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In this paper we consider the concept of $KM$ -fuzzy metric spaces and we introduce a novel concept of $KM$ -single valued neutrosophic metric graphs based on $KM$ -fuzzy metric spaces. Then we investigate the finite $KM$ -fuzzy metric spaces with respect to $KM$ -fuzzy metrics and we construct the $KM$ -fuzzy metric spaces on any given non-empty sets. We try to extend the concept of $KM$ -fuzzy metric spaces to a larger class of $KM$ -fuzzy metric spaces such as union and product of $KM$ -fuzzy metric spaces and in this regard we investigate the class of products of $KM$ -single valued neutrosophic metric graphs. In the final, we define some operations such as tensor product, Cartesian product, semi-strong product, strong product, union, semi-ring sum, suspension, and complement of $KM$ -single valued neutrosophic metric graphs.

In this paper, a special type of polysemantic words, that is, words with multiple meanings for the same part of speech, are analyzed under the name of neutrosophic words. These words represent the most difficult cases for the disambiguation algorithms as they represent the most ambiguous natural language utterances. For approximate their meanings, we developed a semantic representation framework made by means of concepts from neutrosophic theory and entropy measure in which we incorporate sense related data. We show the advantages of the proposed framework in a sentiment classification task.

As an expansion of 2-tuple linguistic intuitionistic fuzzy set, the newly developed 2-tuple linguistic neutrosophic set (2-TLNS) is more satisfactory to define decision maker's assessment information in decision-making problems. 2-TLN aggregation operators are of great significance in multiple attribute group decision making (MAGDM) problems with a 2-tuple linguistic environment. Therefore, in this paper, our main contribution is to develop novel 2-TLN power Heronian aggregation (2-TLNPHM) operators. First, we develop new operational laws established on Dombi T-norm (DTN) and Dombi T-conorm (DTCN). Second, Taking full advantages of the power average (PA) operator and Heronian mean (HM) operator, we develop some new novel power Heronian mean operator and discuss its related properties and special cases. The main advantages of developed aggregation operators are that they not only remove the effect of awkward data which may be too high or too low but also have a good capacity to model the extensive correlation between attributes, making them more worthy for successfully solving more and more complicated MAGDM problems. Thus, we develop a new algorithm to handle MAGDM based on developed aggregation operators. Finally, we apply the proposed method and algorithm to risk assessment for the construction of engineering projects to show the efficiency of the developed method and algorithm. The dominant novelties of this contribution are triplex. First, new operational laws are proposed for 2-TLNNs. Second, novel 2-TLNPHM operators are developed. Third, a new approach for 2-tuple linguistic neutrosophic MAGDM is developed.

In recent years, “mathematical orientations on real-life problems”, which continue to increase, began to make a significant impact. Information systems for many decision-making problems consist of uncertain, incomplete, indeterminate and indiscernible structures and components. Classical set theory and interpretation methods fail to represent, express and solve the problems of these types or cause to make wrong decisions. For this reason, in this study, we provide definitions and methods to present information and problem representations in more detail and precision. This paper introduces three new topologies called covering-based rough fuzzy, covering-based rough intuitionistic fuzzy and covering-based rough neutrosophic nano topology. Some fundamental definitions such as open set, closed set, interior, closure and basis are given. Neutrosophic definitions and properties are mainly investigated. We give some real life applications of covering-based rough neutrosophic nano topology in the final part of the paper and an explanatory example of decision making application by defining core point.

Dermoscopic images suffer from irregular and vague boundaries. New directions established the neutrosophic set (NS) approaches for clustering, and segmenting the dermoscopic images. In this work, an accurate segmentation process was developed by mapping initially the dermoscopic images to the NS domain. Thus, the neutrosophic image was defined by three subsets, namely True (T), Indeterminacy (I) and False (F). For accurate boundary detection and segmentation, different high pass (HP) filter types were used in the definition of I subset and low pass (LP) filter types in the definition of T. These filters form a new way to obtain an NS image for segmenting dermoscopy images. A comparative study was carried on the ISIC2016 skin lesion dermoscopic images dataset using different combinations of NS filter types and sizes. The results depicted the superiority of using an unsharp filter in implementing the I subset and an average filter for the T subset. 96% segmentation accuracy was reported using the proposed design compared to 92% accuracy using the default NS definition.

Personnel selection is a critical obstacle that influences the success of the enterprise. The complexity of personnel selection is to determine efficiently the proper applicantion to fulfill enterprise requirements. The decision makers do their best to match enterprise requirements with the most suitable applicant. Unfortunately, the numerous criterions, alternatives, and goals make the process of choosing among several applicants is very complex and confusing to decision making. The environment of decision making is a multi-criteria decision making surrounded by inconsistency and uncertainty. This paper contributes to support personnel selection process by integrating neutrosophic analytical hierarchy process (AHP) with the technique for order preference by similarity to an ideal solution (TOPSIS) to illustrate an ideal solution amongst different alternatives. A case study on smart village Cairo Egypt is developed based on decision maker’s judgments recommendations. The proposed study applies neutrosophic AHP and TOPSIS to enhance the traditional methods of personnel selection to achieve the ideal solutions. By reaching the ideal solutions, the smart village will enhance the resource management for attaining the goals to be a successful enterprise. The proposed method demonstrates a great impact on the personnel selection process rather than the traditional decision-making methods.

In current decade the researchers addressed uncertainty issues. It becomes major issues in case of an effective shortest path in the given network system. This work tried to introduce a mathematical model to characterize the uncertainty in network based on truth, falsity and indeterminacy using interval-valued membership values. The motive is to provide an improved algorithm for shortest path problem. The distance among one node to another node is ranked using interval-valued neutrosophic membership-values. A comparison of our proposed algorithm with that of existing approaches is also established which shows the advantages of new algorithm over the existing ones.

International audience; In this paper, we propose a new fusion approach to combine basic belief assignments (BBAs) defined on a di-chotomous frame of discernment based on their canonical decomposition. In a companion paper, we have already proved that the canonical decomposition of this type of BBA (called dichotomous BBA) is always possible and unique thanks to the proportional conflict redistribution rule No 5 (PCR5). More precisely, any dichotomous BBA is always the PCR5 combination of two simpler basic belief assignments named respectively the pro-evidence, and the contra-evidence. From this interesting canonical decomposition, we present a new way of combining many dichotomous BBAs and we show that the computational time for fusing these dichotomous BBAs based on their canonical decomposition is quasi-linear with the number of sources to combine, contrary to the direct fusion of the dichotomous BBAs altogether.

Deep convolutional Neural networks(CNN) has recognized much advances in recent years. Many CNN models have been proposed in few years ago which focused by first on improving accuracy, next minimize number of parameters using squeeze architecture, then CNN model adapted for embedded and mobile systems. But face the huge applications of CNN in computer vision, few papers discuss what is the theory behind building CNN models combining some components. In this paper, we present a survey of recent advances in CNN architecture design taking into account the three periods listed above.

This paper presents a short contribution for content-based image retrieval (CBIR) systems using refined neutrosophic sets. First, images are represented with dominant color descriptor (DCD) which is an efficient tool for compact color representation. Then, each dominant color and its corresponding partition in DCD is considered as an object in image. Objects are modeled as refined neutrosophic subsets. With respect to CBIR application, new definitions of true (T) and indeterminacy (I) subsets are presented in refined neutrosophic domain which address some challenges in DCD. This is done by considering spatial information of pixels in DCD partitioning and refining wrong labels assigned to pixels. A new operation in refined neutrosophic space is also proposed. Furthermore, a new similarity measure is proposed for transformed images to refined neutrosophic domain. Benefits and weaknesses of the proposed method are explained in discussion section. Experiments show the improvement of at least 4% with respect to precision measure in comparison with other CBIR methods.

In this research paper, we present an new concept named uniform intuitionistic fuzzy graph (uniform-IFG) with an example and studied some of their properties. Next, we develop an algorithmic approach for computing the complement of intuitionistic fuzzy graph (IFG) and present a numerical example for computing the complement of (IFGs) and uniform-IFGs.

A single valued neutrosophic graph is a generalized structure of fuzzy graph, intuitionistic fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs and intuitionistic fuzzy graphs. This paper addresses for the first time, the shortest path in an acyclic neutrosophic directed graph using ranking function. Here each edge length is assigned to single valued neutrosophic numbers instead of a real number. The neutrosophic number is able to represent the indeterminacy in the edge (arc) costs of neutrosophic graph. A proposed algorithm gives the shortest path and shortest path length from source node to destination node. Finally an illustrative example also included to demonstrate the proposed method in solving path problems with single valued neutrosophic arcs.

In this article, we extend the concept of neutrosophic graph-based multicriteria decision making method (NGMCDM) to the case of interval valued neutrosophic graph theory. The new concept is called interval valued neutrosophic graph-based multicriteria decision making method (IVNGMCDM for short). Finally, an illustrative example is given and a comparison analysis is conducted between the proposed approach and other existing methods, to verify the feasibility and effectiveness of the developed approach.

Personality tests are most commonly objective type, where the users rate their behaviour. Instead of providing a single forced choice, they can be provided with more options. A person may not be in general capable to judge his/her behaviour very precisely and categorize it into a single category. Since it is self rating there is a lot of uncertain and indeterminate feelings involved. The results of the test depend a lot on the circumstances under which the test is taken, the amount of time that is spent, the past experience of the person, the emotion the person is feeling and the person's self image at that time and so on. In this paper Triple Refined Indeterminate Neutrosophic Set (TRINS) which is a type of the refined neutrosophic set is introduced. It provides the additional possibility to represent with sensitivity and accuracy the imprecise, uncertain, inconsistent and incomplete information which are available in real world. More precision is provided in handling indeterminacy; by classifying indeterminacy (I) into three, based on membership; as indeterminacy leaning towards truth membership (I T ), indeterminacy membership (I) and indeterminacy leaning towards false membership (I F ). This kind of classification of indeterminacy is not feasible with the existing Single Valued Neutrosophic Set (SVNS), but it is a particular category of the refined neutrosophic set (where each T, I, F can be refined into T 1 , T 2 , … ; I 1 , I 2 , … ; F 1 , F 2 , … ). TRINS is better equipped at dealing indeterminate and inconsistent information, with more accuracy than SVNS and Double Refined Indeterminate Neutrosophic Set (DRINS), which fuzzy sets and Intuitionistic Fuzzy Sets (IFS) are incapable of. TRINS can be used in any place where the Likert scale is used. Personality test usually make use of the Likert scale. In this paper a indeterminacy based personality test is introduced for the first time. Here personality classification is made based on the Open Extended Jung Type Scale test and TRINS.

In this paper, the authors propose an extended version of Dijkstra' algorithm for finding the shortest path on a network where the edge weights are characterized by an interval valued neutrosophic numbers. Finally, a numerical example is given to explain the proposed algorithm.

This paper presents relevant aspects of the idea of using the digital medicine in cancer, so that to shape a viable strategy for creating and implementing an interactive digital platform, NEO-VIP, that should be the basic support to design the strategy for integration of basic, clinical and environmental research on neoplasia progression to cancer. The two main components of the VIPRO Platform are represented by the workstation “Engineering Station” for CPS (Cyber Physical System) and “omics” technology and by the “Graphical Station” for the development of a virtual mechatronic system environment and virtual reality for system components' motion. The NEO-VIP Platform will consolidate the collaboration of specialized institutions in IT, medicine, health, life standards so that to enhance their capabilities to work as a consortium. The results lead to the possibility developing NEO-VIP Platform in the IT modelling field, applied on bio-medical data, as a new player alongside with the existing ones. So, new improved methodologies for investigating social implications of machines working with and for people will be applied.

In the process of development a control strategy for mobile robots, simulation is important for testing the software components, robot behavior and control algorithms in different surrounding environments. In this paper we introduce a simulation environment for mobile robots based on ROS and Gazebo. We show that after properly creating the robot models under Gazebo, the code developed for the simulation process can be directly implemented in the real robot without modifications. In this paper autonomous navigation tasks and 3D-mapping simulation using control programs under ROS are presented. Both the simulation and experimental results agree very well and show the usability of the developed environment.

In this paper, (1) one simplified the standard TOPSIS to new Multi-Criteria Decision-Making (MCDM) called Simplified-TOPSIS. Simplified-TOPSIS gives the same results and simplifies the calculation of the classical TOPSIS. An example is presented distinctions between Simplified-TOPSIS and classical TOPSIS are underlined. (2) extend the new Simplified-TOPSIS method to Neutrosophic-simplified-TOPSIS using single valued Neutrosophic information. An example showing the interest of Neutrosophic-simplified-TOPSIS to manipulate the uncertainty linked to information presented in Multi-Criteria Decision-Making.

The single valued neutrosophic graph is a new version of graph theory presented recently as a generalization of fuzzy graph and intuitionistic fuzzy graph. The single valued neutrosophic graph (SVN-graph) is used when the relation between nodes (or vertices) in problems are indeterminate. In this paper, we examine the properties of various types of degrees, order and size of single valued neutrosophic graphs and a new definition for regular single valued neutrosophic graph is given.

Fuzzy sets and intuitionistic fuzzy sets can't handle imprecise, indeterminate, inconsistent, and incomplete information. Neutrosophic sets play an important role to overcome this difficulty. A neutrosophic set has a truth membership function, indeterminate membership function, and a falsehood membership functions that can handle all types of ambiguous information. New type of union and intersection has been proposed in this paper. In this paper, δ -equalities of neutrosophic sets have been introduced. Further, some basic properties of δ - equalities have been discussed. Moreover, these δ - equalities have been applied to set theoretic operations of neutrosophic set such as union, intersection, complement, product, probabilistic sum, bold sum, bold intersection, bounded difference, symmetrical difference, and convex linear sum of min and max. These δ -equalities of neutrosophic sets have been further extended to neutrosophic relations and neutrosophic norms respectively. In this paper, δ -equalities also applied in the composition of neutrosophic relations, Cartesian product and neutrosophic triangular norms. The applications and utilizations of δ -equalities have been presented in this paper. In this regards, δ -equalities have been successfully applied in Fault Tree Analysis and Neutrosophic Reliability (generalization of Profust Reliability).

R-unions and R-intersections of T-external (Iexternal, F-external) neutrosophic cubic sets are considered. Examples to show that the R-intersection and R-union of Texternal (I-external, F-external) neutrosophic cubic sets may not be a T-external (I-external, F-external) neutrosophic cubic set are provided. Conditions for the R-union and R-intersection of T-external (I-external, F-external) neutrosophic cubic sets to be a T-external (I-external, F-external) neutrosophic cubic set are discussed.

This study introduces the concept of uncertainty analysis of Neutrosophic Theory in the sphere of Maintenance Operating System (MOS). The aim of this study is to underline the importance of uncertainties solving in Maintenance Operating System. In maintenance process appear ambiguous states that can't be assimilated neither true, nor false, meaning that the threshold state is a neutral one, being defined as fault in most of cases. In this regard, this uncertaintymaking decision process can be associated as functioning according to rules of Neutrosophy, and can be evaluated using elements of Neutrosophic Structures, Pareto Charts, maintenance metrics. Identification of uncertainties and study of their impact on maintenance, making the right decision, is the main focus of this paper. The study is useful for business area, especially manufacturing lines endowed with complex equipment and facilities, also for researchers interested to make improvements for maintenance procedures.

A survey of some author's concepts on the dynamic systems stability regions, in the general case of dynamic systems that depend on parameters is related in the paper. The property of separation of stable regions in the free parameters domain is assumed in the paper as an important property of the environment that is carry out and in the specified case of walking robot analyzed in the paper. The matrix that defines the linear dynamic system has the components of the matrix, assumed to be with real values, and the matrices that intervene in the exposure of the method are also, with real values of the components. We assumed that the matrices from the exposure have the complex values such that the real values are also taken into account as particular case of the complex values. This hypothesis assures a new method of analysis, in the complex domain, on the dynamic systems stability. Our theory on the stability control of the dynamic systems is applied here for specified walking robot model that depend on parameters. The critical position of the walking robot evolution is defined and analyzed on some cases of the walking robot leg, and possible application for robot walking up stairs is exposed. The further way of research is emphasized.

In this paper, we introduce concept of bipolar neutrosophic set and its some operations. Also, we propose score, certainty and accuracy functions to compare the bipolar neutrosophic sets. Then, we develop the bipolar neutrosophic weighted average operator and bipolar neutrosophic weighted geometric operat\"or to aggregate the bipolar neutrosophic information. Furthermore, based on the neutrosophic weighted geometric(aritmetic) operat\"or and the score, certainty and accuracy functions, we develop a bipolar neutrosophic multiple criteria decision-making approach, in which the evaluation values of alternatives on the attributes take the form of bipolar neutrosophic numbers to select the most desirable one(s). Finally, a numerical example of the method was given to demonstrate the application and effectiveness of the developed method., Comment: Thanks

In this paper we present several counter-examples to the Conjunctive rule and to Dempster rule of combinations in information fusion.

In this paper we present three new examples of using the α-Discounting Multi-Criteria Decision Making Method in solving non-linear problems involving algebraic equations and inequalities in the decision making process.

In this paper we generalize the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Several examples are presented. Also, a geometric interpretation of the Neutrosophic Set is given using a Neutrosophic Cube. Many distinctions between NS and IFS are underlined.

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Then we show some applications of the neutrosophic logic to robotics.

International audience; This paper presents a new approach for combining sources of evidences with different importances and different reliabilities. Usually, the combination of sources of evidences with different reliabilities is done by the classical Shafer's discounting approach and very often the taking account of different importances of sources, if any, is done with a simliar discounting way by assimilating the notion of importance with the notion reliability. These two notions are actually different and appears fundamental in most of hierarchical Multi-Criteria Decision Analysis (MCDA) problems, and thus they must be treated differently. We show in this paper how this can be done and we provide simple examples to show the differences between both solutions for managing importances and reliabities of sources. We also discuss the possibility for mixing them in a global fusion process.

In this paper we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty's Analytical Hierarchy Process (AHP). It works for any set of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is generalized to a set of preferences that can be transformed into a system of linear and/or nonlinear homogeneous and/or non-homogeneous equations and/or inequalities. Consistent, weak consistent, and strong consistent examples are presented in the sequel for linear and non-linear decision making problems.

Most of modern systems for information retrieval, fusion and management have to deal more and more with information expressed quatitatively (by linguistic labels) since human reports are better and easier expressed in natural language than with numbers. In this paper, we propose to use Herrera-Martinez' 2-tuple linguistic representation model (i.e. equidistant linguistic labels with a numeric value assessment) for reasoning with uncertain and qualitative information in Dezert-Smarandache theory (DSmT) framework to preserve the precision and the efficiency of the fusion of linguistic information expressing the expert's qualitative beliefs. We present operators to deal with the 2-tuples and show from a simple example how qualitative DSmT-based fusion rules can be used for qualitative reasoning and fusioning under uncertainty.

This paper presents a new approach for solving the paradoxical Blackmanpsilas association problem. It utilizes the recently defined new class fusion rule based on fuzzy T-conorm/T-norm operators together with Dezert-Smarandache theory based, relative variations of generalized pignistic probabilities measure of correct associations, defined from a partial ordering function of hyper-power set. The ability of this approach to solve the problem against the classical Dempster-Shaferpsilas method, proposed in the literature is proven. It is shown that the approach improves the separation power of the decision process for this association problem.

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

In this paper we propose anew family of fusion rules for the combination of uncertainty and conflicting information. This family of rules is based on new Proportional Conflict Redistributions (PCR) allowing us to deal with highly conflicting sources for static and dynamic fusion applications. Here five PCR rules (PCR1-PCR5) are presented, analyzed and compared through several numerical examples. From PCR1 up to PCR5 one increases in one hand the complexity of the rules, but in other hand one improves the exactitude of the redistribution of conflicting masses. The basic common principle of PCR rules is to redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. Alongside of these new five PCR rules, there are infinitely many ways these redistributions (through the choice of the set of weighting factors) can be chosen. PCR1 is equivalent to the weighted average operator (WAO) on Shafer's model only for static fusion problems but these two operators do not preserve the neutral impact of the vacuous belief assignment (VBA). The PCR2-PCR5 rules presented here, preserve the neutral impact of VBA and turn out to be what we consider as reasonable and can serve as alternatives to the hybrid DSm rule. PCR4 is an improvement of minC and Dempster's rules of combination and PCR5 is what we feel is the most exact PCR fusion rule developed up to now. The hybrid DSm rule manages the transfer of the belief committed to the conflict through a simple and direct way while the transfer used within PCR rules is more subtle and complex. The PCR rules can be used also and naturally as new efficient alternatives to the Dempster's rule and its other alternatives already proposed in the Dempster-Shafer theory (DST) over the last twenty years.

In this paper, we examine several issues for ordering or partially ordering elements of hyper-powertsets involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT or Dezert-Smarandache Theory) developed by the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation of belief functions., Comment: 13 pages, 6 tables, 2 graphs. Presented to the Sixth International Conference on Information Fusion, Cairns, Queensland, Australia, 8-11 July 2003

The recent theory of plausible and paradoxical reasoning (DSmT for short, or Dezert-Smarandache Theory), developed by the authors, appears to be a nice promising theoretical tools to solve many information fusion problems (for example in military defense, medicine, etc.), where the Shafer's model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work on the hyper-powerset of the frame of discernment of the problem under consideration. Although the definition of hyper-powerset is well established, the major difficulty in practice is to generate such hyper-powersets in order to implement DSmT fusion rule on computers. We present in this paper a simple algorithm for generating hyper-powersets and discuss the limitations of our actual computers to generate such hyper-powersets when the dimension of the problem increases., Comment: 11 pages, 2 tables, one graph, one computer program. Presented to The Sixth International Conference on Information Fusion, Cairns, Queensland, Australia, 1118-1125, 8-11 July 2003