Fuzzy Information and Engineering

Varghese, Ginu; Mathew, Sunil C.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0079-4

AbstractThis paper is on the level decompositions corresponding to the elements in the range of an L-fuzzy topology on a given set and an investigation into the lattice structure of the same. In general, this lattice is not complete and distributive. However, certain necessary and sufficient conditions for it to be modular, distributive, complete and complemented are derived. Atoms and dual atoms of it along with the conditions for their existence are obtained. Certain related properties of it are also discussed here.

Liu, Yi; Qin, Ke-yun; Xu, Yang

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0080-y

AbstractIn this paper, some properties of fuzzy filters are given. Besides, the structure of fuzzy filters are further studied. And finally, the concept of fuzzy prime filter is proposed with some equivalent conditions of fuzzy prime filters obtained.

Ardehali, M.M.; Emam, S.H.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0081-x

AbstractThe objective of this study is to develop and design fuzzy-based controllers for experimental examination and application to a laboratory scale sun tracking heliostat with dynamic movement about azimuth and elevation axes. The experimental approach accounts for unknown parameters such as, nonlinear static and dynamic frictions, nonlinear and variant effect of gravity on system, magnetic saturation of motors, limitations of power source in supplying rush and steady current and variation in heliostat dynamics due to different spacial and time passing conditions. To meet the objective, a classical PI and PID as well as Fuzzy-PI (F-PI) and Fuzzy-PID (F-PID) controllers are designed and experimentally implemented. The performance of each controller is measured by means of evaluating a cost function that is based on the integral of absolute value of error signal. The results show that for azimuth-axis angle, the cost of F-PI controller for deviation from set point is 67% lower as compared with that of PI controller. Also, it is shown that the application of F-PI controller results in lower cost for elevation-axis angle by 36%, 40%, and 50%, when compared with PI, PID, and F-PID controllers, respectively.

Sen, Mausumi; Debnath, Pradip

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0082-9

AbstractThe aim in our article is to introduce the notion of statistical convergence and statistically Cauchy sequences in intuitionistic fuzzy n-normed linear spaces. The paper shows that some properties of statistical convergence of real sequences also hold for sequences in this space. Characterization for statistically convergent and statistically Cauchy sequences is also given. Further, the concept of statistical limit points and statistical cluster points are introduced and their relation with limit points of sequences have been investigated.

Cheng, Yang-jin; Xu, Lin-xi

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0083-8

AbstractIn this paper, we investigate the following problem: give a quasi-Boolean function Ψ(x1 ···, xn) = (a ∧ C) ∨ (a1 ∧ C1) ∨ ··· ∨ (ap ∧ Cp), the term (a ∧ C) can be deleted from Ψ(x1, ···, xn)? i.e., (a ∧ C) ∨ (a1 ∧ C1) ∨ ··· ∨ (ap ∧ Cp) = (a1 ∧ C1) ∨ ··· ∨ (ap ∧ Cp)? When a = 1: we divide our discussion into two cases. (1) ℑ1(Ψ, C) = ∅, C can not be deleted; ℑ1(Φ, C) ≠ #X2205;, if S0i ≠ #X2205; (1 ≤ i ≤ q), then C can not be deleted, otherwise C can be deleted. When a = m: we prove the following results: (m ∧ C) ∨ (a1 ∧ C1) ∨ ··· ∨ (ap ∧ Cp) = (a1 ∧ C1) ∨ ··· ∨ (ap ∧ Cp) ⇔ (m ∧ C) ∨ C1 ∨ ··· ∨ Cp = C1 ∨ ··· ∨ Cp. Two possible cases are listed as follows, (1) ℑ2(ψ, C) = ∅, the term (m ∧ C) can not be deleted; (2) ℑ2(Ψ, C) ≠ ∅, if (Ǝi0) such that S'i0 = ∅, then (m ∧ C) can be deleted, otherwise ((m ∧ C) ∨ C1 ∨ ··· ∨ Cq)(v1, ···, vn) = (C1 ∨ ··· ∨ Cq)(v1, ···, vn)(∀(v1, ···, vn) ∈ Ln3) ⇔ (C'1 ∨ ··· ∨ C'q)(u1, ···, uq) = 1(∀ (u1, ···, uq) ∈ B2n).

Chatterjee, S.; Nigam, S.; Singh, J.B.; Upadhyaya, L.N.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0084-7

AbstractSince last seventies, various software reliability growth models (SRGMs) have been developed to estimate different measures related to quality of software like: number of remaining faults, software failure rate, reliability, cost, release time, etc. Most of the exiting SRGMs are probabilistic. These models have been developed based on various assumptions. The entire software development process is performed by human being. Also, a software can be executed in different environments. As human behavior is fuzzy and the environment is changing, the concept of fuzzy set theory is applicable in developing software reliability models. In this paper, two fuzzy time series based software reliability models have been proposed. The first one predicts the time between failures (TBFs) of software and the second one predicts the number of errors present in software. Both the models have been developed considering the software failure data as linguistic variable. Usefulness of the models has been demonstrated using real failure data.

Niftiyev, A.A.; Zeynalov, C.I.; Poormanuchehri, M.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0085-6

AbstractIn this paper, we introduce a new space of fuzzy numbers equipped with a scalar product defined in this space. The notion of a derivative of a fuzzy function in this space is defined. By employing these notions, an optimal control problem with non-linear functional is formulated and an optimality condition is obtained in the form of maximum principle. Using this result, the numerical algorithm is offered for the solution of such problems.

Thomas, K.V.; Nair, Latha S.

2011 Fuzzy Information and Engineering

doi: 10.1007/s12543-011-0086-5

AbstractWe study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals of a lattice. Some characterization and properties of these intuitionistic fuzzy sublattices and ideals are established. Also we introduce the sum and product of two intuitionistic fuzzy ideals and prove that the sum and product of two Intuitionistic fuzzy ideals of a distributive lattice is again an intuitionistic fuzzy ideal. Moreover, we study the properties of intuitionistic fuzzy ideals under lattice homomorphism.