• International Journal of Fuzzy Logic and Intelligent Systems
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• v.11 no.4
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• pp.299-304
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• 2011

In this paper, we investigate the properties of rough approximations defined by preordered sets. We study the relations among the lower and upper rough approximations, closure and interior systems, and closure and interior operators.

• Korean Journal of Mathematics
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• v.19 no.2
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• pp.219-232
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• 2011

We investigated the properties of rough approximations induced by two families of preordered sets and closure systems. We study the relations among the lower and upper rough approximations, closure and interior systems, preordered sets.

• Journal of applied mathematics & informatics
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• v.25 no.1_2
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• pp.551-562
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• 2007

This paper concerns a relationship between rough sets, intuitionistic fuzzy sets and ring theory. We consider a ring as a universal set and we assume that the knowledge about objects is restricted by an intuitionistic fuzzy ideal. We apply the notion of intutionistic fuzzy ideal of a ring for definitions of the lower and upper approximations in a ring. Some properties of the lower and upper approximations are investigated.

• Journal of the Korean Institute of Intelligent Systems
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• v.20 no.4
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• pp.596-601
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• 2010

Weinvestigatethevariousoperationsoflowerandupperapproximationsonastscquantalelattice L.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.15 no.3
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• pp.208-215
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• 2015

Since upper and lower approximations could be induced from the rough set structures, rough sets are considered as approximations. The concept of fuzzy rough sets was proposed by replacing crisp binary relations with fuzzy relations by Dubois and Prade. In this paper, we introduce and investigate some properties of intuitionistic fuzzy rough approximation operators and intuitionistic fuzzy relations by means of topology.

• Journal of applied mathematics & informatics
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• v.27 no.3_4
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• pp.737-748
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• 2009

Using the notion of intuitionistic fuzzy subgroups, its roughness is discussed. With respect to a congruence relation on a group, several properties about the lower and upper approximations of a subset of a group are investigated.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.451-460
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• 2016

The notion of a rough fuzzy filter in a BE-algebra is introduced and some properties of such a filter are investigated. The relations between the upper (lower) rough filters and the upper (lower) approximations of their homomorphism images are discussed.

• Journal of Communications and Networks
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• v.18 no.2
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• pp.182-189
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• 2016

The focus in this paper is on obtaining tight, simple algebraic-form bounds and invertible expressions for the average symbol error probability (ASEP) of M-ary phase shift keying (MPSK) in a class of composite fading channels. We employ the mixture gamma (MG) distribution to approximate the signal-to-noise ratio (SNR) distributions of fading models, which include Nakagami-m, Generalized-K ($K_G$), and Nakagami-lognormal fading as specific examples. Our approach involves using the tight upper and lower bounds that we recently derived on the Gaussian Q-function, which can easily be averaged over the general MG distribution. First, algebraic-form upper bounds are derived on the ASEP of MPSK for M > 2, based on the union upper bound on the symbol error probability (SEP) of MPSK in additive white Gaussian noise (AWGN) given by a single Gaussian Q-function. By comparison with the exact ASEP results obtained by numerical integration, we show that these upper bounds are extremely tight for all SNR values of practical interest. These bounds can be employed as accurate approximations that are invertible for high SNR. For the special case of binary phase shift keying (BPSK) (M = 2), where the exact SEP in the AWGN channel is given as one Gaussian Q-function, upper and lower bounds on the exact ASEP are obtained. The bounds can be made arbitrarily tight by adjusting the parameters in our Gaussian bounds. The average of the upper and lower bounds gives a very accurate approximation of the exact ASEP. Moreover, the arbitrarily accurate approximations for all three of the fading models we consider become invertible for reasonably high SNR.

• Korean Journal of Mathematics
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• v.20 no.1
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• pp.61-75
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• 2012

We investigate the properties of various frames and connections on partially ordered sets. In particular, we study the relations between various connections and various frames.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.33 no.2
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• pp.97-104
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• 2010

Using the known result of the expected busy period for the triadic Min (N, T, D) operating policy applied to a controllable M/G/1 queueing model, its upper and lower bounds are derived to approximate its corresponding actual value. Both bounds are represented in terms of the expected busy periods for the dyadic Min (N, T), Min (N, D) and Min (T, D) and simple N, T and D operating policies. All three input variables N, T and D are equally contributed to construct such bounds for better approximations.