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Authors:Khaista Rahman Pages: 211 - 230 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 211-230, July 2020. Interval-valued Pythagorean fuzzy set is one of the successful extensions of the interval-valued intuitionistic fuzzy set for handling the uncertainties in the data. Under this environment, in this paper we introduce the notion of induced interval-valued Pythagorean fuzzy Einstein ordered weighted geometric (I-IVPFEOWG) operator and induced interval-valued Pythagorean fuzzy Einstein hybrid geometric (I-IVPFEHG) operator along with their some basic properties such as, idempotency, boundedness, commutatively, monotonicity. The main advantage of the induced aggregation operators is that, these operators are more suitable to aggregate the individual preference relations into a collective preference relation. Therefore these methods play a vigorous role in daily life problems. Furthermore, a method for multi-attribute group decision-making (MAGDM) problems based on these operators was developed, and the operational procedures were explained in detail. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500131 Issue No:Vol. 16, No. 02 (2020)

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Authors:Mandrita Mondal, Kumar S. Ray Pages: 231 - 254 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 231-254, July 2020. In this paper, we propose a wet lab algorithm for prediction of visibility under radiation fog by DNA computing. The model is based on a concept of similarity based fuzzy reasoning suitable for wet lab implementation. The concept of similarity based fuzzy reasoning using DNA sequences is different from conventional approach to fuzzy reasoning. It replaces the logical aspect of classical fuzzy reasoning by DNA chemistry. By the proposed algorithm the tedious job to choose suitable implication operator, which is absolutely necessary for classical fuzzy reasoning, can be avoided. If the fuzzified forms of five observed parameters, i.e. dew point, dew point spread, the rate of change of dew point spread per day, wind speed and sky condition are given, the newly proposed algorithm efficiently predicts the possibility of visibility under radiation fog. The final result of the wet lab algorithm, which is in form of fuzzy DNA, produces multi valued status which can be linguistically interpreted to match the perception of an expert. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500143 Issue No:Vol. 16, No. 02 (2020)

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Authors:B. Praba, G. Gomathi, M. Aparajitha Pages: 255 - 269 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 255-269, July 2020. Rough sets defined in terms of soft sets play a vital role in decision making problems. Covering-based soft rough sets and modified soft rough sets are some of the recently developing concepts. In this paper, for a given soft sets [math] on a universe [math] we define a novel rough set called as minimal soft rough sets using minimal soft description of the objects. The relation between modified soft rough set and minimal soft rough set is analyzed. The set of all minimal soft rough sets is proved to be a Poset with the inclusion relation having a GLB and LUB and hence is a lattice. An attempt is made in applying this concepts in medical diagnoses and also in analyzing the organizational culture system. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500155 Issue No:Vol. 16, No. 02 (2020)

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Authors:Justin Dzuche, Christian Deffo Tassak, Jules Sadefo Kamdem, Louis Aimé Fono Pages: 271 - 290 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 271-290, July 2020. Possibility, necessity and credibility measures are used in the literature in order to deal with imprecision. Recently, Yang and Iwamura [L. Yang and K. Iwamura, Applied Mathematical Science 2(46) (2008) 2271–2288] introduced a new measure as convex linear combination of possibility and necessity measures and they determined some of its axioms. In this paper, we introduce characteristics (parameters) of a fuzzy variable based on that measure, namely, expected value, variance, semi-variance, skewness, kurtosis and semi-kurtosis. We determine some properties of these characteristics and we compute them for trapezoidal and triangular fuzzy variables. We display their application for the determination of optimal portfolios when assets returns are described by triangular or trapezoidal fuzzy variables. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500167 Issue No:Vol. 16, No. 02 (2020)

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Authors:Sutapa Mahato, S. P. Tiwari Pages: 291 - 304 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 291-304, July 2020. The objective of this paper is to establish the relationship between fuzzy approximation operators and fuzzy transformation systems. We show that for each upper fuzzy transformation system there exists a fuzzy reflexive approximation space and vice-versa. We further establish such relationship between lower fuzzy transformation systems and fuzzy reflexive approximation spaces under the condition that the underline lattice structure satisfies double negation law. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500179 Issue No:Vol. 16, No. 02 (2020)

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Authors:Jyoti D. Thenge, B. Surendranath Reddy, Rupali S. Jain Pages: 305 - 318 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 305-318, July 2020. The theory of soft set offers a mathematical tool to deal with uncertainty. Nowadays, work on soft graph theory is progressing rapidly. In this paper, we define connected soft graph and derive some results. We also define cut vertex and bridge of soft graph along with some results on it. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500180 Issue No:Vol. 16, No. 02 (2020)

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Authors:Kei Katahira, Yu Chen Pages: 319 - 325 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 319-325, July 2020. The speculation game is an agent-based toy model to investigate the dynamics of the financial market. Our model has achieved the reproduction of 10 of the well-known stylized facts for financial time series. However, there is also a divergence from the behavior of real market. The market price of the model tends to be anti-persistent to the initial price, resulting in the quite small value of Hurst exponent of price change. To overcome this problem, we extend the speculation game by introducing a perturbative part to the price change with the consideration of other effects besides pure speculative behaviors. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500192 Issue No:Vol. 16, No. 02 (2020)

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Authors:John N. Mordeson, Matthew A. Mordeson, Sunil Mathew Pages: 327 - 338 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 327-338, July 2020. All member states of the United Nations adopted Agenda 2030 and the Sustainable Development Goals (SDGs) in 2015. The 17 SDGs describe a universal agenda that applies to and must be implemented by all countries. We take the metrics and data provided in the SDG Index and Dashboards Reports and the Report of a Study by Stakeholder Forum and transform them into a fuzzy logic setting. This allows for the analysis of the results in these reports by using techniques of mathematics of uncertainty. We focus on countries making up the Organization for Economic Cooperation and Development (OECD). We provide a ranking of the countries in the OECD as to their achievement of the SDGs. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500209 Issue No:Vol. 16, No. 02 (2020)

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Authors:F. Abbasi, T. Allahviranloo Pages: 339 - 361 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 339-361, July 2020. In this paper, the probability of failure of the components is introduced as a new type of fuzzy number called Gaussian patchy fuzzy number to insert parameters’ uncertainty. The reason for the use of such fuzzy numbers is also due to their realistic estimation. Hence, in order to obtain a more accurate estimate of each failure occurrence and overall system reliability analysis, we assume that the fundamental events of fault tree are in the form of Gaussian patchy fuzzy number on [0, 1], and then, by applying the fuzzy transmission average (TA) [F. Abbasi, T. Allahviranloo and S. Abbasbandy, A new attitude coupled with fuzzy thinking to fuzzy rings and fields, Journal of Intelligent and Fuzzy Systems 29 (2015) 851–861.], we will model the reliability of the fuzzy system (especially the series and the parallel). Applying such fuzzy operations and numbers will lead to a more realistic analysis of the reliability of the fuzzy system. Finally, the proposed model has been used for the lack of satisfaction of the University’s administrative and financial assistant. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500210 Issue No:Vol. 16, No. 02 (2020)

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Authors:Anupam K. Singh, S. P. Tiwari Pages: 363 - 376 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 363-376, July 2020. The purpose of this work is to introduce the concept of fuzzy regular languages (FRL) accepted by fuzzy finite automata, and try to introduce the categorical look of fuzzy languages where the codomain of membership functions are taken as a complete residuated lattice, instead of [math]. Also, we have introduced pumping lemma for FRL, which is used to establish a necessary and sufficient condition for a given fuzzy languages to be non-constant. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500222 Issue No:Vol. 16, No. 02 (2020)

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Authors:K. Vela Velupillai Pages: 377 - 396 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 377-396, July 2020. In this essay, which began as a Review Article of the book X, Y & Z: The Real Story of How Enigma was Broken by Dermot Turing, I discuss some of the background details of the Enigma Cypher Machine. The machine was supposed to be ‘unbreakable’, as claimed (in particular) by the manufacturers. It was repeatedly broken by Polish and British mathematicians, employed in their respective countries’ (and France’s) bureaus; in particular, heroically, by Alan Turing (at Bletchley Park, UK) and Marian Rejewski (in Poznań, Warsaw and France) — but others played important parts, too. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500234 Issue No:Vol. 16, No. 02 (2020)

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Authors:R. A. Borzooei, R. Almallah, Y. B. Jun, H. Ghaznavi Pages: 397 - 418 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 397-418, July 2020. Rosenfeld [A. Rosenfeld, Fuzzy Graphs, Fuzzy Sets and Their Applications, eds. L. A. Zadeh, K. S. Fu and M. Shimura (Academic Press, New York, 1975), pp. 77–95.] defined the fuzzy relations on the fuzzy sets and developed the structure of fuzzy graph, as a graph with a membership degree (between zero and one) for the vertices and edges such that the membership degree of every edge is less than or equal to the minimum of the membership degree of its endpoints. Although this model of graph has many applications in the real life, it fails to solve a lot of problems, which we can use graph for its representation. This paper aimed to demonstrate a new type of graph with a membership degree (between zero and one) for the vertices and edges so that the membership degree of every edge becomes more than or equals the minimum of the membership degrees of its endpoints. This new type of graph is called inverse fuzzy graph “or” I-fuzzy graph, which can play a role in solving many problems which are not solved by fuzzy graph. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500246 Issue No:Vol. 16, No. 02 (2020)

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Authors:Somayeh Motamed, Samira Ehterami Pages: 419 - 435 Abstract: New Mathematics and Natural Computation, Volume 16, Issue 02, Page 419-435, July 2020. In this paper, we defined the concepts of [math]-derivation and [math]-derivation for [math]-algebras and discuss some related results. We study the connection between these derivations on an [math]-algebra [math]. Also we study these derivations on Boolean center [math], [math] center, Godel center of a [math]-algebra [math]. Citation: New Mathematics and Natural Computation PubDate: 2020-08-03T07:00:00Z DOI: 10.1142/S1793005720500258 Issue No:Vol. 16, No. 02 (2020)