1. α-e-Almost Compact Crisp Subsets of a Fuzzy Topological Space

   Anjana Bhattacharyya

   Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata – 700009, India.

   Abstract: Fuzzy e-open set is introduced and studied in [8]. Using this concept as a basic tool, in this paper we introduce α-e-almost compactness for crisp subsets of a topological space by using the concept of α-shading initiated by Gantner et.al [12], a generalized version of fuzzy covering. α-almost compactness is introduced in [13]. Here it is shown that α-e-almost compactness implies α-almost compactness [13], but not conversely. To achieve the converse here we introduce α-e-regular space. We characterize α-e-almost compactness via ordinary net and power set filterbases.

   Keywords: Fuzzy e-open set, α-e-almost compact set (space), α-e-regularity, α^e–adherent point of net and filterbase, α-e-interiorly finite intersection property.

   Pages: 285 – 294 | Full PDF Paper

2. A Bayesian approach to Generalized Signed-Rank Estimation for Nonlinear Models with Multidimensional Indices

   Eddy Kwessi^*, Brice M. Nguelifack, Guy-vanie Miakonkana

   Trinity University, 1 Trinity Place, San Antonio, TX 78258, USA.
   United States Naval Academy, Annapolis, MD 21402 , USA.
   African School of Economics, Princeton University, Princeton, NJ 08544, USA.

   Abstract: In this paper, we propose a Bayesian estimation method for generalized signed-rank estimates in nonlinear models with multidimensional indices. Simulations of the Bayesian posterior parameters using Markov Chain Monte Carlo approach are given.

   Keywords: Bayesian, Generalized signed-rank, Nonlinear, Multidimensional, Estimation.

   Pages: 295 – 318 | Full PDF Paper

3. Kernel Optimization Techniques for Price Prediction

   Hayato Kijima¹, Hideyuki Takada²

   1. Graduate School of Information Science, Toho University, Miyama 2-2-1, Funabashi, 274-8510, Chiba, Japan.
   2. Department of Information Science, Toho University, Miyama 2-2-1, Funabashi, 274-8510, Chiba, Japan.

   Abstract: In this paper, we employ Support Vector Machine to predict future directions of the Nikkei 225 futures by learning from the dynamics of Limit Order Book. In order to improve its accuracy, as our previous paper Kijima and Takada (2017) reported, we apply the method of conformal transform of the kernel function pioneered by Amari and Wu (1999). For comparison we also apply Fisher Criteria based data-dependent kernel optimization method proposed by Xiong, Samy and Ahmad (2005) to evaluate their performance. In this sense the paper is a companion to Kijima and Takada (2017) and we conclude, by comparing empirical results, that the conformal transform of Amari and Wu with ex-ante calibrated model parameters improved the precision more than 3.5% in average compared to the standard Gaussian kernel, while the method of Xiong, Samy and Ahmad improved only 1.5% in average.

   Keywords: Limit Order Book, Support Vector Machine, Conformal transformation, Empirical feature space.

   Pages: 319 – 333 | Full PDF Paper

4. α^e–Closed Set, α^e-Continuity and α-e-Almost Compactness For Crisp Subsets of a Fuzzy Topological Space

   Anjana Bhattacharyya

   Department of Mathematics, Victoria Institution (College), 78 B, A.P.C. Road, Kolkata – 700009, India.

   Abstract: This paper is a continuation of [3]. In this paper we introduce a new type of crisp set viz., α^e-closed set which inherits α-e-almost compactness [3] of a fuzzy topological space. In the last section we introduce α^e-continuous function between two fuzzy topological spaces under which α-e-almost compactness for crisp subsets remains invariant.

   Keywords: α-e-almost compact space, α-e-almost compact set, α-e-Urysohn space, α^e–closed set, α-e-continuity, fuzzy e-open function.

   Pages: 334 – 339 | Full PDF Paper