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In contrast to a fuzzy and intuitionistic fuzzy (AInF) set, a picture fuzzy (PIF) set may be taken as an effective tool to tackle decision-making problems. Fuzzy and intuitionistic fuzzy set theory can be extended to PIF-set theory. In light of the insufficiency of existing information and knowledge measures, this work proposes a knowledge measure for PIF-sets. The suggested knowledge measure efficacy and consistency are proven using numerical examples by comparing it to existing information andproper knowledge measures in the PIF-context. Aside from that, the proposed knowledge measure is used to develop an accuracy measure for PIF-sets. In pattern identification problems, the use of proposed accuracy measure is presented. Their effectiveness is demonstrated by using numerical examples. A modified version of the Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR) approach based on the proposed accuracy measure is presented with the goal to address a multi-criteria decision-making (MCDM) difficulty in a picture fuzzy context. Finally, a case study on how to choose the most suitable method to treat wastewater is provided. [ABSTRACT FROM AUTHOR]

In response to the shortcomings of existing image noise detection algorithms that rely on the flawed intuitionistic fuzzy entropy (IFE) theory, a method of image noise detection and removal based on intuitionistic fuzzy amount of knowledge (IFAK) is proposed by introducing the latest knowledge measure (KM) theory and model. In the noise detection stage, the optimal average intensity of the noisy image foreground and background is determined based on the maximum IFAK, and the parametric model of noise detection is constructed accordingly to mark the probability of noise pixels and suspected noise pixels, showing excellent performance of noise detection. In the noise removal stage, a denoising model based on IFAK and probability of noise pixels is proposed by using the noise probability matrix, which can not only effectively denoise, but also better protect the characteristics of image edges and non-noise extreme pixels. Comparative experiments are carried out on standard datasets and classical test images, respectively. Experimental results show that the proposed method can accurately identify the image impulse noise and effectively realize image denoising. The overall performance outperforms other similar algorithms. The key metrics PSNR and SSIM are increased by 14.81% and 11.35%, respectively. In this paper, the latest KM theory is applied to image denoising, and excellent evaluation metrics and visual effects are obtained, while innovative applications of this theory in other related fields are also achieved.

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As we all know, when describing knowledge measures in the context of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets, it is always considered as dual measures of entropy. However, information content and information clarity is closely related with the amount of knowledge. Motivated by this fact, in this study, we focus on a new axiomatic definition of knowledge measures for intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets. First, we present the formulas of the knowledge measures using different abstract functions, and we proved these functions satisfy the axioms. On the basis of mathematical analysis and numerical examples, we further analyze the characteristics of the suggested knowledge measure. Finally, in order to demonstrate how rational and useful the system we developed is, we provide medical diagnoses and specific multi-attribute decision problems. [ABSTRACT FROM AUTHOR]

The complementary dual of entropy is termed “knowledge measure” in recent studies concerning fuzzy and intuitionistic fuzzy sets. A picture fuzzy set is an extended and generalized form of fuzzy and intuitionistic fuzzy sets. The broader perspective of the picture fuzzy set inculcated the possibility of the formulation of a picture fuzzy knowledge measure and its potential implications. In this paper, we set up an axiomatic framework for obtaining a complementary dual of the picture fuzzy entropy. Subsequently, we derive two new knowledge measures that strictly follow the axiomatic requirements. Some empirical investigations establish the advantages of our proposed knowledge measure over the existing measures. We also present a novel multiple attribute decision-making (MADM) algorithm, wherein the proposed knowledge measure computes attribute weights and exhibits encouraging performance. The comparative analysis shows the potential implications and advantages of the proposed measures.

The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure. [ABSTRACT FROM AUTHOR]

The complementary dual of entropy is termed “knowledge measure” in recent studies concerning fuzzy and intuitionistic fuzzy sets. A picture fuzzy set is an extended and generalized form of fuzzy and intuitionistic fuzzy sets. The broader perspective of the picture fuzzy set inculcated the possibility of the formulation of a picture fuzzy knowledge measure and its potential implications. In this paper, we set up an axiomatic framework for obtaining a complementary dual of the picture fuzzy entropy. Subsequently, we derive two new knowledge measures that strictly follow the axiomatic requirements. Some empirical investigations establish the advantages of our proposed knowledge measure over the existing measures. We also present a novel multiple attribute decision-making (MADM) algorithm, wherein the proposed knowledge measure computes attribute weights and exhibits encouraging performance. The comparative analysis shows the potential implications and advantages of the proposed measures [ABSTRACT FROM AUTHOR]

Aiming at the differences in the contribution of feature data to the cluster centers in the clustering algorithm and the sensitivity of the algorithm to the initial cluster centers, this paper proposes a Weighted Knowledge Amountbased Intuitionistic Fuzzy C-means Method（WKAIFCM）. Firstly, this method fuzzed the original dataset intuitionistically and improved the latest intuitionistic fuzzy knowledge measure to calculate the knowledge amount which utilized in the feature weighting of dataset. Secondly, this method initialized the cluster centers to improve the calculation accuracy and clustering efficiency of high-dimensional feature dataset by kernel space density and kernel distance. Finally, based on the principle of sample distance between clusters and the principle of minimum knowledge amount, this method established a clustering optimization model to get the optimal iterative algorithm. The experimental results based on the UCI artificial dataset show that the proposed method can greatly improve the accuracy and iterative efficiency of clustering. The classification accuracy and execution efficiency are increased by 10.63% and 31.75% respectively, and this method has good universality and stability. This paper introduces a new theory of knowledge measure into fuzzy clustering for the first time and gets extraordinary results, which creates a new case for the potential application of this theory in other related fields. [ABSTRACT FROM AUTHOR]

The Pythagorean fuzzy sets are more robust than fuzzy sets and intuitionistic fuzzy sets in dealing with the problems involving uncertainty. To compare two Pythagorean fuzzy sets, distance measures play a crucial role. In this paper, we have proposed some novel distance measures for Pythagorean fuzzy sets using t-conorms. We have also discussed their various desirable properties. With the help of suggested distance measures, we have introduced some new knowledge measures for Pythagorean fuzzy sets. Through numerical comparison and linguistic hedges, we have established the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean fuzzy setting. At last, we have demonstrated the application of the suggested measures in pattern analysis and multi-attribute decision-making. [ABSTRACT FROM AUTHOR]

Abstract The Pythagorean fuzzy sets are more robust than fuzzy sets and intuitionistic fuzzy sets in dealing with the problems involving uncertainty. To compare two Pythagorean fuzzy sets, distance measures play a crucial role. In this paper, we have proposed some novel distance measures for Pythagorean fuzzy sets using t-conorms. We have also discussed their various desirable properties. With the help of suggested distance measures, we have introduced some new knowledge measures for Pythagorean fuzzy sets. Through numerical comparison and linguistic hedges, we have established the effectiveness of the suggested distance measures and knowledge measures, respectively, over the existing measures in the Pythagorean fuzzy setting. At last, we have demonstrated the application of the suggested measures in pattern analysis and multi-attribute decision-making.

The knowledge measure or uncertainty measure for constructing interval-valued intuitionistic fuzzy sets has attracted much attention. However, many uncertainty measures are measured by the entropy of interval-valued intuitionistic fuzzy sets, which cannot adequately reflect the knowledge of interval-valued intuitionistic fuzzy sets. In this paper, we not only extend the axiomatic definition of the knowledge measure of the interval-valued intuitionistic fuzzy set to a more general level but also establish a new knowledge measure function complying with the distance function combined with the technique for order preference by similarity to ideal solution (TOPSIS). Further, we investigate the properties of the proposed knowledge measure based on mathematical analysis and numerical examples. In addition, we create the entropy function by calculating the distance from the interval-valued fuzzy set to the most fuzzy point and prove that it satisfies the axiomatic definition. Finally, the proposed entropy is applied to the multi-attribute group decision-making problem with interval-valued intuitionistic fuzzy information. Experimental results demonstrate the effectiveness and practicability of the proposed entropy measure.

A single-valued neutrosophic set (SVNS) is a subcategory of neutrosophic set that is used to represent uncertainty and fuzziness in three tiers, namely truthfulness, indeterminacy, and falsity. The measure of entropy of a SVNS plays an important role to determine the ambiguity in a variety of situations. The knowledge measure is a dual form of entropy and is helpful in certain counterintuitive situations. In this paper, we introduce a knowledge measure for the SVNS and contrast the same with existing measures. The comparative study reveals that the proposed knowledge measure is more effective in modeling the structured linguistic variables. We provide the relations of the proposed knowledge measure with single valued neutrosophic similarity and distance measures. We also investigate the application of the proposed measure in multi-attribute group decision making (MAGDM). The proposed MAGDM model is helpful when the decision makers in the group have varied background and the hiring organization is unable to assign the level of importance or weight to a decision-maker. [ABSTRACT FROM AUTHOR]

Information quantification in numerical form for any given data is very useful in decision-making problems. In Atanassov intuitionistic fuzzy sets (A-IFSs), such quantification becomes more important due to uncertainties such as intuitionism and fuzziness. Distribution of these uncertainties is a key to determine knowledge associated with Atanassov intuitionistic values (A-IFVs). In this paper, first distribution of the above-mentioned uncertainties and their relationship are discussed. Then, knowledge measures are defined as a function of entropy and uncertainty index, with certain desired properties. Existence of such knowledge measures has been established. Further, it is shown that how proposed knowledge measures are useful in multi-criteria group decision-making (MCGDM) problems. [ABSTRACT FROM AUTHOR]

IFS is the further extension of ordinary fuzzy set, widely used in distinct applications to tackle uncertainty and fuzzy problems. Generally, similarity/distance measures are significant technique to discriminate between two sets and further they can applied to the problems of pattern recognition and decision-making. Though various similarity measures have already been suggested, still a lot of scope is there because some of them could not satisfy the properties of similarity measures and provide contradictory results. In this paper, we suggested new similarity measures having ability to contrast intuitionistic fuzzy (IF) sets. Furthermore, we have also analyzed their properties to validate the existence of proposed measure. After that, we provided some experimental analysis to verify the effectiveness of proposed measures which includes numerical experiment pattern recognition and clustering analysis. In experimental analysis, firstly we included numerical experiment by taking different cases to study the performance of proposed measures. Then, we dealt with the problems of pattern recognition and incorporated a performance index in terms of "Degree of Confidence" (DOC). Furthermore, we introduced a IF-MST clustering algorithm to deal with IFSs using the notion of MST ("Maximum Spanning Tree"). Additionally, we have modified similarity measure into knowledge measure and contrasted its performance with others knowledge measures to show the superiority of proposed measure. [ABSTRACT FROM AUTHOR]

A single-valued neutrosophic set (SVNS) is a subcategory of neutrosophic set that is used to represent uncertainty and fuzziness in three tiers, namely truthfulness, indeterminacy, and falsity. The measure of entropy of a SVNS plays an important role to determine the ambiguity in a variety of situations. The knowledge measure is a dual form of entropy and is helpful in certain counterintuitive situations. In this paper, we introduce a knowledge measure for the SVNS and contrast the same with existing measures. The comparative study reveals that the proposed knowledge measure is more effective in modeling the structured linguistic variables. We provide the relations of the proposed knowledge measure with single valued neutrosophic similarity and distance measures. We also investigate the application of the proposed measure in multi-attribute group decision making (MAGDM). The proposed MAGDM model is helpful when the decision makers in the group have varied background and the hiring organization is unable to assign the level of importance or weight to a decision-maker.

The q-rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set (IFS) and Pythagorean fuzzy sets (PyFSs). In this paper, we define the knowledge measure for qROFS by using the cosine inverse function. The information precision and information content are two facets of knowledge measure. Both facets of knowledge measure are considered. The properties of knowledge measure and their graphical explanations are discussed. An application of the knowledge measure in multi-attribute group decision-making (MAGDM) problem under the confidence level approach is given. A numerical example of the selection of renewable energy sources is discussed.

Background: Genomic testing is increasingly employed in clinical, research, educational, and commercial contexts. Genomic literacy is a prerequisite for the effective application of genomic testing, creating a corresponding need for validated tools to assess genomics knowledge. We sought to develop a reliable measure of genomics knowledge that incorporates modern genomic technologies and is informative for individuals with diverse backgrounds, including those with clinical/life sciences training. Methods: We developed the GKnowM Genomics Knowledge Scale to assess the knowledge needed to make an informed decision for genomic testing, appropriately apply genomic technologies and participate in civic decision-making. We administered the 30-item draft measure to a calibration cohort (n = 1,234) and subsequent participants to create a combined validation cohort (n = 2,405). We performed a multistage psychometric calibration and validation using classical test theory and item response theory (IRT) and conducted a post-hoc simulation study to evaluate the suitability of a computerized adaptive testing (CAT) implementation. Results: Based on exploratory factor analysis, we removed 4 of the 30 draft items. The resulting 26-item GKnowM measure has a single dominant factor. The scale internal consistency is α = 0.85, and the IRT 3-PL model demonstrated good overall and item fit. Validity is demonstrated with significant correlation (r = 0.61) with an existing genomics knowledge measure and significantly higher scores for individuals with adequate health literacy and healthcare providers (HCPs), including HCPs who work with genomic testing. The item bank is well suited to CAT, achieving high accuracy (r = 0.97 with the full measure) while administering a mean of 13.5 items. Conclusion: GKnowM is an updated, broadly relevant, rigorously validated 26-item measure for assessing genomics knowledge that we anticipate will be useful for assessing population genomic literacy and evaluating the effectiveness of genomics educational interventions. [ABSTRACT FROM AUTHOR]

Two new methods for mining incomplete data based on interval-valued fuzzy set theory and rough set theory, particularly maximal consistent blocks were proposed, and their application to the fall detection system, exactly to the posture detection system. The suggested methods are based on interval-valued aggregation operators supporting decision-making involving uncertainty. Additionally, the new measure of knowledge was used in two aspects: in the imputation of missing data and during the inference process. The usage of the knowledge measure allowed for a reduction of the uncertainty due to incompleteness and imprecision of data, while increasing the efficiency of the decision-making process, through the additional selection of objects for which the degree of the information measure is the highest. The developed hybrid approach to mining incomplete data and its application in a real decision-making problem yield stable performance despite the increase in missing data. • New methods for incomplete data based on interval-valued fuzzy set theory and rough set theory for the fall detection system. • The knowledge measure for reducing the uncertainty of data while increasing the efficiency of the decision-making process. • Knowledge measure is a very interesting measure because it gives information on the level of fuzziness and uncertainty. • The effectiveness of the developed hybrid approach to mining incomplete data and its application. [ABSTRACT FROM AUTHOR]

The q‐rung orthopair fuzzy set (qROFS) defined by Yager is a generalization of Atanassov intuitionistic fuzzy set and Pythagorean fuzzy sets. In this paper, we define the knowledge measure for qROFS by using the tangent inverse function. This is the first approach to quantify the knowledge associated with qROFS. The membership and nonmembership functions as well as the hesitancy margin are used to define the knowledge measure which makes it capable of considering both knowledge and fuzziness. The entropy measure which is the dual of the knowledge measure is also defined. The properties of the proposed knowledge measure with graphical explanations are discussed. An application of the proposed knowledge measure in multiattribute group decision making problem under confidence level approach is given. [ABSTRACT FROM AUTHOR]

Considering that the population is aging rapidly, the demand for technology for aging-at-home, which can provide reliable, unobtrusive monitoring of human activity, is expected to expand. This research focuses on improving the solution of the posture detection problem, which is a part of fall detection system. Fall detection, using depth maps obtained by the Microsoft Kinect sensor, is a two-stage method. We concentrate on the first stage of the system, that is, pose recognition from a depth map. For lying pose detection, a new hybrid FRSystem is proposed. In the system, two rule sets are investigated, the first one created based on a domain knowledge and the second induced based on the rough set theory. Additionally, two inference aggregation approaches are considered with and without the knowledge measure. The results indicate that the new axiomatic definition of knowledge measures, which we propose has a positive impact on the effectiveness of inference and the rule induction method reducing the number of rules in a set maintains it.

A knowledge-measuring method applicable to enterprises' production is constructed and a simulation is carried out to prove the applicability of the method. First, the total amount of knowledge increases exponentially with the increase of task modularisations. Second, the relationship between single-task modularisations makes the amount at a lower level; however, as the types of relationship between modularisations become increasingly rich and when various relationships between modularisations achieve equilibrium, the total amount would reach a higher level. Meanwhile, the total amount of knowledge in knowledge networks shows a linear growth with the increase of comprehensive measuring of relationship between inter-modularisation elements. [ABSTRACT FROM AUTHOR]

The differentiation procedure of intuitionistic fuzzy sets (IFSs) is very important in multiple criteria decision-making (MCDM). The aim here is to introduce a fruitful class of knowledge measures related to the information provided in terms of IFSs. We present a class of knowledge measures of IFSs that are based on the two notions: the fuzziness and the intuitionism of an IFS. An experimental problem is employed to illustrate the weight determination method based on the proposed knowledge measures. [ABSTRACT FROM AUTHOR]

This paper addresses the commonly used methods for solving multiple attribute group decision-making problems under an interval-valued intuitionistic fuzzy environment. It is shown that either the most popular score function and its latterly improved versions or other related methods may lead to the undesirable results. Apart from these seemly heuristic methods, we propose a generalized p-norm knowledge-based score function for the interval-valued intuitionistic fuzzy set, which is a generalization of the score function for intuitionistic fuzzy sets as well. The proposed score function is defined as the average amount of knowledge of information depicted in terms of the interval-valued intuitionistic fuzzy sets, that regards their quantitative level of information referred to a reference level, fuzziness and qualitative significance of information. It is proved that the proposed score function has good algebraic properties, such as monotonicity under multiplication or aggregation operator, which are not preserved in the case of existing score functions. We show that the proposed score function is a simple, easily interpreted approach, which provides intuitive results in ranking the IvIFSs as well as IFSs, particularly. Several illustrative examples are performed to demonstrate the superiority of the proposed method in measuring and discriminating the IvIFSs. A comparative analysis with the preceding methods in solving decision-making problems is conducted to show the effectiveness of the proposed method in real-life applications. [ABSTRACT FROM AUTHOR]

This paper proposes a new order relation for Pythagorean fuzzy numbers (PFNs) and applies to multi-attribute group decision making (MAGDM). The main contributions are outlined as five aspects: (1) the concepts of relative distance and information reliability of PFN are proposed. Then, a new order relation is developed to compare PFNs. Moreover, the new order relation of PFNs is demonstrated to be an admissible order. (2) Knowledge measure of PFN is defined to describe the amount of information. The desirable properties of knowledge measure of PFN are studied concretely. (3) For MAGDM with PFNs, the comprehensive distance between individual Pythagorean fuzzy matrices and a mean one are defined. Then, the decision makers' weights are obtained by the comprehensive distances. Thus, a collective Pythagorean fuzzy matrix is derived by using the Pythagorean fuzzy weighted average operator. (4) To determine attribute weights, a multi-objective programming model is constructed by maximizing the overall knowledge measure of each alternative. This model is further transformed into a single-objective mathematical program to resolve. (5) According to the defined new order relation of PFNs, the ranking order of alternatives is generated by the comprehensive values of alternatives. Therefore, a new method is proposed to solve MAGDM with PFNs. Finally, an example of venture capital investment selection is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The hesitant intuitionistic fuzzy set integrates the advantages of the intuitionistic fuzzy set and the hesitant fuzzy set, and can deal with the uncertainty problems with inconsistent preferences of decision makers perfectly. By considering the hesitancy and fuzziness of information provided by decision makers, the axiomatic definition of the knowledge measure on the hesitant intuitionistic fuzzy set is proposed. Besides, a class of parametric knowledge measure model that comply the axiom is developed, which can not only effectively depict the information in the hesitant intuitionistic fuzzy set, but also indicate the attitude characteristics of decision makers. Next, based on the discussion of the parameters in the knowledge measure, an amount of knowledge measures representing different attitude characteristics of decision makers are obtained. Furthermore, it is verified that the knowledge measure is proportional to the change of the attitude coefficient. Finally, a multiple attribute group decision making method based on the constructed knowledge measure of the hesitant intuitionistic fuzzy set is proposed. Meanwhile, a practical application, i. e., air conditioning installation company selection of an Internet company, demonstrates the effectiveness and practicability of the developed measure. [ABSTRACT FROM AUTHOR]

In contrast to a fuzzy and intuitionistic fuzzy (IF) set, a picture fuzzy (PF) set may be taken as an effective tool to tackle decision-making problems. Fuzzy and intuitionistic fuzzy set theory can be extended to PF-set theory. As per our knowledge, there is no PF-knowledge measure has been proposed by any researcher so far. A novel picture fuzzy knowledge measure is proposed in the present manuscript. Its mathematical properties are investigated along with its validation. Its performance is evaluated using four distinct examples. Besides this, the newly presented PF-knowledge measure is used to derive a new PF-Accuracy measure. The derived PF-accuracy measure is checked for its validation and its properties are explained. The applications of the derived PF-accuracy measure are given in pattern recognition. Furthermore, a VIKOR-TOPSIS approach based on the proposed PF-knowledge and accuracy measure is designed. Finally, the suggested approach is utilized to identify an appropriate adsorbent for extracting hexavalent chromium from wastewater. • A Novel knowledge measure for picture fuzzy sets is proposed. • Shortcomings of some present PF-information measures are shown by examples. • We derived an accuracy measure from the proposed knowledge measure in the picture fuzzy environment. • Traditional VIKOR Method is combined with the TOPSIS method. • Use the proposed method to opt for the best adsorbent to eliminate the Hexavalent Chromium from wastewater. [ABSTRACT FROM AUTHOR]

Much attention has been paid to construct an applicable knowledge measure or uncertainty measure for Atanassov’s intuitionistic fuzzy set (AIFS). However, many of these measures were developed from intuitionistic fuzzy entropy, which cannot really reflect the knowledge amount associated with an AIFS well. Some knowledge measures were constructed based on the distinction between an AIFS and its complementary set, which may lead to information loss in decision making. In this paper, knowledge amount of an AIFS is quantified by calculating the distance from an AIFS to the AIFS with maximum uncertainty. Axiomatic properties for the definition of knowledge measure are extended to a more general level. Then the new knowledge measure is developed based on an intuitionistic fuzzy distance measure. The properties of the proposed distance-based knowledge measure are investigated based on mathematical analysis and numerical examples. The proposed knowledge measure is finally applied to solve the multi-attribute group decision-making (MAGDM) problem with intuitionistic fuzzy information. The new MAGDM method is used to evaluate the threat level of malicious code. Experimental results in malicious code threat evaluation demonstrate the effectiveness and validity of proposed method.

A measure of knowledge should not be viewed simply as a dual measure of entropy in the context of intuitionistic fuzzy sets as there is no natural logic between these two kinds of measures with the introduction of hesitancy, nor in the context of interval-valued intuitionistic fuzzy sets (IVIFSs), for that matter. This work is devoted to the introduction of an axiomatic definition of knowledge measure for IVIFSs. In order to do that, a set of new axioms is presented with which knowledge measure should comply in the context of IVIFSs. A concrete model following these axioms is then developed to measure the amount of knowledge associated with an IVIFS. Two facets of knowledge associated with an IVIFS, i.e., the information content and the information clarity, are simultaneously taken into account in the construction of the model to truly reflect the nature of an IVIFS. In particular, the connection between knowledge measure and fuzzy entropy is investigated under this axiomatic framework. A series of tests is also provided to examine the performance of the developed measure. Finally, a concept of knowledge weight on attribute in multi-attribute decision making is presented and an illustrative example is used as a demonstration of the application of the developed technique to decision making under uncertainty. [ABSTRACT FROM AUTHOR]

This paper is devoted to an entropy-independent measure of knowledge in the context of intuitionistic fuzzy sets (IFSs). We point out and justify that there are at least two facets of knowledge associated with an IFS, namely the information content and the information clarity. Having this in mind, we put forward a novel axiomatic definition of knowledge measure for IFSs. More specifically, a set of new axioms is presented with which knowledge measure should comply in the context of IFSs. A parametric model following these axioms is then developed to realize this measure. Both facets mentioned above are simultaneously taken into account in the axioms and the model so as to better capture the unique features of an IFS. In particular, we suggest the concept of the amount of potential knowledge related to the hesitancy or non-specificity of an IFS. This allows us to introduce the idea of an attitudinal-based knowledge measure for IFSs. We believe that the knowledge measure provided in this manner could truly reflect the nature of IFSs, and what people really want with different attitudes towards the unknown. Finally, a practical application of the developed technique to decision making under uncertainty is illustrated. As such, the developed measure could be considered as a safe and effective alternative to help tackle some special problems that are difficult to handle by using entropy alone, especially when dealing with the complex situation in which different attitudes of users have to be considered. [ABSTRACT FROM AUTHOR]

Entropy in a fuzzy set measures the amount of ambiguity/imprecision present in the fuzzy set. In this paper, we introduce a knowledge measure of a fuzzy set and its generalization (accuracy measure). The knowledge measure may be considered as a dual measure of fuzzy entropy. We also investigate the effectiveness and application of the proposed knowledge measure in multiple attribute decision making. Furthermore, we provide a result for obtaining a class of knowledge measure. We also prove a general method for obtaining a knowledge measure using accuracy measure. Among some suggested implications of the proposed fuzzy accuracy measure, we demonstrate the application of fuzzy accuracy measure in image thresholding. [ABSTRACT FROM AUTHOR]

A measure of knowledge may be viewed as a dual measure of entropy in a fuzzy system; thus, it appears that the less entropy may always accompany the greater amount of knowledge. In this paper, we propose a novel measure of knowledge for an intuitionistic fuzzy set (IFS) through an axiomatic approach. We investigate the effectiveness of the proposed knowledge measure through some comparative studies with some existing entropy measures and knowledge measures of IFS. We also introduce one parametric generalized version of this knowledge measure. This paper also provides application of the proposed knowledge measures in multi-attribute decision-making (MADM). We also give two characterization results to obtain a general framework for defining new knowledge measures. Further, similarity and dissimilarity measures may also be viewed as dual concepts to deal with the problems related to pattern recognition. In this paper, we provide an accuracy measure of an intuitionistic fuzzy set relative to a given intuitionistic fuzzy set. The proposed accuracy measure seems to serve as an effective alternative to similarity and dissimilarity measures in some pattern recognition problems. We also give proof of some properties related to accuracy measure.

Our aim was to examine the responsiveness of a lung cancer screening brief knowledge measure (LCS-12). Eligible participants were aged 55-80 years, current smokers or had quit within 15 years, and English speaking. They completed a baseline pretest survey, viewed a lung cancer screening video-based patient decision aid, and then filled out a follow-up posttest survey. We performed a paired samples t-test, calculated effect size, and calculated absolute and relative percent improvement for each item. Participants (n = 30) were primarily White (63%) with less than a college degree (63%), and half were female (50%). Mean age was 61.5 years (standard deviation [SD] = 4.67) and average smoking history was 30.4 pack-years (range = 4.6-90.0). Mean score on the 12-item measure increased from 47.3% correct on the pretest to 80.3% correct on the posttest (mean pretest score = 5.67 vs. mean posttest score = 9.63; mean score difference = 3.97, SD = 2.87, 95% CI = 2.90, 5.04). Total knowledge scores improved significantly and were responsive to the decision aid intervention (paired samples t-test = 7.57, p < .001; Cohen's effect size = 1.59; standard response mean [SRM] = 1.38). All individual items were responsive, yet two items had lower absolute responsiveness than the others (item 8: "Without screening, is lung cancer often found at a later stage when cure is less likely?" pretest correct = 83.3% vs. posttest = 96.7%, responsiveness = 13.4%; and item 10: "Can a CT scan find lung disease that is not cancer?" pretest correct = 80.0% vs. posttest = 93.3%, responsiveness = 13.3%). The LCS-12 knowledge measure may be a useful outcome measure of shared decision making for lung cancer screening. [ABSTRACT FROM AUTHOR]

This contribution first addresses axiomatic definitions of some important information measures of Atanassov's intuitionistic fuzzy sets (AIFSs), such as, distance measure, similarity measure, entropy measure, and recently developed knowledge measure. After that, we study the relationship between similarity measures and knowledge measures, and that between distance measures and knowledge measures for AIFSs. In particular, we investigate the transformations of similarity measures into knowledge measures for AIFSs and vice versa. These transformations can induce more formulae to define the distance measures, the similarity measures, and the knowledge measures for AIFSs. In addition, to support these processes, suitable examples are provided for each of the introduced transformations. The contribution ends by introducing numerical examples with a discussion of results by using several types of knowledge measures and similarity measures. [ABSTRACT FROM AUTHOR]

As the complementary concept of intuitionistic fuzzy entropy, the knowledge measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) has attracted more attention and is still an open topic. The amount of knowledge is important to evaluate intuitionistic fuzzy information. An entropy-based knowledge measure for AIFSs is defined in this paper to quantify the knowledge amount conveyed by AIFSs. An intuitive analysis on the properties of the knowledge amount in AIFSs is put forward to facilitate the introduction of axiomatic definition of the knowledge measure. Then we propose a new knowledge measure based on the entropy-based divergence measure with respect for the difference between the membership degree, the non-membership degree, and the hesitancy degree. The properties of the new knowledge measure are investigated in a mathematical viewpoint. Several examples are applied to illustrate the performance of the new knowledge measure. Comparison with several existing entropy and knowledge measures indicates that the proposed knowledge has a greater ability in discriminating different AIFSs and it is robust in quantifying the knowledge amount of different AIFSs. Lastly, the new knowledge measure is applied to the problem of multiple attribute decision making (MADM) in an intuitionistic fuzzy environment. Two models are presented to determine attribute weights in the cases that information on attribute weights is partially known and completely unknown. After obtaining attribute weights, we develop a new method to solve intuitionistic fuzzy MADM problems. An example is employed to show the effectiveness of the new MADM method.

In this paper, firstly we discuss some entropy measures for the interval-valued intuitionistic fuzzy sets (IvIFSs). Then we extend the knowledge measure for the intuitionistic fuzzy sets (IFSs) to propose a new interval-valued knowledge measure for the IvIFSs. Based on the proposed knowledge measure we construct a new interval-valued information entropy measure for IvIFSs, which is an extended notion of the entropy measures for IFSs. The proposed knowledge measure is defined as an interval of amounts of knowledge measured on an IvIFS, related to the uncertain information in terms of interval membership degree and interval non-membership degree. In comparison with other existing measures, it seems to be simpler and more intuitively appealing. Several illustrative examples are performed to demonstrate the effectiveness and practicality of the proposed method in handling with the increasing complexity of the decision making problems. [ABSTRACT FROM AUTHOR]

The aim of this study is to propose an objective method for determining weights of criteria (also called attributes) based on a new measure of intuitionistic fuzzy information, called knowledge measure, in a real-world multi-criteria decision-making problem under intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. To address this issue, we first analyze the existing entropy measures and show that their use in objective weight determination process may lead us to produce unreliable weights of criteria by citing appropriate examples. Then we analyze important properties of knowledge measure of intuitionistic fuzzy set (IFS) and also define knowledge measure for interval-valued intuitionistic fuzzy set. Then a new method to determine the weights of criteria is developed on the basis of knowledge measure where information about criteria weights is completely unknown and partly known. A real-life example is presented to illustrate the proposed weight determination method and a comparative analysis is carried out to indicate the practicality and effectiveness of knowledge-based weight-generation method under both intuitionistic fuzzy and interval-valued intuitionistic fuzzy environment. Finally, we formulate the axioms for knowledge measure associated with IFSs and we also propose families (classes) of knowledge measures. [ABSTRACT FROM AUTHOR]

Objective: To develop a psychometrically sound tool for measuring the knowledge of nursing and care staff about the experience, assessment and management of pain in older people (including people with dementia) for use in the residential aged care setting.Methods: The Pain in Older Adults Knowledge Survey (POAKS) was developed and tested in two phases. Phase 1 involved developing an initial item pool with good content validity based on a review of the research literature and a modified Delphi technique involving national and international experts. A pool of 24 items was developed for testing. Initial testing of the psychometric properties of the POAKS with 30 university employees led to refinement and final wording of items. Phase 2 involved testing of the psychometric properties of the POAKS with 279 respondents, including first year (n = 176) and third year (n = 70) nursing students and staff in a residential aged care service (n = 33).Results: Results established the content validity and internal consistency of the POAKS and supported its use as an instrument to measure nursing staff knowledge about the experience, assessment and management of pain in older people.Conclusions: The POAKS will enable residential aged care facilities to measure the level of knowledge among nursing and care staff about pain in older people (including people with dementia). The measure provides a basis for the development and implementation of educational interventions to address knowledge gaps that may impact on the quality of care provided. [ABSTRACT FROM AUTHOR]

Since introduced by K. Atanassov as a generalization of fuzzy sets, intuitionistic fuzzy sets (IFSs) have been investigated by many researchers and applied in many different areas, e.g. for solving multi-attribute group decision-making. It is important to find an appropriately reliable measure in order to differentiate IFSs in comparison or ranking order. Although there exist several measures, many unreasonable cases can be made by such measures. This paper introduces a new measure of amount of knowledge related to information provided in terms of IFSs. The new measure takes into account relationship between membership and non-membership degrees and hesitancy for a lack of information, making it capable to measure both degree of fuzziness and intuitionism of IFSs simultaneously. First we present a new knowledge measure for IFSs and prove some properties of the proposed measure. Based on the proposed knowledge measure we construct a new entropy measure for IFSs, a new similarity measure between IFSs and prove some properties of them. Then we use some examples to illustrate that the proposed measures, though simple in concept and calculus, can overcome the drawbacks of the existing measures. Finally, we apply the proposed knowledge measure for IFSs to deal with the multiple attribute group decision making problem. [ABSTRACT FROM AUTHOR]