A prioritization technique for order preference by similarity to the ideal solution based on interval-valued intuitionistic fuzzy soft sets of correlation coefficients and the weighted correlation coefficient is introduced. We also proposed interval-valued intuitionistic fuzzy soft weighted average and interval-valued intuitionistic fuzzy soft weighted geometric operators and developed decision-making techniques based on the proposed operators. By using the developed techniques, a method for solving decision-making problems is proposed. To ensure the applicability of the proposed methods, an illustrative example is given. Finally, we present a comparison of some existing methods with our proposed techniques.

Interval-Valued Intuitionistic Fuzzy Soft Sets Based Decision-Making and Parameter Reduction

In a typical formulation of decision-making under uncertainty, a decision-maker must choose a single-optimal option among many possible options. However, the problem of selecting a unique and optimal choice has remained a significant challenge to solve. In this article, we propose a new interval-valued intuitionistic fuzzy soft set (IVIFSS) based decision-making approach to address this problem. The proposed approach is based on the choice value and score value of membership/nonmembership degrees. Furthermore, three parameter reduction algorithms are proposed. We apply the proposed approaches on a real application to demonstrate their working and effectiveness. We also compare the proposed approach against the adjustable IVIFSSs approach and show that the proposed approach has lower computation overhead and enable a decision-maker to choose top options to make a proper decision.

An extension of grey relational analysis for intuitionistic and interval-valued intuitionistic fuzzy soft sets

Objectives: Neither any analytical (or numerical) nor any statistical approach is often helpful in these situations due to the reason that every person has his/her own choice. To cope with such situations usually we have to use fuzzy sets in combination with soft sets, which consist of predicates and approximate value sets as their images. Material: Choice values and comparison table techniques are two common decision-making techniques, which often don’t result in same preference order or optimal choice. To overcome this kind of situation in decision-making problems, grey relational analysis method is used to get on a final decision. Method: Here we have used grey relational analysis method involving “intuitionistic fuzzy soft set” and “interval-valued intuitionistic fuzzy soft set” and “AND operation” to deal with such kind of problems. Findings: The proposed method is effective in seeking on an optimal choice in the case when common decision-making techniques fail to get on a final decision. Novelty: By using grey relational analysis, a suitable method to choose one object from different choices has been proposed. It overcome the greyness in decisionmaking problems for getting on a final decision when one gets too many options and finds it difficult to choose an optimal choice. Keywords: Fuzzy soft set; intuitionistic fuzzy soft set; grey relational analysis; interval-valued intuitionistic fuzzy soft set

Data Analysis Approach for Incomplete Interval-Valued Intuitionistic Fuzzy Soft Sets

The model of interval-valued intuitionistic fuzzy soft sets is a novel excellent solution which can manage the uncertainty and fuzziness of data. However, when we apply this model into practical applications, it is an indisputable fact that there are some missing data in many cases for a variety of reasons. For the purpose of handling this problem, this paper presents new data processing approaches for an incomplete interval-valued intuitionistic fuzzy soft set. The missing data will be ignored if percentages of missing degree of membership and nonmember ship in total degree of membership and nonmember ship for both the related parameter and object are below the threshold values; otherwise, it will be filled. The proposed filling method fully considers and employs the characteristics of the interval-valued intuitionistic fuzzy soft set itself. A case is shown in order to display the proposed method. From the results of experiments on all thirty randomly generated datasets, we can discover that the overall accuracy rate is up to 80.1% by our filling method. Finally, we give one real-life application to illustrate our proposed method.

Interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets and their application in decision-making

Although some statistical tools, such as mean and median, used for modelling a problem containing parameters or alternatives with multiple intuitionistic fuzzy values because these values are obtained in a specific period, decrease uncertainty, they lead to data loss. However, interval-valued intuitionistic fuzzy values can overcome such a concern. For this reason, the present study proposes the concept of interval-valued intuitionistic fuzzy parameterized interval-valued intuitionistic fuzzy soft sets (d-sets) and presents several of its basic properties. Moreover, by using d-sets, we suggest a new soft decision-making method and apply it to a problem concerning the eligibility of candidates for two vacant positions in an online job advertisement. Since it is the first method proposed in relation to this structure (d-sets), it is impossible to compare this method with another in this sense. To deal with this difficulty, we introduce four new concepts, i.e. mean reduction, mean bireduction, mean bireduction-reduction, and mean reduction-bireduction. By using these concepts, we apply four state-of-the-art soft decision-making methods to the problem. We then compare the ranking performances of the proposed method with those of the four methods. Besides, we apply five methods to a real problem concerning performance-based value assignment to some filters used in image denoising and compare the ranking performances of these methods. Finally, we discuss d-sets and the proposed method for further research.

Research on Multi-Objective Attribute Decision Algorithm Based on Inclusion Degree

By studying the arising problem in the decision-making of multi-objective attributes in regard to interval valued intuitionistic fuzzy soft set of interval-valued intuitionistic fuzzy soft set in the process of decision-making of multi-objective attributes, redefine the triangular interval-valued intuitionistic fuzzy soft set based on the triangular fuzzy number and the inclusion degree, and discuss their related properties and operations. At the same time, aiming at the problem that the equal inclusion degree value cannot determine in the previous algorithms, a new approach of decision-making of multi-objective attributes based on triangular interval-valued intuitionistic fuzzy soft set inclusion degree is proposed. In this method, we introduce the mean and variance, which can select the sum of the largest inclusion degrees, and choose the smaller variance as the best decision goal. At last, the validity and the correctness will be proved through instances.

Group Decision Making Through Interval Valued Intuitionistic Fuzzy Soft Sets

This article describes how the lack of adequate parametrization in some of the earlier uncertainty based models like fuzzy sets, rough sets motivated Molodtsov to introduce a new model in soft set. A suitable combination of individual models leads to hybrid models, which are more efficient than their individual components. So, the authors find the introduction of many hybrid models of soft sets, like the fuzzy soft set (FSS), intuitionistic fuzzy soft sets (IFSS), interval valued fuzzy soft set (IVFSS) and the interval valued intuitionistic fuzzy soft set (IVIFSS). Following the characteristic function approach to define soft sets introduced by Tripathy et al., they re-define IVIFSS in this article. One of the most attractive applications of soft set theory and its hybrid models has been decision making in the form of individual decision making or group decision making. Here, the authors propose a group decision making algorithm using IVIFSS, which generalises many of our earlier algorithms. They compute its complexity and establish the computation experimentally with graphical illustrations.

A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information

Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decision-making processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.

An Adjustable Reduction Approach of Interval-valued Intuitionistic Fuzzy Soft Sets for Decision Making

An Adjustable Reduction Approach of Interval-valued Intuitionistic Fuzzy Soft Sets for Decision Making

GROUP GENERALIZED INTERVAL-VALUED INTUITIONISTIC FUZZY SOFT SETS AND THEIR APPLICATIONS IN DECISION MAKING

Interval-valued intuitionistic fuzzy sets (IVIFSs) are widely used to handle uncertainty and imprecision in decision making. However, in more complicated environment, it is difficult to express the uncertain information by an IVIFS with considering the decision-making preference. Hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (G-GIVIFSS) which contains the basic description by interval-valued intuitionistic fuzzy soft set (IVIFSS) on the alternatives and a group of experts' evaluation of it. It contributes the following threefold: 1) A generalized interval-valued intuitionistic fuzzy soft set (GIVIFSS) is proposed by introducing an interval-valued intuitionistic fuzzy parameter, which reflects a new and senior expert's opinion on the basic description. The operations, properties and aggregation operators of GIVIFSS are discussed. 2) Based on GIVIFSS, a G-GIVIFSS is then proposed to reduce the impact of decision-making preference by introducing more parameters by a group of experts. Its important operations, properties and the weighted averaging operator are also defined. 3) A multi-attribute group decision making model based on G-GIVIFSS weighted averaging operator is built to solve the group decision making problems in the more universal IVIF environment, and two practical examples are taken to validate the efficiency and effectiveness of the proposed model.

Uncertainty measures of interval-valued intuitionistic fuzzy soft sets and their applications in decision making

Soft set theory offers a general mathematical tool for dealing with uncertainty. An interval-valued intuitionistic fuzzy soft set is a combination of interval-valued intuitionistic fuzzy set and soft set. The chief aim of this paper is to investigate the decision making based on interval-valued int uitionistic fuzzy soft sets. By means of the uncertainty measures of interval-valued intuitionistic fuzzy soft sets, we develop a novel approach to solve the problems of decision making and give an example to illustrate the developed approach, which demonstrates that our proposed method is more flexible and effective. Furthermore, we present an adjustable approach to weighted interval-valued intuitionistic fuzzy soft sets based decision making problems by using distance measures.