Indeterminacy Functions Research Articles

Properties of interval-valued quadripartitioned neutrosophic graphs with real-life application

The interval-valued quadripartitioned neutrosophic set is represented by the partition of the interval-valued neutrosophic set’s indeterminacy function into contradiction and ignorance parts. This article introduces the properties of interval quadripartitioned single valued neutrosophic graph. The properties like complementary, self-complementary, strong and complete interval-valued quadripartitioned neutrosophic graphs are investigated. The finest illustration of locating a climate conducive to apricot cultivation in Ladakh is provided by the notion that has been offered. The model gives us details on the location that should be chosen for apricot farming. Using the proposed concepts, we highlight potential applications of the usual apricot plant that thrives in extremely cold climates and is appropriate for higher production. The adopted approach makes a superior fit to consider the problems in application viewpoint.

Neutrosophic Sets and Metaheuristic Optimization: A Survey

Smarandache presents neutrosophic sets and provides a domain area that is made up of three separate subsets to reflect the various kinds of uncertainty. Neutrosophic sets are defined as the sets where every other element of the universe possesses a degree of truthiness, indeterminacy, and falsity, which range from 0 to 1, and where these degrees are subsets of the neutrosophic sets that are independent of each other. Neutrosophic sets are also known as neutrosophical subsets. In the neutrosophic sets, impreciseness is represented as truth and falsity functions, but the indeterminacy function represents degrees of belongingness and non-belongingness and differentiates between absoluteness and relativeness. Neutrosophic sets can deal with the unpredictability of the system and cut down on the paralysis brought on by conflicting information thanks to this notation. As a result, one might argue that this capacity is the single most significant benefit offered by neutrosophic sets in comparison to the many other forms of fuzzy extensions. By making use of these three functions, neutrosophic sets are able to create a domain area. This area makes it possible for various kinds of mathematical operations to be carried out separately despite the presence of uncertainty. Due to the fact that the behavior of these methodologies is inspired by Nature and its capacity for adapting to issues, in addition to the potential for combining more than one method to reach the best alternatives, metaheuristic algorithms are employed to initiate the finest or the best possible alternatives to a lot of optimization techniques. This is possible because metaheuristic algorithms have the ability to adapt to problems. The fact that numerous academics have utilized these techniques with neutrosophic science to offer several systems in recent years was the impetus for writing this overview study in the first place, which was based on the above rationale.

New Concepts on Quadripartitioned Bipolar Single Valued Neutrosophic Graph

The partition of indeterminacy function of the neutrosophic set into the contradiction part and the ignorance part represent the quadripartitioned single valued neutrosophic set. In this work, the new concept of quadripartitioned bipolar single valued neutrosophic graph is established, and the operations on it are studied. The Cartesian product, cross product, lexicographic product, strong product and composition of quadripartitioned bipolar single valued neutrosophic graph are investigated. The proposed concepts are illustrated with examples.

$${\mathcal {N}}$$-version of the neutrosophic cubic set: application in the negative influences of Internet

The Internet is one of the most significant human inventions in the twentieth century. Like other human inventions, the Internet has affected human society in ways that have positive as well as negative aspects. This paper aims at discussing a new concept called N-neutrosophic cubic sets (NNCSs) aimed at assessing the negative aspects of the Internet. The notions of N-cubic indeterminacy function and N-cubic falsity function have been added with the N-cubic set to obtain a novel concept of N-neutrosophic cubic sets (NNCSs). The novelty of the N-neutrosophic cubic set (NNCS) may be associated with the fact that there is a larger range of values to discuss uncertainty and vagueness as compared to the N-cubic set. The basic operations of the N-neutrosophic cubic sets (NNCSs) along with some interesting properties are discussed. Analysis has also been focused on examining the negative rating function and aggregation operators of N-neutrosophic cubic sets (NNCSs). Finally, as an application, a numerical example is given to test the applicability of the proposed model.

Decision making for energy investments by using neutrosophic present worth analysis with interval-valued parameters

Due to the increasing energy consumption of the world, new alternative energy sources are needed. The alternative energy resources can be classified into three categories such as fossil fuels energy resources, renewable energy resources, and nuclear energy resources. Solar energy is a very commonly used renewable energy resource for generating electricity and heating water. In this paper, establishing a solar energy system is handled as an investment analysis problem whose parameters are defined under uncertainty. Therefore, neutrosophic sets as a mean of dealing with uncertainty have been preferred to capture this vagueness and impreciseness. Neutrosophic sets are one of the extensions of intuitionistic fuzzy sets, which use an indeterminacy function unlike the other extensions of fuzzy sets. This paper proposes a new neutrosophic investment analysis method by using interval-valued parameters to evaluate solar energy systems. In the application section, three different types of solar energy systems are evaluated by the proposed method. It is observed that the proposed method presents big flexibility to experts and it gives effective and efficient results.

Composition and Application of Extended Colored Logic Petri Nets to E-Commerce Systems

Extended colored logic Petri nets (ECLPNs) are extensions of logic Petri nets (LPNs) and colored logic Petri nets (CLPNs). They are equivalent to LPNs and CLPNs, which can describe the batch processing and indeterminacy functions of resources in cooperative systems. The advantage of ECLPNs is that their net structures are much simpler than their equivalent CLPNs, and therefore, ECLPNs can be easily used to model and analyze cooperative systems. For systems containing several subsystems with the same function and structure, we can describe them by a single ECLPN. Then we propose a composition method of ECLPNs. We define the robustness of a system based on ECLPN which reflects the validity of the collaboration of subsystems. We define a strict conservativeness that guarantees data security. The robustness and strict conservativeness of composed ECLPNs are analyzed. An E-commerce example is presented to illustrate the modeling capacity and the advantage of ECLPNs.

Modeling Neutrosophic Data by Self-Organizing Feature Map: MANETs Data Case Study

Network security is a major research area for both scientists and business. Intrusion Detection System (IDS) is one of the most challenging problems in Mobile Ad Hoc Networks (MANETs). The main reason resides behind the changing and uncertain nature of MANETs networks. Hence, a compensate evolving in the IDS would be converting the whole system to rely on uncertainty and indeterminacy concepts. These concepts are the main issues in the fuzzy system and consequently in neutrosophic system. In neutrosophic system, each attack is determined by MEMEBERSHIP, INDETERMINACY and NONMEMEBERSHIP degrees. The main obstacle is that most data available are regular values which are not suitable for neutrosophic calculation. This paper is concerned by the preprocessing phase of the neutrosophic knowledge discovery system. Converting the regular data to neutrosophic values is a problem of generating the MEMEBERSHIP, NONMEMEBERSHIP and INDETERMINACY functions for each variable in the system. Self-Organized Feature Maps (SOFM) are unsupervised artificial neural networks that were used to build fuzzy MEMEBERSHIP function, hence they could be utilized to define the neutrosophic variable as well. SOFMs capabilities to cluster inputs using self-adoption techniques have been utilized in generating neutrosophic functions for the subsets of the variables. The SOFM are used to define the MEMEBERSHIP, NONMEMEBERSHIP and INDETERMINACY functions of the KDD network attacks data available in the UCI machine learning repository for further processing in knowledge discovery. Experimental results show the features and their corresponding functions.

3D surface orientation based on a novel representation of the orientation disparity field

The orientation disparity field from two orthographic views of an inclined planar surface patch (covered by straight lines) is analyzed, and a new tool to extract the patch orientation is provided: the function coupling the average orientation of each pair of corresponding surface contours with their orientation disparity. This function allows identifying the tilt of the surface, and two indeterminacy functions describing the set of surface inclinations (around the vertical and horizontal axes) over convergence angle values compatible with the orientation disparity field. Results of simulations show that the selection of inclination values matching the difference between the areas below the indeterminacy functions are consistent with some surface orientation effects found in psychophysical and computational experiments, like: the unbiased tilt vs. biased slant estimates, the slant underestimation, the surface orientation anisotropy, and the slant/tilt covariation.

Analysis of characteristics of composite ultra-wideband signals with amplitude and positional code modulation

The paper considers composite ultra-wideband signals with amplitude code modulation and with intrablock positional pulse modulation. Investigation of the generalized indeterminacy function for these signals is implemented. Analytical expressions for the correlation matrix of simultaneously effective estimates of delay time and period of these signals are derived. Analysis of potential accuracy of these parameters’ estimates is performed for various modulation techniques. An algorithm is suggested for generation of modulating shift sequences.

Generation of the indeterminacy function for signals discretely coded in frequency with prescribed properties

An expression of the indeterminacy function (IF) is derived for signals discretely coded in frequency (SDCF) (Kostas’ signals) with the use of weighted processing. The paper introduces an optimal frequency weight function for assigning weights to the amplitudes of SDCF. Analysis of calculation results for sections of the SDCF IF, at the zero Doppler shift of frequency and zero delay, corresponding to different parameters of the weight function for different lengths of SDCF, shows the possibility for considerable lowering of IF side lobes’ level at high resolving capacity in terms of delay and frequency.