Authors:Santanu Acharjee Pages: 1 - 9 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 1-9, March 2018. This paper focuses on two very important questions: “what is the future of a hybrid mathematical structure of soft set in science and social science'” and “why should we take care to use hybrid structures of soft set'”. At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:21Z DOI: 10.1142/S1793005718500011

Authors:S. Z. Stefanov, Paul P. Wang Pages: 11 - 20 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 11-20, March 2018. Dragon-Kinga is introduced in this paper as the manifestation of a disaster incident for a Smart Grid’s blackout for a day-ahead. The quintessential incident is being generated by an artificial black hole, it then spreads quickly into transmission lines. Consequently, it bursts into space-time transition regions. This paper reveals all the essential characteristics of the Dragon-King, it has non-isotropic stochastic kinematics. Regardless of its huge manifestation of unwanted phenomena, the Dragon-King is controllable. We also describe the mechanism of an updated complexity, spinning cosmic string and a messenger system in this paper. Furthermore, the control strategy of the feedback controller which ultimately leads to a stable normal operation is also reported in this paper. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:23Z DOI: 10.1142/S1793005718500023

Authors:Irina Georgescu, Ana María Lucia Casademunt Pages: 21 - 35 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 21-35, March 2018. In this paper, the effect of posibilistic or mixed background risk on the level of optimal prevention is studied. In the framework of five purely possibilistic or mixed models, necessary and sufficient conditions are found such that the level of optimal saving decreases or increases as a result of the actions of various types of background risk. This way our results complete those obtained by Courbage and Rey for some prevention models with probabilistic background risk. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:21Z DOI: 10.1142/S1793005718500035

Authors:E. Darabian, R. A. Borzooei Pages: 37 - 52 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 37-52, March 2018. A vague graph is a generalized structure of a fuzzy graph that gives more precision, exibility, and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the concepts of eccentricity of nodes, radius and diameter of vague graphs are introduced. The special types of graphs such as eccentrice and antipodal vague graphs are investigated. Then, the relation between eccentrice and antipodal vague graphs are discussed. Finally, an application of eccentrice and antipodal vague graphs in human traffickingn studied. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:22Z DOI: 10.1142/S1793005718500047

Authors:Samajh Singh Thakur, Alpa Singh Rajput Pages: 53 - 71 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 53-71, March 2018. In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:20Z DOI: 10.1142/S1793005718500059

Authors:Fereshteh Forouzesh Pages: 73 - 89 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 73-89, March 2018. In this paper, we introduce the notions of fuzzy semi-maximal ideals and fuzzy primary ideals of an [math]-algebra and investigate some of their properties. Also, several characterizations of these fuzzy ideals are given. In addition, we show that [math] is a fuzzy semi-maximal ideal of [math] if and only if [math] is a semi-simple [math]-algebra and [math] is a fuzzy primary ideal of [math] if and only if [math] is local [math]-algebra. By using the notions of the maximal and normal fuzzy semi-maximal ideals, we show that under certain conditions a fuzzy semi-maximal ideal is two-valued and takes the values 0 and 1. The radical of a fuzzy ideal is defined as against the (maximal) radical of a fuzzy ideal and some of their properties are proved. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:23Z DOI: 10.1142/S1793005718500060

Authors:Abhishekh, Surendra Singh Gautam, S. R. Singh Pages: 91 - 111 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 91-111, March 2018. Intuitionistic fuzzy set plays a vital role in data analysis and decision-making problems. In this paper, we propose an enhanced and versatile method of forecasting using the concept of intuitionistic fuzzy time series (FTS) based on their score function. The developed method has been presented in the form of simple computational steps of forecasting instead of complicated max–min compositions operator of intuitionistic fuzzy sets to compute the relational matrix [math]. Also, the proposed method is based on the maximum score and minimum accuracy function of intuitionistic fuzzy numbers (IFNs) to fuzzify the historical time series data. Further intuitionistic fuzzy logical relationship groups are defined and also provide a forecasted value and lies in an interval and is more appropriate rather than a crisp value. Furthermore, the proposed method has been implemented on the historical student enrollments data of University of Alabama and obtains the forecasted values which have been compared with the existing methods to show its superiority. The suitability of the proposed model has also been examined to forecast the movement of share market price of State Bank of India (SBI) at Bombay Stock Exchange (BSE). The results of the comparison of MSE and MAPE indicate that the proposed method produces more accurate forecasting results. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:20Z DOI: 10.1142/S1793005718500072

Authors:Sunil Mathew, Hai Long Yang, Jill K. Mathew Pages: 113 - 128 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 113-128, March 2018. Edges of a fuzzy graph are mainly classified into [math], [math] and [math]. In this paper, we study certain saturation counts with respect to the classification of edges. Characterizations for fuzzy cycles, fuzzy trees, blocks in fuzzy graphs and complete fuzzy graphs are also obtained using saturation counts. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:23Z DOI: 10.1142/S1793005718500084

Authors:John N. Mordeson, Sunil Mathew Pages: 129 - 143 Abstract: New Mathematics and Natural Computation, Volume 14, Issue 01, Page 129-143, March 2018. We generalize the definition of a fuzzy graph by replacing minimum in the basic definitions with an arbitrary [math]-norm. The reason for this is that some applications are better modeled with a [math]-norm other than minimum. We develop a measure on the susceptibility of trafficking in persons for networks by using a [math]-norm other than minimum. We also develop a connectivity index for a fuzzy network. In one application, a high connectivity index means a high susceptibility to trafficking. In the other application, we use a method called the eccentricity of an origin country to determine the susceptibility of a network to trafficking in persons. The models rest on the vulnerabilities and the government responses of countries to trafficking. Citation: New Mathematics and Natural Computation PubDate: 2018-03-13T10:39:20Z DOI: 10.1142/S1793005718500096