Search

The three-way decision paradigm is a decision-making approach that is analogous to human reasoning. It involves a neutrosophic set as an efficient tool for handling ambiguity. Using cotangent similarity, the Hamming distance, and the innovative Vicis-Wave Hedges distance for ranking, this study proposes three novel three-way decision models based on the Bayes decision. In particular, single-valued neutrosophic numbers are employed to represent each loss function. The proposed models are then condensed into an algorithm. Subsequently, an example is presented to demonstrate the validity and rationality of the proposed models. Finally, we compare the three models. This research provides a new method for decision-making problems. [ABSTRACT FROM AUTHOR]

We introduce and investigate neutrosophic soft contra e-continuous maps and contra e-irresolute maps in neutrosophic soft topological spaces with examples. Also, neutrosophic soft contra econtinuous maps are compared with neutrosophic soft continuous maps, d-continuous maps, d-semi continuous maps, d-pre continuous maps and e* continuous maps in neutrosophic soft topological spaces. We derive some useful results and properties related to them. An application in decision making problem using distance measure is given. An example of a candidate selection from a company interview is formulated as neutrosophic soft model problem and the hamming distance measure is applied to calculate the distance between the interview candidates and the ideal candidate. The candidate having less distance with the ideal solution is the desirable candidate. [ABSTRACT FROM AUTHOR]

In this article, we discuss a few fresh approaches to the spherical vague normal set (SVNS) approach to multiple attribute decision‐making (MADM) problems. A new generalization of the vague set (VS) and the spherical interval valued fuzzy set (SIVFS) is the spherical vague set (SVS). The spherical vague number (SVN) concepts consolidate normal fuzzy number (NFN) and we defined the spherical vague normal number (SVNN) and some of its intriguing fundamental operations. The purpose of this article is to discuss a novel idea of spherical vague normal weighted averaging (SVNWA), spherical vague normal weighted geometric (SVNWG), generalized spherical vague normal weighted averaging (GSVNWA) and generalized spherical vague normal weighted geometric (GSVNWG) operators. We talked about a flowchart with an algorithm that uses this operators and the MADM approach. With the help of a numerical example, we interact the extended euclidean and hamming distance measures. In this communication, it is also important to elaborate on some key SVN approach characteristics based on various algebraic operations, such as idempotency, boundedness, commutativity, and monotonicity. They are quicker to find the best option, more straightforward and practical. Think about five farmers. The four factors that are taken into account for each of the five farmers are climate, water, soil, disease, and flood, and their corresponding weights are displayed. We want to select the best option from a large number of choices by comparing expert assessments with the criteria. As a result, the conclusions of the defined models are more precise and closely related to Θ. We contrast some of the current models with the ones that have been proposed in order to demonstrate the dependability and utility of the models under investigation. The study's findings are also intriguing and fascinating. [ABSTRACT FROM AUTHOR]

Everything in the world almost resembles each other which could find out with the help of some measures. Similarity measure (SM) is one of them that play a dominant role in decision-making (D M g ). The higher the value of the SM, the more the things will match perfectly. Weights of criteria appear to specify that the decision-makers (DMs) recognize the significance of public views and their influence on reaching an ideal solution. Sometimes DMs hesitate or they are uncertain to assign the weights to the criteria because of their similar nature. Linear programming (LP) technique has been implemented to evaluate the weights of criteria to reduce the complexity of DMs so that they can avoid biasedness. An extension of fuzzy sets (FSs) named dual hesitant fuzzy sets (DHFSs) is utilized to handle ambiguous and uncertain information. Based on the Hausdorff metric and the Hamming distance, SM is developed to establish the multiple criteria decision-making (MCDM) approach to resolve the problems. Moreover, based on the proposed SM, the technique for order of preference similar to the ideal solution (TOPSIS) is extended to strengthen the obtained outcomes. The effectiveness of the suggested approach is validated by considering a practical example. To support the outcomes obtained by using the proposed model, sensitivity analysis (SA) and time complexity (TC) analysis have been performed. A comprehensive comparison with other techniques is performed to validate the proposed MCDM model. [ABSTRACT FROM AUTHOR]

Multi-attribute group decision making is widely used in the real world, and many scholars have done a lot of research on it. The public's focus on emergencies can provide an important reference for emergency handling decision making in the social media big data environment. Due to the complexity of emergency handling decision making, the asymmetry of user evaluation information is easy to cause the loss of important information. It is very important to mine valuable information for decision making through online reviews. Then, a generalized extended hybrid distance measure method between the probabilistic linguistic term sets is proposed. Based on this, an extended GDMD-PROMETHEE large-scale multi-attribute group decision-making method is proposed as well, which can be used to decision making under symmetric information and asymmetric information. Firstly, web crawler technology is used to explore the topics of public concern of emergency handling on social media platforms, and use k -means cluster analysis to classify the crawling variables, then the attributes and subjective weights of emergency handling plans are obtained by TF-IDF and Word2vec technology. Secondly, in order to better retain the linguistic evaluation information from decision-makers, a new generalized probabilistic hybrid distance measure method based on Hamming distance is proposed. Considering the difference of decision makers' evaluation, the objective weight of decision makers is calculated by combining the maximum deviation method with the new extended hybrid Euclidean distance. On this basis, the comprehensive weights of the attributes are calculated by combining subjective and objective factors. Meanwhile, this paper realizes the distance measures and information fusion of probabilistic linguistic term sets under cumulative prospect theory, and the ranking results of the emergency handling plans based on the extended GDMD-PROMETHEE algorithm are given. Finally, the feasibility and effectiveness of the extended GDMD-PROMETHEE algorithm are verified by the case study of the explosion accident handling decision making of Shanghai "6.18" Petrochemical, and the comparative analyses between the several traditional algorithms demonstrate the extended GDMD-PROMETHEE algorithm is more scientific and superior in this paper. [ABSTRACT FROM AUTHOR]

With regard to the interval number-based uncertain multi-attribute decision making problem, in which the attribute weights are unknown and there is no preference on decision-making alternative objects, this paper presents a new decision-making approach. In this method, Hamming distance firstly is used to define the Hamming similarity degree of normative interval numbers, and the Hamming similarity degree of decision-making alternative objects, and then the Hamming similarity superiority relation theory to the comparison of interval numbers is proposed and some relevant results are obtained. Thus, by drawing on the idea of deviations maximization, an interval number-based decision-making object Hamming similarity programming model (IN-DMOHSPM) is established to calculate and solve the weight vector of attributes. Next, all of the selected alternative objects set is screened and sorted by using the overall Hamming similarity degree of each decision-making object compared with the ideal optimal object, and a new algorithm of Hamming similarity programming model for interval number-based multiple attribute decision-making objects is presented. Finally, the feasibility and utility of this model used in this paper are demonstrated by a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, we present novel approaches to multi-attribute decision-making problems using q -rung normal fuzzy numbers. The q -rung normal fuzzy sets are an important way to express uncertain information, and they are superior to the intuitionistic fuzzy sets, Pythagorean fuzzy sets and normal Pythagorean fuzzy sets. A combination of the q -rung fuzzy number and the normal fuzzy number becomes q -rung normal fuzzy numbers. The new averaging and geometric operations of q -rung normal fuzzy numbers are studied using the general aggregation function. There are both commutative, associative, idempotent and boundedness compatible using q -rung normal fuzzy numbers. There are four new aggregating operators presented such as q -rung normal fuzzy interaction weighted averaging, q -rung normal fuzzy interaction weighted geometric, q -rung generalized normal fuzzy interaction weighted averaging and q -rung generalized normal fuzzy interaction weighted geometric. Usually, the aggregation functions are taken to be the Euclidean distance and Hamming distance. The existence of these operators enables the development of algorithms that solve multi-attribute decision-making problems. We demonstrate the application of enhanced Euclidean and Hamming distances to problems arising in real-world situations. An important component of a robot sensor is computer science and machine tool technology. There are four factors that can be used to evaluate robotics systems: resolution, sensitivity, error and accuracy. In order to determine the best alternative, expert opinions should be compared to the criteria. The accuracy of these models is better and they are closer to q. Finally, we used some practical examples to illustrate the validity and superiority of the proposed method by comparing with other existing methods. [ABSTRACT FROM AUTHOR]

In this paper, considering the traditional geometric operation laws and Pythagorean fuzzy information, a varies of new distance measures of Pythagorean fuzzy set are proposed, such as generalized Pythagorean fuzzy ordered geometric distance (GPFOWGD) measures and generalized Pythagorean fuzzy hybrid weighted geometric distance (GPFHWGD) measures. Besides, some special issues including Hamming distance, Euclidean distance and Hausdorff distance of these raised geometric distance measures are investigated. To testify the valid of these new presented distance measures, a decision-making model is built and illustrated by a mathematical calculation example to evaluate the service quality of sports clubs using Pythagorean fuzzy information. The results display that the approach is uncomplicated, valid and simple to compute. The example illustrates that the method presented in the paper can be used to deal with problems of uncertainty such as dynamic multiple attribute decision making. [ABSTRACT FROM AUTHOR]

The idea of an interval complex neutrosophic soft set (I-CNSS) emerges from the interval neutrosophic soft set (I-NSS) by the extension of its three membership functions (T, I, F) from real space to complex space (unit disc) to better handle uncertainties, vagueness, indeterminacy, and imprecision of information in the periodic nature. The novelty of I-CNSS lies in its more significant range of activity compared to CNS. Measures of similarity and distance are important tools that can be used to solve many problems in real life. Hence, this paper presents some interval complex neutrosophic soft similarities based on Hamming and Euclidean distances of I-CNSSs to deal with real-life problems that include uncertain information such as decision-making issues and medical diagnosis stats. Firstly, this paper reviews the definition of an interval complex neutrosophic soft set. Secondly, we defined distance Hamming measures and distance Euclidean measures on I-CNSSs. Next, the axiomatic definition of similarity measures based on Hamming and Euclidean distances of I-CNSSs is proposed. Moreover, a numerical example is given and relations between these measures are introduced and verified. Meanwhile, some applications are given to show how similarity can be used to help the user in making decisions and making medical diagnoses. Finally, a comparison of some current approaches is used to back up this study. [ABSTRACT FROM AUTHOR]

Generalized hesitant fuzzy numbers (GHFNs) are able to directly manage situations in which we may encounter a finite set of known values with a finite set of degrees of doubt as quantitative approximations of an uncertain situation/quantification of a linguistic expression. They are new extensions of hesitant fuzzy sets, which have been considered in this paper. In fact, in this paper, GHFNs will be utilized to model the uncertainty of the assessment values of options against criteria in multi-attribute decision making (MADM) problems. It means that all of the elements of decision matrix are GHFNs. Then, the technique for order of preference by similarity to ideal solution (TOPSIS) method, as a very successful method in solving MADM problems, will be updated to be used with GHFNs. To this end, the distance between GHFNs must be defined to obtain the distances between given alternatives from each of two subjective alternatives (positive/negative ideal solutions). Thus, three existing famous distance measures, i.e., general distance ( d g ), Hamming distance ( d h ), and Euclidean distance ( d e ) measures, have been updated for GHFNs firstly. Then, the new TOPSIS method will be proposed based on GHFNs. Finally, the numerical examples have been appointed to illustrate the proposed method, analyze comparatively and validate it. [ABSTRACT FROM AUTHOR]

Fuzzy parameterized fuzzy soft matrices (fpfs-matrices) which can model problems involving fuzzy objects and parameters are one of the mathematical tools used to deal with decision-making problems. To utilize soft decision-making methods via fpfs-matrices in machine learning is likely to draw much scholarly attention. In this paper, we propose Comparison Matrix-Based Fuzzy Parameterized Fuzzy Soft Classifier (FPFS-CMC) in order to transfer modeling success of fpfs-matrices to machine learning. We then compare FPFS-CMC with Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy k-Nearest Neighbor (Fuzzy kNN) in consideration of accuracy, precision, recall, macro-F-score, and micro-F-score performance metrics, and 15 datasets in UCI Machine Learning Repository. Besides, we compare the proposed classifier with the state-of-the-art Support Vector Machine (SVM), Decision Tree (DT), and Adaptive Boosting (AdaBoost) in terms of five performance metrics herein. Afterward, the results from the experiments are analyzed by employing the Friedman and Nemenyi tests to assess the statistical significance of the differences in performances. Both experimental and statistical results show that FPFS-CMC outperforms the others. Finally, we provide the conclusive remarks and some suggestions for further research. [ABSTRACT FROM AUTHOR]

Atanassov's intuitionistic fuzzy sets play a vital role in handling vagueness and uncertainty successfully as they associate an additional non-membership degree to each element of the universal set. Interval-valued intuitionistic fuzzy (IVIF) sets are more generalized quantities in this direction as they use intervals (⊂ [ 0 , 1 ]) to define the membership and non-membership grades of each element of the set. However, without defining basic arithmetic operations on the IVIF values/sets, the study is incomplete. This paper broadly examines the division and subtraction operations over any arbitrary IVIF values/sets using the concept of Hamming distance between them. A deterministic linear optimization model is proposed and solved in order to obtain the complete expressions for these operations. Next, various fundamental properties and relationships are examined and proved for the proposed arithmetic operations over IVIF values/sets. Furthermore, an example of a multi-criteria decision-making problem under uncertain conditions is studied and analyzed using the developed arithmetic operations on IVIF numbers. • Derived the generalized subtraction and division operations for IVIF values/sets. • The notion of Hamming distance and dual-simplex algorithm are used. • A deterministic LPP is proposed to obtain the expressions for the operations. • The fundamental properties and relationships for the basic operations are explored. • A case study of multi-criteria decision-making problems has been discussed. [ABSTRACT FROM AUTHOR]

Intuitionistic fuzzy (IF) theory has become main approach to representing imprecision and vagueness. The IF divergence measure (IFDivM) based on Jensen–Shannon divergence is perhaps the most widely used measure to compare the similarity of multiple intuitionistic fuzzy sets (IFSs). In the present paper, this IFDivM is examined and applied to multiple examples. It is found that some extant IFDivMs hardly satisfy the axiomatic definition, and in a few cases even unable to show divergence of trivial IFSs. To address these inconsistencies, a new IFDivM based on Jensen–Shannon divergence is proposed, free from these problems. The effectiveness of the proposed IFDivM is tested on several critical cases, and precise analysis of its properties is performed. It is proved that the proposed IFDivM satisfies the axiomatic definition of IFDivMs. To illustrate the practical significance of the IFDivM, a novel intuitionistic fuzzy (IF) TODIM method, based on the proposed IFDivM, is developed, termed as GIF-TODIM method. Unlike the existing IF-TODIM methods, GIF-TODIM does not suffer from the revere ordering inconsistencies. The proposed GIF-TODIM method and the proposed IFDivM are applied to a real-world case study on supplier selection. A detailed comparative analysis is performed taking the TOPSIS method and other IFDivMs as baselines. The role of attitude on the final choice is analyzed in great detail. It is found that the proposed GIF-TODIM method is indeed useful, effective, and superior to the counterpart methods, when it comes to real-world situations. Concomitantly, in the present work, it is also revealed that the TOPSIS method based on the 2-D Hamming distance is a special form of the proposed GIF-TODIM method, when decision-makers have the same attitude towards losses and gains. Thus, an interesting relationship between TOPSIS and TODIM is identified under the intuitionistic fuzzy environment, which is bound to propel significant research in the area of decision making under uncertain conditions. As a whole, the article offers comprehensive analyses of IFDivMs and the TODIM method under the intuitionistic fuzzy environment. • Construct a new IF divergence measure (IFDivM) based on Jensen–Shannon divergence. • Develop a GIF-TODIM method based on the new IFDivM. • Apply the proposed GIF-TODIM method to a supplier selection problem. • Provide parameter analysis and comparative analysis with TOPSIS and other IFDivMs. • Show that TOPSIS based on 2-D Hamming distance is a special form of our GIF-TODIM. [ABSTRACT FROM AUTHOR]

The objective of this paper is to develop Pythagorean fuzzy (PF) multi‐objective optimization by ratio analysis (PF‐MOORA) plus full MULTIplicative form (PF‐MULTIMOORA) method for solving multicriteria decision making (MCDM) problems with completely unknown information of criteria weights. In the model formulation process, a new distance measure is defined to quantify the difference between PF sets by combining Hamming distance and Hausdorff metric. This distance measure is, subsequently, implemented in entropy weight model for determining unknown weights of criteria, and also in reference point approach for obtaining preference indices of alternatives. To overcome the deficiencies occurred in existing MULTIMOORA method, like multiple comparisons, circular reasoning, and so on, an aggregation‐based approach is recommended in the proposed PF‐MULTIMOORA. To demonstrate the feasibility and practicality of the proposed method, an example concerning strategy prioritization of a tiles manufacturing company is presented. In the strategy evaluation process, at first, the judgement values provided by the decision maker are expressed in linguistic terms, and then those are converted into PF numbers through a PF weighting scale. The sensitivity of the proposed model is validated by changing of weights of criteria which impact on the ranks of the strategies. To show robustness of the developed method, the result attained by applying PF‐MULTIMOORA is compared with existing techniques, not only in crisp and fuzzy quantitative strategic planning matrix context, but also using four other MCDM methods, namely, modified PF‐MOORA, as a particular case of the proposed PF‐MULTIMOORA technique, PF weighted sum, PF‐TOPSIS and PF‐VIKOR. [ABSTRACT FROM AUTHOR]

Multi-Criteria Decision Making (MCDM) aims to support decision-makers more effectively. This paper presents modifications for the criteria ranking methods, CRITIC and Distance-correlation CRITIC (D-CRITIC). These modifications involve the normalization procedure to silence criteria attribution by utilizing fuzzy logic and the hamming distance. Also, some adjustment to the weighting technique of the CRITIC method is done to capture linear and nonlinear correlations more precisely. These modifications that are applied to the CRITIC method by considering some reference point (RP), produced our proposed (M-CRITIC-RP) method. An illustrative example to rank performance criteria of display advertisement for a digital marketing campaign is used to demonstrate the method's workability. Comparative analysis with appropriate MCDM methods reveals that the distance correlation values for the weights of the M-CRITIC-RP and comparative methods exhibit higher consistency than those between other criteria ranking methods. Moreover, M-CRITIC-RP has a high average value of Spearman rank statistic, indicating high rank consistency. Regarding accuracy, the Symmetric Mean Absolute Percentage Error (sMAPE) and the Log Accuracy Ratio (LAR) error metrics show lower values for M-CRITIC-RP in comparison to the corresponding values of other criteria ranking methods. M-CRITIC-RP demonstrates sensitivity with changes in the number of alternatives and also to variations in the RPs. The results of the sensitivity analysis guide the analyst to pay ample attention when selecting the RP. Findings also suggest considering a sufficient sample size for better accuracy and consistency of weights and ranks. Several implications were discussed along with advantages and limitations to be addressed for future work. [ABSTRACT FROM AUTHOR]