Fuzzy Information Measures Research Articles

Generalized Parametric Fuzzy Information Measure

Objective: To generalize an existing fuzzy information measure and verify its important properties. Methods: Both objective and descriptive methods have been adopted; problem-solving and problem-posing methods have been used. A collection of properties presented by De Luca and Termini is used as a standard for establishing new fuzzy information measures. Findings: This study has analysed the different features of the parametric measure of fuzzy information that we have presented. The suggested fuzzy entropy measure is a legitimate measure of fuzzy information since it meets all necessary requirements. Its monotonic behaviour has also been studied. Comparisons between the proposed measure of fuzzy information and the corresponding measure of probabilistic information have been discussed. Novelty: The unique quality of the suggested fuzzy information measure is found in its monotonic behaviour corresponding to parameter α. When conducting a multicriteria decision analysis and directing the decision-making process, monotonic fuzzy information measures are more useful. Because the suggested measure satisfies fundamental set features, it can be applied in soft computing for economics, decision-making, and data aggregation. Mathematics Subject Classification: 94 D 05 Keywords: Fuzzy Entropy, Uncertainty, Fuzziness, Measures of Information, Shannon Entropy

Parametric circular intuitionistic fuzzy information measures and multi-criteria decision making with extended TOPSIS

Parametric circular intuitionistic fuzzy information measures and multi-criteria decision making with extended TOPSIS

SemiFREE: Semisupervised Feature Selection With Fuzzy Relevance and Redundancy

Feature selection, as an effective dimensionality reduction technique, is favored in preprocessing data. However, most existing algorithms are solely liable for labeled or unlabeled data, whereas a limited portion of real-world data is annotated with labels. In this paper, we therefore propose a novel scheme named SemiFREE, i.e., Semi-supervised feature selection with Fuzzy RElevance and rEdundancy. Firstly, both labeled and unlabeled samples are assigned with fuzzy decisions that allow class membership to naturally express the fuzziness or uncertainty in data labeling. Secondly, sample similarities in feature space and fuzzy decision are captured to induce fuzzy information measures for redefining the feature relevance and redundancy. Finally, adhering to the principle of relevance-maximization and redundancy-minimization, SemiFREE leverages the forward sequential searching strategy to identify qualified features progressively. Extensive experiments demonstrate the superiority of SemiFREE in the presence of partially labeled data against some other well-established feature selection algorithms.

Normal [formula omitted] functions-based fuzzy information measures with applications in MADM and pattern recognition

Fuzzy and non-standard fuzzy information measures act upon vague information entailed in linguistic variables or uncertain numerical data following some goal for which they discover the “best alternative” or “correct pattern”. This paper introduces the concept of normalKN functions instrumental to generate a class of fuzzy knowledge measures. In addition to the axiomatic approach, we investigate various general methods to obtain normalKN functions from the notions of auto-morphisms, restricted equivalence functions, and restricted dissimilarity functions. Further, aggregatingnormal KNfunctions, we propose three knowledge measures of a fuzzy set and exploit their significance in practical applications. This concerns Multiple Attribute Decision Making (MADM) problems, the issue of appropriate weight computation, and the understanding of structured linguistic variables. Additionally, we consider the real case study for the ranking of universities. A novel methodology to transform a given fuzzy knowledge measure into a family of similarity measures of fuzzy sets is also suggested. Furthermore, we discuss an application of the proposed similarity measures in the context of pattern recognition and the MADM problem using artificial and real data sets. The comparative study of the proposed measures shows their advantage over existing ones because of specific theoretical and practical aspects.

On utilizing modified TOPSIS with R-norm q-rung picture fuzzy information measure green supplier selection.

The present communication introduces a new discriminant measure coined as R-norm q-rung picture fuzzy discriminant information measure which is more generalized in nature and has the capability to handle more flexibility inherited in the inexact information. The notion of q-rung picture fuzzy set (q-RPFS) has an integrated advantage of picture fuzzy set and q-rung orthopair fuzzy set with flexibility of qth level relations. The proposed parametric measure is then applied in the conventional "technique for order preference by similarity to the ideal solution (TOPSIS) method" for solving a green supplier selection problem. The numerical illustration to exhibit the proposed methodology for the green supplier selection problem has been presented in an empirical form to establish the consistency of the model. Also, the advantageous features of the proposed scheme in the setup of impreciseness have been discussed.

Multiattribute group decision making based on novel score function considering both the angle and fuzzy information under interval-valued intuitionistic fuzzy environment

The interval-valued intuitionistic fuzzy values (IVIFVs) have been widely employed for multiattribute group decision making (MAGDM). However, the existing decision making method using IVIFVs has some drawbacks. The recognition degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable and effective decision method is obvious. In this paper, a novel score function considering both the angle and fuzzy information of IVIFVs is proposed, which ensures the effective fusion of the fuzzy information measure and angle measure and overcomes the shortcomings of the existing methods. Then, the weights of decision makers (DMs) are set as IVIFVs and subjective values are determined by the optimization model to ensure the objectivity and authenticity of the weights of DMs. Furthermore, a novel MAGDM method based on the proposed score function is proposed. Finally, the proposed method is implemented on the regional innovation resource allocation efficiency evaluation. The results show that our method possesses a higher recognition degree than the other methods, and it ensures relatively high ranking accuracy. The ideology and results of this research will help the DMs to evaluate the alternatives effectively.

Investment decision making in the fuzzy context: An integrated model approach

With the implementation and steady progress of the Belt and Road (B&R) initiative, China’s investment in countries along the B&R has maintained a high growth trend. Generally speaking, investment problems are often accompanied by high risk and uncertainty, and how to make the suitable investment decision is a difficult issue. This paper investigates an investment decision approach under the probabilistic hesitant fuzzy environment. Firstly, a new probabilistic hesitant fuzzy distance and correlation coefficient are defined to overcome the defects of the existing probabilistic hesitant fuzzy information measures. Secondly, an attribute weight integrated model is constructed by combining the maximum deviation method, the CRITIC method and the maximum entropy principle, which is able to take into account the correlation between attributes and make full use of the decision information. In addition, a disappointment theory-based probabilistic hesitant fuzzy multi-attribute decision making (PHFMADM) method is proposed to solve the investment decision problem, which can integrate the psychological behavior of decision makers into the decision making process and make the decision results more authentic and reliable. Finally, the rationality and validity of the method are verified by comparing with the existing methods.

Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical Diagnosis.

Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases.

Multi-attribute group decision-making problem of medical consumption products based on extended TODIM-VIKOR approach with Fermatean fuzzy information measure

The fundamental goal of this research is to develop a MAGDM (Multi-Attribute Group Decision Making) problem of Medical Consumption Products. We propose TODIM–VIKOR approach in this paper, which combines the TODIM (an acronym in Portuguese for Interactive and Multi-criteria Decision-Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) procedures under Fermatean fuzzy information. A new Fermatean fuzzy scoring function is presented for dealing with comparison problems. In addition, we introduce a novel entropy measure for assessing the degree of fuzziness associated with an FFS. We also offer a Jensen–Shannon divergence measure for the Fermatean Fuzzy set that can be used to compare the discrimination information of two FFSs. This suggested measure meets all mathematical standards for being considered a measure. We introduced entropy and divergence measures to determine the objective weight in the TODIM–VIKOR approach. Meanwhile, to deal with multiple attribute group decision-making, a new decision procedure based on the suggested Entropy and Jensen–Shannon divergence measure was proposed in a Fermatean Fuzzy environment. In this article, TODIM has in view to find out the overall dominance degree, and VIKOR is to determine the compromise solution. Finally, we manage a supplier selection problem to verify the performance of the suggested Fermatean fuzzy TODIM–VIKOR method by comparing the ranking solution to the rankings of existing methodologies. We investigate the reliability and effectiveness of our proposed methodology.

Novel exponential fuzzy information measures

Novel exponential fuzzy information measures

On prioritization of hydrogen fuel cell technology utilizing bi-parametric picture fuzzy information measures in VIKOR & TOPSIS decision-making approaches

The present communication proposes a novel computational model for the assessment of hydrogen fuel cell (HFC) technology which provides an analytical framework for the decision makers. This model has been developed by considering the evaluation criteria, criteria weights and step-wise performance evaluation of HFC technologies for each criterion under picture fuzzy environment. A novel bi-parametric picture fuzzy discriminant measure has been proposed and utilized in the VIKOR and TOPSIS decision-making methodologies. The incorporation of bi-parametric discriminant measure gives additional flexibility and better comprehensiveness to the formal computational procedures in literature. A case study involving a group of experts, selected criteria indicators in context with HFC components, has been considered in order to show the step-wise implementation of the proposed integrated approaches. Finally, a comparative study and sensitivity analysis along with some advantageous remarks have been presented to illustrate the efficiency of the proposed contributions.

Effective fuzzy joint mutual information feature selection based on uncertainty region for classification problem

Classification problem widely exists in real-world applications. Unfortunately, data quality is the main challenge of the classification models, especially when the data includes irrelevant and redundant features. Feature selection (FS) is an effective preprocessing technique to enhance the quality of the data. For this, an integration of information theory and fuzzy sets introduced powerful measures, such as fuzzy information measures, to develop many feature selection methods. However, estimating fuzzy information measures is not only costly in the space and runtime but also may be affected by the bias between the certainty and uncertainty regions. This paper proposes a novel instance selection based on uncertainty region (ISUR) to overcome these limitations. Then, a state-of-the-art FS method, called fuzzy joint mutual information (FJMI), has been adapted to design an effective FS method, called fuzzy joint mutual information feature selection based on uncertainty region (FJMIUR). The proposed method consists of two processes: instance selection and feature selection. The former selects the uncertainty region that improves the estimation of fuzzy information measures and reduces the consumed cost while the latter selects the most significant features. Using 20 real-world classification datasets, comparative experiments, including well-known and state-of-the-art FS methods, were conducted to evaluate the effectiveness of FJMIUR. The results show the outperformance of FJMIUR in most cases according to six classification measures, average percentage of selected features, space, and runtime.

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.

Methods for Detecting COVID-19 Patients Using Interval-Valued T-Spherical Fuzzy Relations and Information Measures

The concepts of relations and information measures have importance whenever we deal with medical diagnosis problems. The aim of this paper is to investigate the global pandemic COVID-19 scenario using relations and information measures in an interval-valued T-spherical fuzzy (IVTSF) environment. An IVTSF set (IVTSFS) allows describing four aspects of human opinions i.e., membership, abstinence, non-membership, and refusal grade that process information in a significant way and reduce information loss. We propose similarity measures and relations in the IVTSF environment and investigate their properties. Both information measures and relations are applied in a medical diagnosis problem keeping in view the global pandemic COVID-19. How to determine the diagnosis based on symptoms of a patient using similarity measures and relations is discussed. Finally, the advantages of dealing with such problems using the IVTSF framework are demonstrated with examples.

Methods for multi-attribute decision making, pattern recognition and clustering based on T-spherical fuzzy information measures

T-spherical fuzzy set (TSFS) is a generalized version of the spherical fuzzy set (SFS) and picture fuzzy set (PFS) to manage awkward and unpredictable information in realistic decision issues. TSFS deals with yes, abstinence, no, and refusal type of fuzzy information. This manuscript aims to observe the drawbacks of some existing dice similarity measures (DSMs) and to propose some new DSMs in the environment of TSFSs. The validation of the new DSMs is proved. The defined DSMs are further extended to introduce some generalized DSMs (GDSMs) and their special cases are studied. Additionally, the TOPSIS method using the entropy measures (EMs) based on TSFSs is also explored and verified with the help of some examples. The proposed new GDSMs and TOPSIS method are applied to the problem of building material recognition, medical diagnosis, clustering, and the results obtained are investigated. A comparison of the new theory is established where the advancement of the proposed DSMs is elaborated under some conditions. The advantages of the new DSMs and the drawbacks of the previous DSMs of IFSs, PyFSs, and PFSs have been studied because of their applicability. The article is comprehensively summarized, and some possible future directions are stated.

Fuzzy joint mutual information feature selection based on ideal vector

Feature selection is an effective preprocess that helps the classification task to improve its performance. Information measures, especially fuzzy information measures have been a powerful solution in feature selection. However, existing feature selection frameworks based on fuzzy information measures suffer from one of two limitations: (1) discarding important feature relations as redundancy and complementarity. (2) requiring a high computational cost. To overcome these limitations, a new feature selection framework is proposed in this paper, called fuzzy joint mutual information based on ideal vector (FJMIIV), to extract all possible feature relations with minimum computational cost. The performance of the proposed framework is compared with some of the state-of-the-art frameworks on various benchmark datasets. The comparison results using four well-known classifiers show that the proposed method can effectively improve the classification performance.

Fuzzy Rough Information Measures and their Applications

The degree of roughness characterizes the uncertainty contained in a rough set. The rough entropy was defined to measure the roughness of a rough set. Though, it was effective and useful, but not accurate enough. Some authors use information measure in place of entropy for better understanding which measures the amount of uncertainty contained in fuzzy rough set .In this paper three new fuzzy rough information measures are proposed and their validity is verified. The application of these proposed information measures in decision making problems is studied and also compared with other existing information measures.

Generalized Fuzzy Divergence Measure, Pattern Recognition, and Inequalities

Many fuzzy information and divergence measures developed by various researchers and authors. Here, authors proposed new fuzzy divergence measure using the properties of convex function and fuzzy concept. The applications of novel fuzzy divergence measures in pattern recognition with case study, are discussed. Obtained various novel fuzzy information inequalities on fuzzy divergence measures. The new relations among new and existing fuzzy divergence measure by new f-divergence, Jensen inequalities, properties of convex functions and inequalities have studied. Finally, verified these results and proposed fuzzy divergence measures by numerical example.

A q-rung orthopair fuzzy ARAS method based on entropy and discrimination measures: an application of sustainable recycling partner selection.

The necessity and policy of eco-economy stimulate enterprises to attain sustainability by executing supply chain management. Generally, the evaluation process of sustainable recycling partner (SRP) selection is treated as a multi-criteria decision-making problem due to existence of numerous influencing aspects. To tackle the uncertain information during the process of SRP selection, the q-rung orthopair fuzzy sets have a good choice, which can refer to a broader range of uncertain decision-making information. Thus, this study presents a combined framework with the additive ratio assessment (ARAS) approach, notions of q-rung orthopair fuzzy set (q-ROFS) and information measures, and further implements to tackle the multi-criteria SRP selection problem with q-ROFSs setting. In this procedure, the criteria weights are evaluated with the integration of the subjective weights given by decision-experts and the objective weights obtain from the entropy and discrimination measures-based approach. For this, new entropy and discrimination measures are introduced for q-ROFSs and discussed the effectiveness of proposed measures. To elucidate the applicability of the present methodology, a case study related to sustainable recycling partner assessment is presented under q-ROFSs context. Sensitivity analysis is conducted over diverse set of criteria weights to verify the robustness of introduced framework. The results of the sensitivity analysis signify that the recycling partner SRP1 constantly secures the best rank and despites how sub-criteria weights differ. A comparison with extant methods is made to validate of the results of proposed one. The findings of the work verify that the developed framework is more valuable and well consistent with formerly proposed decision-making models.

Extended TODIM method based on VIKOR for q‐rung orthopair fuzzy information measures and their application in MAGDM problem of medical consumption products

Nowadays, supply chain management (SCM) has achieved considerable attention from all over the world. q-rung orthopair fuzzy set, developed by Yager, is the entirety of the most prominent tool to express fuzzy data in the decision-making problems. In this study, the introduction of two new generalised measures (entropy and Jensen–Tsalli divergence measure) of q-rung orthopair fuzzy information involving one real parameter is given. The proposed measures have satisfied all the necessary mathematical properties of being a measure. Then the introduced entropy and divergence measure is used to obtain the objective weights. Based on the proposed entropy and divergence measure, we proposed a new decision method to deal with multiple-attribute group decision-making problems under the q-rung orthopair fuzzy environment. Then, on the basis of the TODIM and VIKOR techniques, an integrated TODIM-VIKOR approach is developed to solve multiattribute group decision-making problem. In this paper, TODIM aims to determine the overall dominance degree and VIKOR aims to determine the compromise solution. Lastly, we handle a supplier selection problem to verify the performance of the proposed q-rung orthopair fuzzy TODIM-VIKOR method and results explore the reliability and effectiveness of our proposed methodology by comparing the ranking solution with the ranking results of the existing approaches.