Intuitionistic Fuzzy Soft Sets Research Articles

Selection of appropriate location of turbines using score function in transversals of an intuitionistic fuzzy soft hypergraphs

The concept of intuitionistic fuzzy soft set is applied to generalize the theory of transversals in hypergraphs. The notion of transversals of an Intuitionistic Fuzzy Soft Hypergraphs (IFSHGs) and locally minimal transversals of IFSHGs are pioneered with some of its specifications. It is also proved that H ˜ is (μ, ν)-tempered IFSHGs if H ˜ is support simple, elementary and simply ordered. Then, an algorithm is developed and proposed to find the minimal transversals of IFSHGs. An application is also identified in selecting appropriate location for the installation of wind turbines. Finally the proposed algorithm works in finding the suitable place for wind turbine installation. As a result the proposed algorithm is helpful in making decisions.

Cosine and cotangent similarity measures for intuitionistic fuzzy hypersoft sets with application in MADM problem

Intuitionistic fuzzy hypersoft sets (IFHSSs) are a novel model that is projected to address the limitations of Intuitionistic fuzzy soft sets (IFSSs) regarding the entitlement of a multi-argument domain for the approximation of parameters under consideration. It is more flexible and reliable as it considers the further classification of parameters into their relevant parametric valued sets. In this paper, we proposed some trigonometric (cosine and cotangent) similarity measures and their weighted trigonometric similarity measures (SMs). Trigonometric Similarity measures (SMs) for intuitionistic fuzzy hypersoft sets (IFHSSs) are significantly implied to check the similarity measures and help to determine the similarity between different factors. Also, in order to evaluate the validity of the significant study and apply the results to a daily life problem. We use them to solve problems involving the selection of renewable energy sources. According to several technical contributing factors, the analysis identifies the ideal location for the implementation of the energy production units. Future case studies with many features and additional bifurcation along with multiple decision-makers can use the suggested methodologies. Also, several existing structures, such as fuzzy, Pythagorean fuzzy, Neutrosophic theories, etc., can be utilized with the suggested method.

Measures of Distance and Entropy Based on the Fermatean Fuzzy-Type Soft Sets Approach

The definition of Fermatean fuzzy soft sets and some of its features are introduced in this study. A Fermatean fuzzy soft set is a parameterized family of Fermatean fuzzy sets and a generalization of intuitionistic and Pythagorean fuzzy soft sets. This paper presents a definition of the Fermatean fuzzy soft entropy. Also acquired are the formulae for standard distance measures such as Hamming and Euclidean distance. Other formulas have also been proposed for calculating the entropy and distance measurements of FFSSs. Even if the entropy and distance measures are defined for other set extensions, they cannot be applied directly to Fermatean fuzzy soft sets. It can be used to determine the uncertainty associated with a Fermatean fuzzy soft set, discover similarities between any two Fermatean fuzzy soft sets using the proposed distance measures, and compare it to other existing structures in the literature. Fermatean fuzzy soft set applications in decision-making and pattern recognition difficulties are also examined. Finally, comparison studies with other known equations are performed.

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.

On Intuitionistic Fuzzy Neutrosophic Soft Ideal Topological Spaces

The purpose of this paper is to introduce the notion of intuitionistic fuzzy neutronsophic soft ideal in Intuitionistic fuzzy neutronsophic soft set theory. The concept of intuitionistic fuzzy neutrosophic soft local function is also introduced. These concepts are discussed with a view to find new intuitionistic fuzzy neutronsophic soft topologies from the original one. The basic structure, respecially a basic for such generated Intuitionistic fuzzy neutronsophic soft topologies also studied here. Finally, the notion of compatibility of intuitionistic fuzzy neutronsophic soft ideals with Intuitionistic fuzzy neutrosophic soft topologies is introduced and some equivalent conditions concerning, this topic are established here.

Intuitionistic Possibility Fermatean Fuzzy Soft Sets

In this study, we introduce a new concept by making Possibility Fermatean fuzzy soft sets into a more general concept, namely Intuitionistic Possibility Fermatean fuzzy soft sets. We present examples of the application of this theory to a decision-making problem. From a theoretical point of view, we review the basic properties of this model and define the operations essential to its framework. Comprehensive definitions of complement, union, and intersection, as well as AND and OR operations are meticulously presented. As a transition from theory to practical application within this innovative context, we present an algorithm for solving decision-making problems, contributing to the practical implementation of this extended concept. This research aims to improve our understanding of the intuitionistic possibility of Fermatean fuzzy soft sets and to bridge the gap between theoretical advances and their real-world utility in decision-making problems.

An approach to multi-attribute decision-making based on intuitionistic fuzzy soft information and Aczel-Alsina operational laws

The intuitionistic fuzzy soft set (IFSS) is a vital technique for tackling uncertainty while the collection of information with the help of the membership function having values from unit interval. Moreover, the Aczel-Alsina t-norm (AATNRM) and Aczel-Alsina t-conorm (AATCRM) are the most generalized and flexible operational laws to operate the information which is the part of the unit intervals. The purpose of this article is to provide a number of aggregation operations (AOs) for information represented by intuitionistic fuzzy soft values (IFSVs) based on AATRM and AATCRM. Therefore, some new operational laws are developed by using on the AATRM and AATCRM for the development of the sum and product laws for IFSVs. Then, intuitionistic fuzzy soft Aczel-Alsina weighted averaging (IFSAAWA) and geometric (IFSAAWG) operators are purposed based on these operational laws. Additionally, some of their characteristics are examined, and the difference of the proposed and existing operators is investigated. Moreover, the proposed approach is applied to the problem of multi-attribute decision-making (MADM) for significance.

Fuzzy Arithmetic–Based Algorithm for Identifying Medical Conditions for Better Treatment

Making the right medical decision is challenging work because, in our daily life, decision-making problems may have the components of membership and non-membership degrees with the possibility of hesitation. Since soft theory offers a theoretical framework for dealing with ambiguous, fuzzy, and ill-defined objects, it is a key development in the field of computer programming as well as other scientific disciplines. Intuitionistic fuzzy soft sets provide an effective tool for solving multiple attribute decision-making with intuitionistic fuzzy information. The most essential issue is how to derive the ranking of alternatives from the information quantified in terms of intuitional fuzzy values. This theory also has the potential to be used to solve such real-world problems. In this work, we explore how Sanchez's medical theory could be used in medical diagnosis and provide a fuzzy arithmetic-based algorithm for identifying medical conditions to address this.

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.

Bipolar Intuitionistic Fuzzy Soft Ideals of BCK/BCI-Algebras and Its Applications in Decision-Making

In this paper, we merge the concepts of soft set theory and a bipolar intuitionistic fuzzy set. A bipolar intuitionistic fuzzy soft ideal in a BCK-algebra is defined as a soft set over the set of elements in the BCK-algebra, with each element associated with an intuitionistic fuzzy set. This relationship captures degrees of uncertainty, hesitancy, and non-membership degrees within the context of BCK-algebras. We investigate basic operations on bipolar intuitionistic fuzzy soft ideals such as union, intersection, AND, and OR. The intersection, union, AND, and OR of two bipolar intuitionistic fuzzy soft ideals is a bipolar intuitionistic fuzzy soft ideal. We also demonstrate how to use a bipolar intuitionistic fuzzy soft set to solve a problem involving decision making. Finally, we provide a general approach for handling decision-making problems using a bipolar intuitionistic fuzzy soft set.

Product Selection Considering Multiple Consumers’ Expectations and Online Reviews: A Method Based on Intuitionistic Fuzzy Soft Sets and TODIM

Large amounts of online reviews from e-commerce sites and social media platforms can help potential consumers to better understand products and play an important part in assisting potential consumers in making purchase decisions. Moreover, while multiple consumers purchase the same product, the index parameters of the product that are of concern among them are usually different, i.e., they have different expectations for the product. Therefore, the question of how to effectively analyze online product reviews and consider multiple consumers’ expectations to select products is an important issue that needs to be addressed. The objective of this study is to propose a product selection method based on intuitionistic fuzzy soft sets and TODIM. Firstly, the online reviews are extracted by the web crawler and are pretreated. Next, the sentiment orientations of each online review concerning product index parameters are recognized using the dictionary-based sentiment analysis algorithm. Then, the evaluation values of sentiment orientations for product index parameters are firstly expressed by intuitionistic fuzzy numbers and are then transformed into intuitionistic fuzzy soft sets. Further, the alternative product set is obtained according to the uni-int decision function and multiple consumers’ expectations, and we then rank the alternative products using the TODIM method. Finally, a case study is provided to illustrate the validity and feasibility of the proposed method.

Implementation of intuitionistic fuzzy soft set theoretic scheme in decision making

Implementation of intuitionistic fuzzy soft set theoretic scheme in decision making

A novel study of spherical fuzzy soft Dombi aggregation operators and their applications to multicriteria decision making

In many decision-making situations, we are not restricted to two kinds of aspects, such as membership degree or nonmembership degree, and sometimes we need to include the abstinence degree (AD). However, many fuzzy set theories fail to cover issues, such as an intuitionistic fuzzy soft set, Pythagorean fuzzy soft set and q-rung orthopair fuzzy soft set. All the above notions can only consider membership degree and a nonmembership degree in their structures. The spherical fuzzy soft set compensates for these drawbacks in its structure. Moreover, the Dombi t-norm and Dombi t-conorm are the fundamental apparatuses to generalize the basic operational laws of sum and product. Therefore, in this article, based on the dominant features of spherical fuzzy soft sets and valuable features of the Dombi t-norm and Dombi t-conorm, we initially developed the basic Dombi operational laws for spherical fuzzy soft numbers. Moreover, based on these newly developed operational laws, we introduced aggregation operators called spherical fuzzy soft Dombi average (weighted, ordered weighted, hybrid) aggregation operators. We discussed the basic properties of these aggregation operators. Additionally, we have developed a multiple criteria decision making (MCDM) approach using an explanatory example via our approach to show its effective utilization. Furthermore, a comparative study of our approach shows the superiority of our introduced notions.

Optimal operation mode selection of sponge city PPP projects using IFSS-prospect theory and VIKOR approach: a case study in China.

The construction of sponge city (SC) public private partnership (PPP) projects is considered to be a feasible measure to solve the "water problems" in China. To ensure the success of SC PPP projects, how to select an appropriate operation mode for SC PPP projects is an urgent problem to be solved. In this paper, first, the evaluation index system of operation mode is established from the aspects of project characteristics, government capabilities, project benefits, project implementation, and cooperative partnership. Second, the DEMATEL method and entropy method are introduced to overcome the drawbacks of a single method, and the combination weights are calculated by game theory. Finally, the decision-making model based on intuitionistic fuzzy soft set (IFSS)-prospect theory and VIKOR approach is constructed to select operation mode for SC PPP projects. In this paper, the framework is applied to select an operation mode for the Qingshan demonstration zone project, and its feasibility and effectiveness are verified through sensitivity analysis and comparative analysis. The results show that BOT is the optimal operation mode for SC PPP projects, and government capabilities and project implementation are critical factors to be considered when selecting an operation mode. This study can provide guidance to the government in the OMS of SC PPP projects and improve the sustainability of the projects.

Impact of Machine Learning and Artificial Intelligence in Business Based on Intuitionistic Fuzzy Soft WASPAS Method

Artificial intelligence (AI) is a well-known and reliable technology that enables a machine to simulate human behavior. While the major theme of AI is to make a smart computer system that thinks like a human to solve awkward problems, machine learning allows a machine to automatically learn from past information without the need for explicit programming. In this analysis, we aim to derive the idea of Aczel–Alsina aggregation operators based on an intuitionistic fuzzy soft set. The initial stage was the discovery of the primary and critical Aczel–Alsina operational laws for intuitionistic fuzzy soft sets. Subsequently, we pioneer a range of applicable theories (set out below) and identify their essential characteristics and key results: intuitionistic fuzzy soft Aczel–Alsina weighted averaging; intuitionistic fuzzy soft Aczel–Alsina ordered weighted averaging; intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators; and intuitionistic fuzzy soft Aczel–Alsina ordered weighted geometric operators. Additionally, by utilizing certain key information, including intuitionistic fuzzy soft Aczel–Alsina weighted averaging and intuitionistic fuzzy soft Aczel–Alsina weighted geometric operators, we also introduce the theory of the weighted aggregates sum product assessment method for intuitionistic fuzzy soft information. This paper also introduces a multi-attribute decision-making method, which is based on derived operators for intuitionistic fuzzy soft numbers and seeks to assess specific industrial problems using artificial intelligence or machine learning. Finally, to underline the value and reasonableness of the information described herein, we compare our obtained results with some pre-existing information in the field. This comparison is supported by a range of numerical examples to demonstrate the practicality of the invented theory.

TOPSIS Technique of MCDM under Cubic Intuitionistic Fuzzy Soft Set Environment

A powerful tool for dealing with ambiguity, attributive values, fuzziness, and inconsistency is the cubic intuitionistic fuzzy soft set. In this paper, multi-criteria group decision-making (MCGDM) technique called extended TOPSIS based on distance and similarity measures is presented. Furthermore, a real-world problem is resolved by applying CIFS-set to support the theoretical visualization. Arguably, the proposed technique works well and has practical uses.

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.

An algebraic approach to the variants of convexity for soft expert approximate function with intuitionistic fuzzy setting

A new area of research called intuitionistic fuzzy soft expert set is expected to overcome the drawbacks of an intuitionistic fuzzy soft set in terms of eligibility for soft expert-argument approximate function. This type of function views the power set of the universe as its co-domain and the cartesian product of attributes, experts, and their opinions as its domain. The domain of this function is larger as compared to the domain of a soft approximation function. It can manage a situation in which several expert opinions are taken into account by a single model. For the soft expert-argument approximate function with intuitionistic fuzzy setting, concepts such as set inclusion, ( α , v ) -convexity(concave) sets, strongly ( α , v ) -convexity (concave) sets, strictly ( α , v ) -convexity (concave) sets, convex hull, and convex cone are conceived in this paper. Some set-theoretic inequalities are established with generalized properties and results on the basis of these specified notions. Additionally, by using a theoretic cum analytical approach, various elements of computational geometry, such as convex hull and convex cone, are theorized and some pertinent results are generalized.

NEW OPERATIONS ON FUZZY ENVIRONMENT

In this paper we introduce the operations and on interval valued intuitionistic fuzzy soft set and establish some properties of these operators. We also develop a decision making method based on information measure of interval valued intuitionistic fuzzy soft set.