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Exchange rate forecasting plays an important role in financial management. However, it is a complex process with high nonlinearity and data irregularity. Moreover, the forecasting of exchange rate is highly involved with imprecise and uncertain data. Analysis of forecasting models which corresponds to the exchange rate has always experienced fluctuations. Therefore, exchange rate forecasting becomes a challenging task in finance. Several studies have shown that stand-alone forecasting models such as time series, fuzzy time series, and Markov chain have their own drawbacks and are not successful enough in forecasting accurately. In this study, we propose a hybrid model of fuzzy time series-Markov chain to forecast the future exchange rate. Fuzzy time series-Markov chain is a combination of the classic fuzzy time series model with Markov chain model used to analyse a set of time series data. The main motivation for this study is to improve the accuracy in exchange rate forecasting. The selected currencies are Malaysian Ringgit (MYR) and Singapore Dollar (SGD). The proposed model was then evaluated by the Mean Absolute Percentage Error (MAPE) performance metric to test the robustness of the model. Lastly, a comparison between the proposed model and fuzzy time series model was conducted with respect to the MAPE. The results showed that the MAPE value for fuzzy time series-Markov chain was 0.9895% which fell under the criterion of highly accurate forecasting. Meanwhile, the MAPE value for fuzzy time series was 3.4306%. Thus, the forecasting performance of the proposed model was better than the fuzzy time series model. This study reveals the potential benefits of the proposed model as a highly accurate forecasting model.

The energy of a graph is defined as the sum of the absolute values of its eigenvalues. Recently, there has been a lot of interest in graph energy research. Previous literature has suggested integrating energy, Laplacian energy, and signless Laplacian energy with single-valued neutrosophic graphs (SVNGs). This integration is used to solve problems that are characterized by indeterminate and inconsistent information. However, when the information is endowed with both positive and negative uncertainty, then bipolar single-valued neutrosophic sets (BSVNs) constitute an appropriate knowledge representation of this framework. A BSVNs is a generalized bipolar fuzzy structure that deals with positive and negative uncertainty in real-life problems with a larger domain. In contrast to the previous study, which directly used truth and indeterminate and false membership, this paper proposes integrating energy, Laplacian energy, and signless Laplacian energy with BSVNs to graph structure considering the positive and negative membership degree to greatly improve decisions in certain problems. Moreover, this paper intends to elaborate on characteristics of eigenvalues, upper and lower bound of energy, Laplacian energy, and signless Laplacian energy. We introduced the concept of a bipolar single-valued neutrosophic graph (BSVNG) for an energy graph and discussed its relevant ideas with the help of examples. Furthermore, the significance of using bipolar concepts over non-bipolar concepts is compared numerically. Finally, the application of energy, Laplacian energy, and signless Laplacian energy in BSVNG are demonstrated in selecting renewable energy sources, while optimal selection is suggested to illustrate the proposed method. This indicates the usefulness and practicality of this proposed approach in real life.

In the last few decades, the computational methods under Multi-Criteria Decision-Making (MCDM) have experienced significant growth in research interests from various scientific communities. Multi-Attributive Border Approximation area Comparison (MABAC) is one of the MCDM methods where its computation procedures are based on distances and areas, and able to express a complex decision systematically. Previous literature have suggested the combination of MABAC with fuzzy sets, in which this combination is used to solve problems that are characterized by uncertain and incomplete information. Differently from the fuzzy MABAC, which directly used single membership, this paper proposes bipolar neutrosophic MABAC of which the positive and negative of truth, indeterminate and false memberships of bipolar neutrosophic set are introduced to enhance decision in sustainable energy selection. Fourteen criteria and seven alternatives of sustainable energy are the main MCDM structures that need to be solved using the proposed method. A group of experts were invited to provide rating of performance values of criteria and alternatives of sustainable energy problem using a bipolar neutrosophic linguistic scale. The distances of alternatives from the Border Approximation Area of bipolar neutrosophic MABAC are the main output of the proposed method prior to making the final decision. The computational results show that &lsquo, Biomass&rsquo, is the optimal alternative to sustainable energy selection. Comparable results are also presented to check the consistency of the proposed method.

© 2018 Wiley Periodicals, Inc. This paper focuses on the aggregation operations in the group decision-making model based on the concept of majority opinion. The weighted-selective aggregated majority-OWA (WSAM-OWA) operator is proposed as an extension of the SAM-OWA operator, where the reliability of information sources is considered in the formulation. The WSAM-OWA operator is generalized to the quantified WSAM-OWA operator by including the concept of linguistic quantifier, mainly for the group fusion strategy. The QWSAM-IOWA operator, with an ordering step, is introduced to the individual fusion strategy. The proposed aggregation operators are then implemented for the case of alternative scheme of heterogeneous group decision analysis. The heterogeneous group includes the consensus of experts with respect to each specific criterion. The exhaustive multicriteria group decision-making model under the linguistic domain, which consists of two-stage aggregation processes, is developed in order to fuse the experts’ judgments and to aggregate the criteria. The model provides greater flexibility when analyzing the decision alternatives with a tolerance that considers the majority of experts and the attitudinal character of experts. A selection of investment problem is given to demonstrate the applicability of the developed model.

We propose a group decision making model based on conflicting bifuzzy sets (CBFS) where evaluation are bi-valued in accordance to the subjective assessment obtained from the experts for the positive and negative views. This paper discusses the weighting methods for particular attribute and subattribute with emphasis given to the unification of subjective and objective weights. The integration of CBFS in the model is naturally done by extending the fuzzy evaluation in parallel with the intuitionistic fuzzy. We introduce a new technique to compute the similarity measure, being the degree of agreement between the experts. We end up the paper by demonstrating the applicability of the proposed model to the empirical case of flood control project, one of the project selection problems.

In this paper, an extension of OWA-TOPSIS model by inclusion of a concept of majority opinion and generalized aggregation operators for group decision making is proposed. To achieve this objective, two fusion schemes in TOPSIS model are designed. First, an external fusion scheme to aggregate the experts’ judgments with respect to the concept of majority opinion on each criterion is proposed. Then, an internal fusion scheme of ideal and anti-ideal solutions that represents the majority of experts is proposed using the Minkowski OWA distance with the inclusion of relative importances of criteria. The advantages of the proposed model include, a consideration of soft majority concept as a group aggregator and a flexibility in applying the decision strategies for analyzing the decision making process. In addition, instead of calculate the majority opinion with respect to the individual experts’ judgments on each alternative, the proposed method takes into account the majority of experts on each criterion, in which reflects the specificity on criteria for overall decision. A numerical example is provided to demonstrate the applicability of the proposed method and comparisons are made between some aggregation operators and distance measures.

Intuitionistic fuzzy sets as proposed by Atanassov, have gained much attention from past and latter researchers for applications in various fields. Similarity measures between intuitionistic fuzzy sets were developed afterwards. However, it does not cater the conflicting behavior of each element evaluated. We therefore made some modification to the similarity measure of IFS by considering conflicting concept to the model. In this paper, we concentrate on Zhang and Fu-s similarity measures for IFSs and some examples are given to validate these similarity measures. A simple modification to Zhang and Fu-s similarity measures of IFSs was proposed to find the best result according to the use of degree of indeterminacy. Finally, we mark up with the application to real decision making problems., {"references":["Atanassov, K., 1986. Intuitionistic fuzzy sets, Fuzzy Sets Systems 20\n(1), 87-96.","Atanassov, K., 1989. More on intuitionistic fuzzy sets. Fuzzy Sets\nSystems 33, 37-46.","Atanassov, K., 1994a. New operations defined over the intuitionistic\nfuzzy sets. Fuzzy Sets Systems 61, 137-142.","Atanassov, K., 1994b. Operations over interval valued intuitionistic\nfuzzy sets. Fuzzy Sets Systems 64, 159-174.","Atanassov, K., 1995. Remarks on the intuitionistic fuzzy sets. Fuzzy\nSets Systems 75 (3), 401-402.","Atanassov, K., 1999. Intuitionistic Fuzzy Sets: Theory and Applications.\nPhysica-Verlag, Heidelberg.","Atanassov, K., Georgeiv, G., 1993. Intuitionistic fuzzy prolog. Fuzzy\nSets Systems 53, 121-128.","Bustince, H., Burillo, P., 1996. Vague sets are intuitionistic fuzzy sets.\nFuzzy Sets Systems 79 (3), 403-405.","Chen, S.M., 1995. Measures of similarity between vague sets. Fuzzy\nSets Systems 74 (2), 217-223.\n[10] Chen, S.M., 1997. Similarity measures between vague sets and between\nelements. IEEE Trans. Syst. Man Cybernet. 27 (1), 153-158.\n[11] De, S.K., Biswas, R., Roy, A.R., 2001. An application of intuitionistic\nfuzzy set in medical diagnosis. Fuzzy Sets Systems 117, 209-213.\n[12] Dengfeng, L., Chuntian, C., 2002. New similarity measure of\nintuitionistic fuzzy sets and application to pattern recognitions. Pattern\nRecognition Lett. 23, 221-225.\n[13] Fan, L., Zhangyan, X., 2001. Similarity measures between vague sets. J.\nSoftware 12 (6), 922-927 (in Chinese).\n[14] Gau, W.L., Buehrer, D.J., 1993. Vague sets. IEEE Trans. Syst. Man\nCybernet. 23 (2), 610-614.\n[15] Hong, D.H., Kim, C., 1999. A note on similarity measures between\nvague sets and between elements. Inform. Science 115, 83-96.\n[16] Hung, W.-L., Yang, M.-S., 2004. Similarity measures of intuitionistic\nfuzzy sets based on Hausdorff distance. Pattern Recognition Lett. 25,\n1603-1611.\n[17] Hyung, L.K., Song, Y.S., Lee, K.M., 1994. Similarity measures between\nfuzzy sets and between elements. Fuzzy Sets Systems 62 (3), 291-293.\n[18] Li, Y., Zhongxian, C., Degin, Y., 2002. Similarity measures between\nvague sets and vague entropy. J. Computer Sci. 29 (12), 129-132 (in\nChinese).\n[19] Li, Y., Olson, D.L., Qin, Z., 2007. Similarity measures between\nintuitionistic fuzzy (vague) sets: A comparative analysis. Pattern\nRecognition Letters 28, 278-285.\n[20] Mitchell, H.B., 2003. On the Dengfeng-Chuntian similarity measure and\nits application to pattern recognition. Pattern Recognition Lett. 24,\n3101-3104.\n[21] Pappis, C.P., Karacapilidis, N.I., 1993. A comparative assessment of\nmeasures of similarity of fuzzy values. Fuzzy Sets Systems 56 (2), 171-\n174.\n[22] Szmidt, E., Kacprzyk, J., 1996. Intuitionistic fuzzy sets in group decision\nmaking. Notes IFS 2 (1), 11-14.\n[23] Szmidt, E., Kacprzyk, J., 2000. Distances between intuitionistic fuzzy\nsets. Fuzzy Sets and Systems 114: 505-518.\n[24] Szmidt, E., Kacprzyk, J., 2006. An application of intuitionistic fuzzy set\nsimilarity measures to a multi-criteria decision making problem. LNAI\n4029, 314-323.\n[25] Xu, Z., 2007, Some similarity measures of intuitionistic fuzzy sets and\ntheir applications to multiple attribute decision making. Fuzzy Optim\nDecis Making, 6, 109-121.\n[26] Zadeh, L.A., 1965. Fuzzy sets. Inform. Control 8, 338-356.\n[27] Zhang, C. et al., 2003. The measures of similarity between vague sets.\nComput. Eng. Appl. 39 (17), 92-94 (in Chinese).\n[28] Zhang, C., Fu, H., 2006. Pattern Recognition Letters 27, 1307-1317.\n[29] Zhizhen, L., Pengfei, S., 2003. Similarity measures on intuitionistic\nfuzzy sets. Pattern Recognition Lett. 24, 2687-2693.\n[30] Atanassov, K. T. (1983). Intuitionistic fuzzy sets. Central Tech. Library,\nBulgarian Academy Science, Sofia, Bulgaria, Rep. No. 1697/84."]}