General Score Function Research Articles

New intuitionistic fuzzy parametric divergence measures and score function-based CoCoSo method for decision-making problems

The present study introduces a decision-making approach with the combined compromise solution (CoCoSo) under intuitionistic fuzzy sets (IFSs) named as the IF-CoCoSo method based on proposed divergence measures and score function. The aim of the presented approach is to obtain an effective solution for multi-criteria decision-making problems on IFSs context. In this line, a new procedure is presented to derive the criteria weights using generalized score function and parametric divergence measures of IFSs. To compute the criteria weight, a generalized score function and parametric divergence measures are developed on IFSs and discussed some interesting properties. Further, the presented approach is applied to rank and evaluate the therapies for medical decision making problems, which demonstrates its applicability and feasibility. Finally, comparative and sensitivity analyses are discussed for validating the developed method.

An Application of the Pythagorean Fuzzy Sets in the Fault Diagnosis

Abstract In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic fuzzy set, and its extensions have been conducted to show their limitations and defects. Then, a novel similarity measure based on the generalized score function has been introduced that incorporates the significance (importance) of information, making it more intuitive to compare them. The proposed method is employed for the fault diagnosis of steam turbine generator unit under Pythagorean fuzzy environment. Ten fault types of rotating machines are established as failure patterns in nine different vibration frequency ranges, expressed in terms of Pythagorean fuzzy numbers. The superiority of the proposed method in dealing with uncertain and vague information is shown by comparing it with some existing measures in numerical examples.

ProBiS-Dock: A Hybrid Multitemplate Homology Flexible Docking Algorithm Enabled by Protein Binding Site Comparison.

The protein data bank (PDB) is a rich source of protein ligand structures, but ligands are not explicitly used in current docking algorithms. We have developed ProBiS-Dock, a docking algorithm complementary to the ProBiS-Dock Database (J. Chem. Inf. Model. 2021, 61, 4097-4107) that treats small molecules and proteins as fully flexible entities and allows conformational changes in both after ligand binding. A new scoring function is described that consists of a binding site-specific scoring function (ProBiS-Score) and a general statistical scoring function. ProBiS-Dock enables rapid docking of small molecules to proteins and has been successfully validated in silico against standard benchmarks. It enables rapid search for new active ligands by leveraging existing knowledge in the PDB. The potential of the software for drug development has been confirmed in vitro by the discovery of new inhibitors of human indoleamine 2,3-dioxygenase 1, an enzyme that is an attractive target for cancer therapy and catalyzes the first rate-determining step of l-tryptophan metabolism via the kynurenine pathway. The software is freely available to academic users at http://insilab.org/probisdock.

Fermatean fuzzy CRITIC-EDAS approach for the selection of sustainable third-party reverse logistics providers using improved generalized score function.

In today’s world, the demand for sustainable third-party reverse logistics providers (S3PRLPs) becomes an increasingly considerable issue for industries seeking improved customer service, cost reduction and sustainability perspectives. However, the assessment and selection of right S3PRLP is a complex uncertain decision-making problem due to involvement of numerous conflicting attributes, imprecise human mind and lack of information. Recently, Fermatean fuzzy set (FFS) has been recognized as one of the suitable tools to tackle the uncertain and inaccurate information. In this paper, we introduce a hybrid methodology based on CRITIC and EDAS methods with Fermatean fuzzy sets (FFSs) to solve the S3PRLP selection problem in which the attributes and decision makers’ weights are completely unknown. In this framework, CRITIC approach is applied to calculate the attribute weight and EDAS method is used to evaluate the priority order of S3PRLP options. To do this, a new improved generalized score function (IGSF) is developed with its elegant properties. Also, a formula is discussed to calculate the decision makers’ weights based on the developed IGSF. Next, developed framework is applied to assess a case study of S3PRLP selection problem with Fermatean fuzzy information, which elucidates the usefulness and practicality of the proposed method. Finally, comparative study is implemented to show the strength of introduced framework with extant approaches. The outcomes of the work confirm that the introduced approach is more feasible and well-consistent with the other extant approaches.

New machine learning and physics-based scoring functions for drug discovery

Scoring functions are essential for modern in silico drug discovery. However, the accurate prediction of binding affinity by scoring functions remains a challenging task. The performance of scoring functions is very heterogeneous across different target classes. Scoring functions based on precise physics-based descriptors better representing protein–ligand recognition process are strongly needed. We developed a set of new empirical scoring functions, named DockTScore, by explicitly accounting for physics-based terms combined with machine learning. Target-specific scoring functions were developed for two important drug targets, proteases and protein–protein interactions, representing an original class of molecules for drug discovery. Multiple linear regression (MLR), support vector machine and random forest algorithms were employed to derive general and target-specific scoring functions involving optimized MMFF94S force-field terms, solvation and lipophilic interactions terms, and an improved term accounting for ligand torsional entropy contribution to ligand binding. DockTScore scoring functions demonstrated to be competitive with the current best-evaluated scoring functions in terms of binding energy prediction and ranking on four DUD-E datasets and will be useful for in silico drug design for diverse proteins as well as for specific targets such as proteases and protein–protein interactions. Currently, the MLR DockTScore is available at www.dockthor.lncc.br.

A novel approach to multi‐attribute group decision making based on power neutrality aggregation operator for q ‐rung orthopair fuzzy sets

In this paper, based on power aggregation (PA) operators, neutrality average and neutrality geometric aggregation operators are proposed. Furthermore, a general score function for q-rung orthopair fuzzy sets (q-ROFSs) is proposed. PA can reduce the impact of excessively high or excessively low arguments. It also emphasizes the interrelationship between attributes on the decision matrix. PA and neutrality aggregations (NAs) were hybrid with more fair and neutral decisions of the DMs evaluations. Also, neutrality aggregation operator provides reliable results by taking into account neutrality among decision-makers. On the one hand, through its dynamic structure, q-ROFSs provide a wider evaluation for decision-makers (DMs). q-ROFSs include many fuzzy sets with varying q ≥ 1 parameters. One of the most important parts of multi-attribute group decision-making problems is that DMs do not take into account their bias. On the other hand, the NA operator evaluates the decisions of the DMs from a neutral attitude perspective. The power neutrality aggregation operator proposed in this study produces more objective results. The proposed operator is more consistent with the advantages of both operators and it deals with the attitude of DMs more objectively. Validity tests are applied to the proposed methods. Also, the superior aspects of the proposed methods are demonstrated by numerical examples. As a result of validity tests and comparisons with other studies in the literature, it is seen that the proposed methods give effective results.

The impact of cataract surgery upon visual acuity and quality of life in patients with cataract in Tripura

Background: The major cause of blindness in India is cataract. Blindness leads to poverty due to reduced productive activity and this leads to reduced quality of life. This study was aimed at evaluating the visual acuity (VA) change pre and post cataract surgery, the post-surgical quality of life (QOL) outcomes and level of satisfaction estimation.Methods: This was a cross sectional, hospital based study carried out in a tertiary care centre in Tripura. It included 200 patients over a period of 1.5 years to compare the VA, QOL, psychosocial status and satisfaction level pre and post cataract surgery. Indian vision function questionnaire 33 (INDVFQ33) was used to assess QOL.Results: Out of 200 patients, in 53% preoperative VA ranged from >20/400 - <20/200 while in 5% patients it was only perception of light. Postoperatively 80% of the patient achieved best corrected VA (BCVA) of 20/30 or better, 18% patient attained BCVA ranging from 20/40 to 20/60. Only 2% had a BCVA of 20/60 or worst. QOL parameters like mean pre and post -operative general function score, psychosocial scale and visual function scale showed improvement following cataract surgery. 69% of the patients were satisfied with the cataract surgery, whereas 31% were not completely satisfied.Conclusions: The study revealed that there was a marked improvement in VA post cataract surgery and it also influenced the QOL in all scales.

A Neutrosophic VIKOR Method-Based Decision-Making with an Improved Distance Measure and Score Function: Case Study of Selection for Renewable Energy Alternatives

In this study, a new score and distance function which provides more accurate results than the studies in the literature and considers the decision maker’s cognition has been proposed. In order to show the effects of the new score function coefficients on neutrosophic numbers, a new representation named “4D Plot” has been proposed. VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje which means multicriteria optimization and compromise solution in Serbian) method, which is based on the creation of a conciliatory solution within the framework of alternatives and evaluation criteria, provides highly effective results in multiple criteria decision-making problems. Neutrosophic numbers play an active role in facilitating the decision-making process in many studies. In this context, extension of the classical VIKOR method is introduced in detail in this study. The framework of the extended neutrosophic VIKOR method has been established. The proposed method has been applied to the renewable energy alternative selection problem in Turkey and compared with different methods and different scenarios. It has been shown that the proposed method gives more effective and accurate results. Furthermore, the sensitivity and accuracy of the study are enhanced by a sensitivity analysis. We have extended the classical VIKOR method for SVN numbers with a newly generalized score function and a distance measure. As a novel and newly presentation named “The 4D Plot” has been developed and applied in this paper to SVN numbers for presenting the effect of the new score function. The renewable energy alternative selection was made in Turkey with the proposed method by the opinions of the experts and the ranking of the alternatives was obtained. A sensitivity analysis has been made to show the accuracy and validity of the study. With the proposed distance measure and score function, it is shown that more accurate results can be found in multiple criteria decision-making problems. The model will provide solutions for many soft computing problems such as engineering and economy by finding more effective and accurate results in the neutrosophic number space according to the preference of decision makers. As a future work, the presented functions and framework can be adapted to different MCDM problems.

Local Whittle likelihood approach for generalized divergence

AbstractThere are many approaches in the estimation of spectral density. With regard to parametric approaches, different divergences are proposed in fitting a certain parametric family of spectral densities. Moreover, nonparametric approaches are also quite common considering the situation when we cannot specify the model of process. In this paper, we develop a local Whittle likelihood approach based on a general score function, with some special cases of which, the approach applies to more applications. This paper highlights the effective asymptotics of our general local Whittle estimator, and presents a comparison with other estimators. Additionally, for a special case, we construct the one‐step ahead predictor based on the form of the score function. Subsequently, we show that it has a smaller prediction error than the classical exponentially weighted linear predictor. The provided numerical studies show some interesting features of our local Whittle estimator.

Novel Parameterized Score Functions on Interval-Valued Intuitionistic Fuzzy Sets With Three Fuzziness Measure Indexes and Their Application

To explore the essential law of fuzziness of interval-valued intuitionistic fuzzy sets (IVIFSs), the entropy brought by interval values is studied. Moreover, together with classical score and accuracy functions, a series of novel parameterized generalized score functions on IVIFSs are proposed. First, the information that IVIFSs load is divided into three parts, where one part is the normalized score value, the second one is the classical accuracy value, and the third one is the newly proposed entropy value which originate from interval values. Second, by using the proposed entropy function and the other two parameter functions, a series of novel generalized score functions for IVIFSs are introduced. Furthermore, some properties on these proposed functions are explored. The main technological innovation of this paper is to express the relationship between the generalized score function and the three parameters introduced by using trigonometric functions. The main characteristic of this paper is that smaller the entropy value of IVIFN, the bigger is the generalized score function value. Finally, an example illustrates that the newly proposed generalized parameterized score functions deal with decision-making information in more detail, where a variety of decision-making plans can be provided for the decision makers. Therefore, the decision-making results obtained by the proposed generalized score functions are more expected.

Uncertainty learning of rough set-based prediction under a holistic framework

Uncertainty learning is an important research direction of rough set theory, wherein the most popular one is rough set-based prediction, whose goal is to extract decision rules from decision systems and then assign the corresponding decision labels for new samples in terms of the decision rules. To design efficient prediction algorithms, it is necessary and meaningful to measure the uncertainty of rough set-based prediction, especially the stability and generalization performance. In this paper, we analyze the generalization performance of rough set-based prediction algorithms in terms of algorithmic stability analysis and give the generalization error bounds. Firstly, we propose a general rough set-based prediction algorithm to predict the labels for new samples, and then define a scoring function and the corresponding loss function. Secondly, we define two kinds of algorithmic stability for this prediction algorithm in terms of their loss functions, by which two general generalization error bounds are obtained according to two different kinds of stability: strong stability and pointwise hypothesis stability. The bounds numerically imply the performance of the proposed rough set-based prediction algorithm is related to the number of samples and stability parameter. Thirdly, we adopt the confidence and max confidence, min support algorithms as the specific scoring functions instead of general scoring functions. The results show the prediction performance of the confidence algorithm is related to the number of samples and stability parameter, as well as that of max confidence, min support algorithm is associated with the number of samples and minimum support threshold. Based on these discussions, a general framework of stability and generalization error bounds analysis for rough set-based prediction is established. Finally, several experiments are performed to test the previous conclusions.

Generalized score functions on interval-valued intuitionistic fuzzy sets with preference parameters for different types of decision makers and their application

In this paper, the interval-valued intuitionistic fuzzy sets (IVIFSs) are studied from the viewpoint of the decision makers’ preference. Firstly, two series of principles are proposed to guide the ranking of interval-valued intuitionistic fuzzy numbers (IVIFNs), and two kinds of illustrative generalized score functions on IVIFSs are proposed according to the newly proposed principles. Secondly, two kinds of generalized score functions on IVIFSs are proposed based on decision-makers’ preference. The two generalized score functions are both of two parameters, which represent the decision makers’ attitudinal characters on the classical score values and the classical accuracy values on IVIFNs, respectively. Thirdly, two kinds of generalized score functions on IVIFSs, which are suitable for ranking IVIFNs when there is no information about the importance weights of the classical score values and accuracy values on IVIFNs, are proposed based on integral. Fourthly, three kinds of multi-criteria decision-making (MCDM) methods in interval-valued intuitionistic fuzzy setting are proposed. Finally, an example shows that when a novel generalized score function on IVIFSs is proposed, its suitable application environments should also be pointed out.

Abrupt change in mean using block bootstrap and avoiding variance estimation

We deal with sequences of weakly dependent observations that are naturally ordered in time. Their constant mean is possibly subject to change at most once at some unknown time point. The aim is to test whether such an unknown change has occurred or not. The change point methods presented here rely on ratio type test statistics based on maxima of the cumulative sums. These detection procedures for the abrupt change in mean are also robustified by considering a general score function. The main advantage of the proposed approach is that the variance of the observations neither has to be known nor estimated. The asymptotic distribution of the test statistic under the no change null hypothesis is derived. Moreover, we prove the consistency of the test under the alternatives. A block bootstrap method is developed in order to obtain better approximations for the test’s critical values. The validity of the bootstrap algorithm is shown. The results are illustrated through a simulation study, which demonstrates computational efficiency of the procedures. A practical application to real data is presented as well.

Conjugate Representations and Characterizing Escort Expectations in Information Geometry

Based on the maximum entropy (MaxEnt) principle for a generalized entropy functional and the conjugate representations introduced by Zhang, we have reformulated the method of information geometry. For a set of conjugate representations, the associated escort expectation is naturally introduced and characterized by the generalized score function which has zero-escort expectation. Furthermore, we show that the escort expectation induces a conformal divergence.

Commentary on “A new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems” [Appl. Soft Comput., 2016(38) 988–999

This commentary points out the major mistakes in “a new generalized improved score function of interval-valued intuitionistic fuzzy sets and applications in expert systems”, which were initially proposed by Garg [Appl. Soft Comput., 2016(38) 988–999]. Firstly, some related basic mathematical symbols are introduced. Secondly, Garg's research results are reviewed. Subsequently, the errors of the generalized weighted averaging operators and the restrictiveness of the generalized score function proposed by Garg are discussed by using four counter-cases. Thereafter, the sources that lead to the errors of the operators and the restrictiveness of the score function are revealed. Finally, this commentary also points out some typo-grammatical errors in the commented paper.

Evaluating competing theories via a common language of qualitative verdicts

Kuhn (The essential tension—Selected studies in scientific tradition and change, 1977) claimed that several algorithms can be defended to select the best theory based on epistemic values such as simplicity, accuracy, and fruitfulness. In a recent paper, Okasha (Mind 129(477):83–115, 2011) argued that no theory choice algorithm exists which satisfies a set of intuitively compelling conditions that Arrow (Social choice and individual values, 1963) had proposed for a consistent aggregation of individual preference orderings. In this paper, we put forward a solution to avoid this impossibility result. Based on previous work by Gaertner and Xu (Mathematical Social Sciences 63:193–196, 2012), we suggest to view the theory choice problem in a cardinal context and to use a general scoring function defined over a set of qualitative verdicts for every epistemic value. This aggregation method yields a complete and transitive ranking and the rule satisfies all Arrovian conditions appropriately reformulated within a cardinal setting. We also propose methods that capture the aggregation across different scientists.

Evaluating the potential of halogen bonding in molecular design: automated scaffold decoration using the new scoring function XBScore.

We present a QM-derived empirical scoring function for the interaction between aromatic halogenated ligands and the carbonyl oxygen atom of the protein backbone. Applying this scoring function, we developed an algorithm that evaluates the potential of protein-bound ligands to form favorable halogen-bonding contacts upon scaffold decoration with chlorine, bromine, or iodine. Full recovery of all existing halogen bonds in the PDB involving the protein backbone was achieved with our protocol. Interestingly, the potential for introducing halogen bonds through scaffold decoration of unsubstituted aromatic carbon atoms appears to easily match the number of previously known halogen bonds. Our approach can thus be used as a blueprint for integration of halogen bonding into general empirical scoring functions, which at present ignore this interaction. Most importantly, we were able to identify a substantial number of protein-ligand complexes where the benefits and challenges of introducing a halogen bond by molecular design can be studied experimentally.

Validated scoring of halogen bonding in molecular design.

As a rather new type of non-covalent interaction, halogen bonding is slowly being integrated into molecular modeling and the drug design process. Aromatic halogenated molecules can theoretically form halogen bonds with any electron donor. Based on quantum chemical calculations, we evaluated the interaction energies between several halobenzenes and the oxygen of N-methylacetamide, representing the carbonyl-function of the protein backbone [1,2]. In a ligand-protein complex very rarely optimal interaction geometries are observed. In order to assess all spatial dependencies of the halogen bond with regards to deviations from optimal geometries, our calculations include variations in distance, bond angles and spherical orientation. On this basis we developed a tool for scaffold decoration applicable to any crystal structure or docking result [3]. For every unsubstituted aromatic atom in a ligand the tool determines whether halogenation leads to a favorable halogen bonding interaction with the binding site. A scoring function, derived from a myriad of QM-calculations on the MP2 TZVPP-level of theory, evaluates the quality of the assumed interaction. To assess the prediction accuracy of our scoring function, we initially chose 50 examples from an exhaustive PDB scan randomly, representing the full range of equally distributed halogen bonding scores. For each file, the geometry was then recreated using iodobenzene representing the ligand system and N-methylacetamide as the backbone structure. Thus, the halogen bonding geometry of the database example was transferred as accurately as possible to our small model system and the interaction was calculated as an MP2 single point. The resulting energy was normalized and plotted against the predicted halogen bonding score. With only a few exceptions, most deviations were below 10% leading to an overall r² of 0.87. This highlights that our present scoring function is a blueprint for integration into general empirical scoring functions, which at present ignore halogen bonding interactions. Hence, recognition of halogen bonding will be implemented soon into protein-ligand docking and scoring. Figure 1

The Multi-Criteria Negotiation Analysis Based on the Membership Function

Abstract In this paper we propose a multi-criteria model based on the fuzzy preferences approach which can be implemented in the prenegotiation phase to evaluate the negotiations packages. The applicability of some multi-criteria ranking methods were discussed for building a scoring function for negotiation packages. The first one is Simple Additive Weighting (SAW) technique which determines the sum of the partial satisfactions from each negotiation issue and aggregate them using the issue weights. The other one is Distance Based Methods (DBM), with its extension based on the distances to ideal or anti-ideal package, i.e. the TOPSIS procedure. In our approach the negotiator's preferences over the issues are represented by fuzzy membership functions and next a selected multi-criteria decision making method is adopted to determine the global rating of each package. The membership functions are used here as the equivalents of utility functions spread over the negotiation issues, which let us compare different type of data. One of the key advantages of the approach proposed is its usefulness for building a general scoring function in the ill-structured negotiation problem, namely the situation in which the problem itself as well as the negotiators preferences cannot be precisely defined, the available information is uncertain, subjective and vague. Secondly, all proposed variants of scoring functions produce consistent rankings, even though the new packages are added (or removed) and do not result in rank reversal.

McGenus: a Monte Carlo algorithm to predict RNA secondary structures with pseudoknots

We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non-trivial pseudoknot topologies. Specifically, McGenus uses a Monte Carlo algorithm with replica exchange for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web server at http://ipht.cea.fr/rna/mcgenus.php.