Search results for: neutrosophic set

Authors: K. M. Alsager, N. O. Alshehri

Abstract:

In this paper, we proposed the notion of single valued neutrosophic hesitant fuzzy rough set, by combining single valued neutrosophic hesitant fuzzy set and rough set. The combination of single valued neutrosophic hesitant fuzzy set and rough set is a powerful tool for dealing with uncertainty, granularity and incompleteness of knowledge in information systems. We presented both definition and some basic properties of the proposed model. Finally, we gave a general approach which is applied to a decision making problem in disease diagnoses, and demonstrated the effectiveness of the approach by a numerical example.

Keywords: Single valued neutrosophic hesitant set, single valued neutrosophic hesitant relation, single valued neutrosophic hesitant fuzzy rough set, decision making method.

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Authors: I. Arockiarani

Abstract:

The focus of the paper is to furnish the entropy measure for a neutrosophic set and neutrosophic soft set which is a measure of uncertainty and it permeates discourse and system. Various characterization of entropy measures are derived. Further we exemplify this concept by applying entropy in various real time decision making problems.

Keywords: Entropy measure, Hausdorff distance, neutrosophic set, soft set.

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Authors: C. Ardil

Abstract:

Fuzzy set and intuitionistic fuzzy set are dealing with the imprecision and uncertainty inherent in a complex decision problem. However, sometimes these theories are not sufficient to model indeterminate and inconsistent information encountered in real-life problems. To overcome this insufficiency, the neutrosophic set, which is useful in practical applications, is proposed, triangular neutrosophic numbers and trapezoidal neutrosophic numbers are examined, their definitions and applications are discussed. In this study, a decision making algorithm is developed using neutrosophic set processes and an application is given in fighter aircraft selection as an example of a decision making problem. The estimation of the fighter aircraft selection with the neutrosophic multiple criteria decision analysis method is examined.  

Keywords: neutrosophic set, multiple criteria decision making analysis, fighter aircraft selection, MCDMA, neutrosophic numbers

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Authors: C. Ardil

Abstract:

In this paper, a neutrosophic multiple criteria decision analysis method is proposed to select stealth fighter aircraft. Neutrosophic multiple criteria decision analysis methods are used to analyze the neutrosophic environment and give results under uncertainty and incompleteness. Neutrosophic numbers are used to evaluate alternatives over a set of evaluation criteria in decision making problems. Finally, the proposed model is applied to a practical decision problem for selecting stealth fighter aircraft.

Keywords: neutrosophic sets, multiple criteria decision making analysis, stealth fighter aircraft, aircraft selection, MCDMA, SVNNs

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Authors: C. Ardil

Abstract:

Neutrosophic logic decision analysis is proposed as a method of stealth fighter aircraft selection for Turkish Air Force. The opinion of experts is employed to rank the alternatives across a set of criteria. The analyst uses neutrosophic logic numbers to describe the experts' preferences. This approach can handle the situation in the case of unavailability of precise data, which is most commonly the case in stealth fighter aircraft selection. Neutrosophic logic numbers can consider the imprecision of the factors affecting decision making such as stealth analysis, survivability analysis, and performance analysis. Neutrosophic logic ranking is achieved using weighted arithmetic operator and weighted geometric operator and the alternatives are ranked from best to worst. An example is also presented to illustrate the applicability and effectiveness of the proposed method. 

Keywords: Neutrosophic set theory, stealth fighter aircraft selection, multiple criteria decision-making, neutrosophic logic decision making, Turkish Air Force, MCDM

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Authors: Debabrata Mandal

Abstract:

The aim of this paper is to define several operations such as Intersection, Union, OR, AND operations of intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Maji and compare these with intuitionistic (resp. generalized) neutrosophic soft sets in the sense of Said et al via examples. At the end of the paper, a new concept - extension is introduced, which can be used to refine our choices in case of decision making.

Keywords: AND, OR, Union, Intersection, Extension, Decision making.

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Authors: Antonios Paraskevas, Michael Madas

Abstract:

For a university to maintain its international competitiveness in education, it is essential to recruit qualitative academic staff as it constitutes its most valuable asset. This selection demonstrates a significant role in achieving strategic objectives, particularly by emphasizing a firm commitment to exceptional student experience and innovative teaching and learning practices of high quality. In this vein, the appropriate selection of academic staff establishes a very important factor of competitiveness, efficiency and reputation of an academic institute. Within this framework, our work demonstrates a comprehensive methodological concept that emphasizes on the multi-criteria nature of the problem and on how decision makers could utilize our approach in order to proceed to the appropriate judgment. The conceptual framework introduced in this paper is built upon a hybrid neutrosophic method based on the Neutrosophic Analytical Hierarchy Process (N-AHP), which uses the theory of neutrosophy sets and is considered suitable in terms of significant degree of ambiguity and indeterminacy observed in decision-making process. To this end, our framework extends the N-AHP by incorporating the Neutrosophic Delphi Method (N-DM). By applying the N-DM, we can take into consideration the importance of each decision-maker and their preferences per evaluation criterion. To the best of our knowledge, the proposed model stands out within the realm of related literature as one of the few studies to employ N-DM in the context of academic staff selection. As a case study, it was decided to use our method to a real problem of academic personnel selection, having as main goal to enhance the algorithm proposed in previous scholars’ work, and thus taking care of the inherit ineffectiveness which becomes apparent in traditional multi-criteria decision-making methods when dealing with situations alike. As a further result, we prove that our method demonstrates greater applicability and reliability when compared to other decision models.

Keywords: Analytical Hierarchy Process, Delphi Method, Multi-criteria decision making methods, neutrosophic set theory, personnel recruitment.

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Authors: Pawalai Kraipeerapun, Chun Che Fung, Kok Wai Wong

Abstract:

This paper proposes a novel approach to the question of lithofacies classification based on an assessment of the uncertainty in the classification results. The proposed approach has multiple neural networks (NN), and interval neutrosophic sets (INS) are used to classify the input well log data into outputs of multiple classes of lithofacies. A pair of n-class neural networks are used to predict n-degree of truth memberships and n-degree of false memberships. Indeterminacy memberships or uncertainties in the predictions are estimated using a multidimensional interpolation method. These three memberships form the INS used to support the confidence in results of multiclass classification. Based on the experimental data, our approach improves the classification performance as compared to an existing technique applied only to the truth membership. In addition, our approach has the capability to provide a measure of uncertainty in the problem of multiclass classification.

Keywords: Multiclass classification, feed-forward backpropagation neural network, interval neutrosophic sets, uncertainty.

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Authors: C. Ardil

Abstract:

Fighter aircraft selection is one of the most critical strategies for defense multiple criteria decision-making analysis to increase the decisive power of air defense and its superior power in the defense strategy. Vague set theory is an adequate approach for modeling vagueness, uncertainty, and imprecision in decision-making problems. This study integrates vague set theory and the technique for order of preference by similarity to ideal solution (TOPSIS) to support fighter aircraft selection. The proposed method is applied in the selection of fighter aircraft for the Air Force. In the proposed approach, the ratings of alternatives and the importance weights of criteria for fighter aircraft selection are represented by the vague set theory. Finally, an illustrative example for fighter aircraft selection is given to demonstrate the applicability and effectiveness of the proposed approach. The fighter aircraft candidates were selected under six criteria including costability, payloadability, maneuverability, speedability, stealthility, and survivability. Analysis results show that the best fighter aircraft is selected with the highest closeness coefficient value. The proposed method can also be applied to solve other multiple criteria decision analysis problems. 

Keywords: fighter aircraft selection, vague set theory, fuzzy set theory, neutrosophic set theory, multiple criteria decision making analysis, MCDMA, TOPSIS

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Authors: C. Ardil

Abstract:

Fuzzy set theory and its extensions (intuitionistic fuzzy sets, picture fuzzy sets, and neutrosophic sets) have been widely used to address imprecision and uncertainty in complex decision-making. However, they may struggle with inherent indeterminacy and inconsistency in real-world situations. This study introduces uncertainty sets as a promising alternative, offering a structured framework for incorporating both types of uncertainty into decision-making processes.This work explores the theoretical foundations and applications of uncertainty sets. A novel decision-making algorithm based on uncertainty set-based proximity measures is developed and demonstrated through a practical application: selecting the most suitable stealth combat aircraft.

The results highlight the effectiveness of uncertainty sets in ranking alternatives under uncertainty. Uncertainty sets offer several advantages, including structured uncertainty representation, robust ranking mechanisms, and enhanced decision-making capabilities due to their ability to account for ambiguity.Future research directions are also outlined, including comparative analysis with existing MCDM methods under uncertainty, sensitivity analysis to assess the robustness of rankings,and broader application to various MCDM problems with diverse complexities. By exploring these avenues, uncertainty sets can be further established as a valuable tool for navigating uncertainty in complex decision-making scenarios.

Keywords: Uncertainty set, stealth combat aircraft selection multiple criteria decision-making analysis, MCDM, uncertainty proximity analysis

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Authors: Xiuqin Ma, Norrozila Binti Sulaiman, Hongwu Qin

Abstract:

In the research field of Rough Set, few papers concern the significance of attribute set. However, there is important relation between the significance of single attribute and that of attribute set, which should not be ignored. In this paper, we draw conclusions by case analysis that (1) the attribute set including single attributes with high significance is certainly significant, while, (2)the attribute set which consists of single attributes with low significance possibly has high significance. We validate the conclusions on discernibility matrix and the results demonstrate the contribution of our conclusions.

Keywords: relation, attribute set, single attribute, rough set, significance

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Authors: Tetsuya Furukawa, Masahiro Kuzunishi

Abstract:

Collected data must be organized to be utilized efficiently, and hierarchical classification of data is efficient approach to organize data. When data is classified to multiple categories or annotated with a set of labels, users request multi-labeled data by giving a set of labels. There are several interpretations of the data expressed by a set of labels. This paper discusses which data is expressed by a set of labels by introducing orders for sets of labels and shows that there are four types of orders, which are characterized by whether the labels of expressed data includes every label of the given set of labels within the range of the set. Desirable properties of the orders, data is also expressed by the higher set of labels and different sets of labels express different data, are discussed for the orders.

Keywords: Classification Hierarchies, Multi-labeled Data, Multiple Classificaiton, Orders of Sets of Labels

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Authors: Serkan Narlı, Ahmet Z. Ozcelik

Abstract:

The theory of rough sets is generalized by using a filter. The filter is induced by binary relations and it is used to generalize the basic rough set concepts. The knowledge representations and processing of binary relations in the style of rough set theory are investigated.

Keywords: Rough set, fuzzy set, membership function, knowledge representation and processing, information theory

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Authors: Mahmoud I. Syam, Kamarulzaman Ibrahim, Amer I. Al-Omari

Abstract:

Stratified double extreme ranked set sampling (SDERSS) method is introduced and considered for estimating the population mean. The SDERSS is compared with the simple random sampling (SRS), stratified ranked set sampling (SRSS) and stratified simple set sampling (SSRS). It is shown that the SDERSS estimator is an unbiased of the population mean and more efficient than the estimators using SRS, SRSS and SSRS when the underlying distribution of the variable of interest is symmetric or asymmetric.

Keywords: Double extreme ranked set sampling, Extreme ranked set sampling, Ranked set sampling, Stratified double extreme ranked set sampling.

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Authors: C. Ardil

Abstract:

Intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PyFS), Picture fuzzy sets (PFS), q-rung orthopair fuzzy sets (q-ROF), Spherical fuzzy sets (SFS), T-spherical FS, and Neutrosophic sets (NS) are reviewed as multidimensional extensions of fuzzy sets in order to more explicitly and informatively describe the opinions of decision-making experts under uncertainty. To handle operations with standard fuzzy sets (SFS), the necessary operators; weighted arithmetic mean (WAM), weighted geometric mean (WGM), and Minkowski distance function are defined. The algorithm of the proposed proximity measure method (PMM) is provided with a multiple criteria group decision making method (MCDM) for use in a standard fuzzy set environment. To demonstrate the feasibility of the proposed method, the problem of selecting the best drone for an Air Force procurement request is used. The proximity measure method (PMM) based multidimensional standard fuzzy sets (SFS) is introduced to demonstrate its use with an issue involving unmanned combat aircraft selection.

Keywords: standard fuzzy sets (SFS), unmanned combat aircraft selection, multiple criteria decision making (MCDM), proximity measure method (PMM).

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Authors: C.Natarajan, S.K.Ayyaswamy

Abstract:

Let G be a fuzzy graph. Then D Ôèå V is said to be a strong (weak) fuzzy dominating set of G if every vertex v ∈ V -D is strongly (weakly) dominated by some vertex u in D. We denote a strong (weak) fuzzy dominating set by sfd-set (wfd-set). The minimum scalar cardinality of a sfd-set (wfd-set) is called the strong (weak) fuzzy domination number of G and it is denoted by γsf (G)γwf (G). In this paper we introduce the concept of strong (weak) domination in fuzzy graphs and obtain some interesting results for this new parameter in fuzzy graphs.

Keywords: Fuzzy graphs, fuzzy domination, strong (weak) fuzzy domination number.

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Authors: Nisha Singhal, Usha Chouhan

Abstract:

At present, application of the extension of soft set theory in decision making problems in day to day life is progressing rapidly. The concepts of fuzzy soft set and its properties have been evolved as an area of interest for the researchers. The generalization of the concepts recently got importance and a rapid growth in the research in this area witnessed its vital-ness. In this paper, an application of the concept of generalized fuzzy soft set to make decision in a social problem is presented. Further, this paper also highlights some of the key issues of the related areas.

Keywords: Soft set, Fuzzy Soft set, Generalized Fuzzy Soft set, Membership and Non-Membership Score.

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Authors: Jian-hua Yeh, Shi-yi Kuo

Abstract:

This paper discusses the classification process for medical data. In this paper, we use the data from ACM KDDCup 2008 to demonstrate our classification process based on latent topic discovery. In this data set, the target set and outliers are quite different in their nature: target set is only 0.6% size in total, while the outliers consist of 99.4% of the data set. We use this data set as an example to show how we dealt with this extremely biased data set with latent topic discovery and noise reduction techniques. Our experiment faces two major challenge: (1) extremely distributed outliers, and (2) positive samples are far smaller than negative ones. We try to propose a suitable process flow to deal with these issues and get a best AUC result of 0.98.

Keywords: classification, latent topics, outlier adjustment, feature scaling

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Authors: Da-kuan Wei, Xian-zhong Zhou, Dong-jun Xin, Zhi-wei Chen

Abstract:

The information systems with incomplete attribute values and fuzzy decisions commonly exist in practical problems. On the base of the notion of variable precision rough set model for incomplete information system and the rough set model for incomplete and fuzzy decision information system, the variable rough set model for incomplete and fuzzy decision information system is constructed, which is the generalization of the variable precision rough set model for incomplete information system and that of rough set model for incomplete and fuzzy decision information system. The knowledge reduction and heuristic algorithm, built on the method and theory of precision reduction, are proposed.

Keywords: Rough set, Incomplete and fuzzy decision information system, Limited valued tolerance relation, Knowledge reduction, Variable rough set model

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Authors: Darwin Gouwanda, S. G. Ponnambalam

Abstract:

Set covering problem is a classical problem in computer science and complexity theory. It has many applications, such as airline crew scheduling problem, facilities location problem, vehicle routing, assignment problem, etc. In this paper, three different techniques are applied to solve set covering problem. Firstly, a mathematical model of set covering problem is introduced and solved by using optimization solver, LINGO. Secondly, the Genetic Algorithm Toolbox available in MATLAB is used to solve set covering problem. And lastly, an ant colony optimization method is programmed in MATLAB programming language. Results obtained from these methods are presented in tables. In order to assess the performance of the techniques used in this project, the benchmark problems available in open literature are used.

Keywords: Set covering problem, genetic algorithm, ant colony optimization, LINGO.

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Authors: S. Balaji, N. Revathi

Abstract:

Connected dominating set (CDS) problem in unit disk graph has signi£cant impact on an ef£cient design of routing protocols in wireless sensor networks, where the searching space for a route is reduced to nodes in the set. A set is dominating if all the nodes in the system are either in the set or neighbors of nodes in the set. In this paper, a simple and ef£cient heuristic method is proposed for £nding a minimum connected dominating set (MCDS) in ad hoc wireless networks based on the new parameter support of vertices. With this parameter the proposed heuristic approach effectively £nds the MCDS of a graph. Extensive computational experiments show that the proposed approach outperforms the recently proposed heuristics found in the literature for the MCD

Keywords: ad hoc wireless networks, dominating sets, unit disk graphs, heuristic.

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Authors: Ghazi S. Kahmmash

Abstract:

New generalization of the new class matrix polynomial set have been obtained. An explicit representation and an expansion of the matrix exponential in a series of these matrix are given for these matrix polynomials.

Keywords: Generating functions, Recurrences relation and Generalization of the new class matrix polynomial set.

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Authors: Hazem. A. Khorshed, Mostafa A. El Gendy, Amer. Abd El-Razik

Abstract:

In this paper, The T-G-action topology on a set acted on by a fuzzy T-neighborhood (T-neighborhood, for short) group is defined as a final T-neighborhood topology with respect to a set of maps. We mainly prove that this topology is a T-regular Tneighborhood topology.

Keywords: Fuzzy set, Fuzzy topology, Triangular norm, Separation axioms.

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Authors: Jaemyoung Lee

Abstract:

We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: System set-up, near field communication, smartphone, Android.

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Authors: Ismat Beg, Asma Rashid Butt

Abstract:

Let (X,) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X, then xn  x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F(x), F(y)) ≤ κd(x, y), for all x  y, (ii) if d(x, y) < ε < 1 for some y ∈ F(x) then x  y, (iii) there exists x0 ∈ X, and some x1 ∈ F(x0) with x0  x1 such that d(x0, x1) < 1. It is shown that F has a fixed point. Several consequences are also obtained.

Keywords: Fixed point, partially ordered set, metric space, set valued mapping.

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Authors: Mahmoud I. Syam

Abstract:

Stratified double median ranked set sampling (SDMRSS) method is suggested for estimating the population mean. The SDMRSS is compared with the simple random sampling (SRS), stratified simple random sampling (SSRS), and stratified ranked set sampling (SRSS). It is shown that SDMRSS estimator is an unbiased of the population mean and more efficient than SRS, SSRS, and SRSS. Also, by SDMRSS, we can increase the efficiency of mean estimator for specific value of the sample size. SDMRSS is applied on real life examples, and the results of the example agreed the theoretical results.

Keywords: Efficiency, double ranked set sampling, median ranked set sampling, ranked set sampling, stratified.

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Authors: S. Balaji, V. Swaminathan, K. Kannan

Abstract:

The Maximum Weighted Independent Set (MWIS) problem is a classic graph optimization NP-hard problem. Given an undirected graph G = (V, E) and weighting function defined on the vertex set, the MWIS problem is to find a vertex set S V whose total weight is maximum subject to no two vertices in S are adjacent. This paper presents a novel approach to approximate the MWIS of a graph using minimum weighted vertex cover of the graph. Computational experiments are designed and conducted to study the performance of our proposed algorithm. Extensive simulation results show that the proposed algorithm can yield better solutions than other existing algorithms found in the literature for solving the MWIS.

Keywords: weighted independent set, vertex cover, vertex support, heuristic, NP - hard problem.

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Authors: Shiping Wang, Peiyong Zhu, William Zhu

Abstract:

Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.

Keywords: Covering, poset, down-set, lattice, topological space, topological base.

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Authors: Sandeep Chandana, Rene V. Mayorga, Christine W. Chan

Abstract:

This article outlines conceptualization and implementation of an intelligent system capable of extracting knowledge from databases. Use of hybridized features of both the Rough and Fuzzy Set theory render the developed system flexibility in dealing with discreet as well as continuous datasets. A raw data set provided to the system, is initially transformed in a computer legible format followed by pruning of the data set. The refined data set is then processed through various Rough Set operators which enable discovery of parameter relationships and interdependencies. The discovered knowledge is automatically transformed into a rule base expressed in Fuzzy terms. Two exemplary cancer repository datasets (for Breast and Lung Cancer) have been used to test and implement the proposed framework.

Keywords: Knowledge Extraction, Fuzzy Sets, Rough Sets, Neuro–Fuzzy Systems, Databases

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Authors: Hrudaya Ku. Tripathy, B. K. Tripathy, Pradip K. Das

Abstract:

Knowledge Discovery in Databases (KDD) has evolved into an important and active area of research because of theoretical challenges and practical applications associated with the problem of discovering (or extracting) interesting and previously unknown knowledge from very large real-world databases. Rough Set Theory (RST) is a mathematical formalism for representing uncertainty that can be considered an extension of the classical set theory. It has been used in many different research areas, including those related to inductive machine learning and reduction of knowledge in knowledge-based systems. One important concept related to RST is that of a rough relation. In this paper we presented the current status of research on applying rough set theory to KDD, which will be helpful for handle the characteristics of real-world databases. The main aim is to show how rough set and rough set analysis can be effectively used to extract knowledge from large databases.

Keywords: Data mining, Data tables, Knowledge discovery in database (KDD), Rough sets.

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