Journal of Intelligent & Fuzzy Systems - Volume 37, issue 4

Authors: Jia, Lifen | Ni, Yaodong

Article Type: Research Article

Abstract: Uncertain Differential equations are a type of differential equations driven by the Liu processes rather than the Wiener processes. Depending on the order of differentials it contains, an uncertain differential equation could be classified into first-order uncertain differential equation, second-order uncertain differential equation, third-order uncertain differential equation, and so on. The concepts of stability in various senses for the uncertain differential equations could be specified and applied to the uncertain spring vibration differential equations. However, to the best knowledge of mine, many types of stability have been proposed for first-order uncertain differential equations, for example, stability in mean, stability in …p -th moment, stability in distribution, almost sure stability and exponential stability. However, stability in measure and stability in mean of high-order uncertain differential equations have been proposed. But only the concept of stability in mean and the concept of stability in measure have been proposed for high-order uncertain differential equations. In this paper, following the concept of stability in p -th moment for first-order uncertain differential equations, we present the concept of stability in p -th moment for general uncertain spring vibration differential equations which are a type of second-order uncertain differential equations. Show more

Keywords: Spring vibration equation, stability, uncertain differential equation, uncertain process, uncertainty theory

DOI: 10.3233/JIFS-182864

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5075-5083, 2019

Authors: Flores-Martínez, M.-A. | Osorio-Gordillo, G.-L. | Vargas-Méndez, R.-A. | Reyes-Reyes, J.

Article Type: Research Article

Abstract: This paper presents an algorithm for the design of a Generalized Dynamic Functional Observer (GDFO) for Takagi-Sugeno systems. A set of conditions are provided for the existence of the observer, which can be applied to the proportional functional observer that is presented as a particular case of the proposed generalized observer. Lyapunov function is used to find stability condition of the observer. Stability conditions are given in terms of linear matrix inequalities (LMIs). A glucose-insulin system example illustrates the performance and effectiveness of the proposed approach.

Keywords: Generalized dynamic functional observer, Takagi-Sugeno systems, glucose-insulin system, feedback control

DOI: 10.3233/JIFS-182872

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5085-5096, 2019

Authors: Wang, Bing | Li, Qing-Hua

Article Type: Research Article

Abstract: The aim of this paper is to study the relations among soft topological spaces, soft L -topological spaces and stratified soft L -topological spaces. Firstly, we construct a Galois correspondence between the category SoTop of soft topological spaces and the category So L -Top of soft L -topological spaces, and obtain that SoTop is a coreflective subcategory of So L -Top . Secondly, we show that there is a Galois correspondence between the category SSo L -Top of stratified soft L -topological spaces and SoTop and obtain that SoTop is a reflective subcategory of …SSo L -Top . Finally, we study the stratification of soft L -topological spaces. We also construct a Galois correspondence between SSo L -Top and So L -Top , and obtain that SSo L -Top is a coreflective subcategory of So L -Top . Show more

Keywords: Soft topology, (Stratified) Soft L-topology, Galois correspondence, Reflective, Coreflective

DOI: 10.3233/JIFS-182887

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5097-5103, 2019

Authors: Li, Shi-ju | Wang, Hui-li

Article Type: Research Article

Abstract: This paper deals with the max-algebraic linear equation system A  ⊗ x  = b . As in the conventional linear algebra such a linear system may have none, exactly one or infinitely many solutions. When the number of solutions is exactly one, Cramer’s rule is given as an analogue of the classical linear algebra. When the number of solutions is infinite, the existence of a minimal solution is shown and the formula of minimal solution is given. Furthermore, it is proved that every solution can be expressed as a linear combination of a respective minimal solution and some special vectors. Finally, an …algorithm to describe all the solutions of a given max-algebraic linear equation system is proposed when its number of solutions is infinite. AMS classification: 15A80,15A06 Show more

Keywords: Max-algebra, linear equation system, solution set, minimal solution, cramer’s rule

DOI: 10.3233/JIFS-182911

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5105-5111, 2019

Authors: Ramadan, Ahmed | Elkordy, Enas | Abdel-Hameed, Usama | Ahmed, Reham

Article Type: Research Article

Abstract: This paper is dedicated to introduce the concept of a new space named "L -fuzzy nearness" and to arise a great deal of relationships among it and most of known spaces, like: L -fuzzy topological spaces (interior, closure, co-topology) and L -fuzzy pre-proximities in complete residuated lattices. We have demonstrated concrete functors between the category of Alexandrov L -fuzzy nearness, Alexandrov L -fuzzy topological structures and Alexandrov L -fuzzy pre-proximities and established the Galois correspondence between these categories.

Keywords: Complete residuated lattice, L-fuzzy nearness, L-fuzzy pre-proximity, L-fuzzy topological spaces, Galois correspondence.

DOI: 10.3233/JIFS-182938

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5113-5128, 2019

Authors: Yang, Jingjing | Zhang, Qinghua | Xie, Qin

Article Type: Research Article

Abstract: As an effective tool for knowledge acquisition, attribute reduction is one of the key issues in rough set theory. In current research, most researchers choose to reduce redundant attributes as many as possible through some attribution reduction algorithms. However, the misclassification cost induced by attribute reduction is ignored. Thus, it is worth studying that how to reduce redundant attributes based on preserving the misclassification cost. Firstly, in this paper, the degree of minimum misclassification is defined. Then, by introducing decision process into variable precision rough set, a new model which is based on minimum misclassification cost with variable precision rough …set (VPRS) is proposed. Moreover, based on the minimum misclassification cost, a heuristic attribute reduction algorithm is proposed. Finally, the simulation result shows that a feasible and reliable set of attributes can be obtained with our algorithm. These results further enrich attribute reduction to effectively deal with the uncertain classification problems. Show more

Keywords: Variable precision rough set, attribute reduction, cost, misclassification, knowledge acquisition

DOI: 10.3233/JIFS-18354

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5129-5142, 2019

Authors: Mei, Kongchun | Peng, Ying | Mao, Junjun

Article Type: Research Article

Abstract: In recent years, interval type-2 fuzzy set has played an increasingly important role in decision-making. The purpose of this paper is firstly to propose fuzzy factor and interval factor of interval type-2 fuzzy sets (IT2FSs) based on α -cuts. Then, entropy and cross-entropy formulas of IT2FSs are put forward to measure the fuzzy information and mutual information between IT2FSs based on the two factors. Furthermore, IT2FS comprehensive cross-entropy formula is brought forward to measure the relative uncertain relationships among IT2FSs based on IT2FS cross-entropy formula and total probability formula. In the next moment, a utility function of IT2FS is proposed …to compare the ordering relationship among IT2FSs. On the other hands, an optimal linear programming model is constructed based on IT2FS entropy, comprehensive cross-entropy and utility function to solve the optimal alternative. Finally, a simple example is utilized to testify the practicability and effectiveness of the proposed approach. Show more

Keywords: IT2FS fuzzy factor, IT2FS interval factor, cross-entropy, comprehensive relative cross-entropy, utility function

DOI: 10.3233/JIFS-18678

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5143-5156, 2019

Authors: Bej, Tripti | Pal, Madhumangal | Davvaz, Bijan

Article Type: Research Article

Abstract: The purpose of this study is to apply the intuitionistic fuzzy hyper filters to hyper BE -algebras and to derive the conditions for an intuitionistic fuzzy set to be a doubt intuitionistic fuzzy hyper filter in hyper BE -algebras. The findings of the study establish the notion that an intuitionistic fuzzy set of a hyper BE -algebra is an intuitionistic fuzzy hyper filter if and only if the complement of this intuitionistic fuzzy set is a doubt intuitionistic fuzzy hyper filter. The content of this manuscript also includes the introduction of the notion of doubt intuitionistic fuzzy implicative hyper filter …in hyper BE -algebras and some related properties. Show more

Keywords: Hyper BE-algebra, doubt intuitionistic fuzzy hyper filter, doubt intuitionistic fuzzy implicative hyper filter

DOI: 10.3233/JIFS-18824

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5157-5166, 2019

Authors: Hu, Chaofang | Yang, Na | Dong, Na | Zhou, Yimin | Ding, Baocang

Article Type: Research Article

Abstract: In this paper, the α -satisfactory goal programming (GP) method is proposed for multi-objective optimization (MOO) with priorities and fuzzy parameters. Fuzzy parameters are treated as fuzzy numbers, and all objectives are modeled into fuzzy goals over α -level sets. The order of α -satisfactory degrees is applied to preemptive priority requirement, where the objectives with higher priority can achieve the higher α -satisfactory degree. In order to guarantee the feasibility and seek the preferred solution, a priority variable is introduced to relax the strict order. For three fuzzy relations, GP is combined with the relaxed order constraint to formulate the different …α -satisfactory optimization models. By regulating optimization parameters λ and α , the most satisfactory solution over fuzzy parameters can be obtained, and the balance between optimization and priority can be realized. The reformulated α -GP models are proved to be feasible, and their solutions are guaranteed to be M-α -Pareto optimal by the test model. In order to decrease optimization burden, the algorithm to compute the α -maximum regulating parameter is proposed, by which the bound of λ can be determined. The effectiveness of the proposed method is well demonstrated by numerical examples. Show more

Keywords: Multi-objective optimization, fuzzy parameter, priority, satisfactory degree, goal programming

DOI: 10.3233/JIFS-18904

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5167-5178, 2019

Authors: Nozari, T. | Ameri, R.

Article Type: Research Article

Abstract:   We introduce the notion of fuzzy soft hypealgebras as an extension of the notion of soft hyperalgebras as well as soft algebras. Also, some basic properties of fuzzy soft sets and homomorphisms between fuzzy soft hypealgebras are presented and discussed. Finally, we study the image and inverse image of a fuzzy soft hypealgebra under a fuzzy soft hyperalgebra homomorphism.

Keywords: Soft set, soft hyperalgebra, fuzzy soft hyperalgebra, homomorphism

DOI: 10.3233/JIFS-190016

Citation: Journal of Intelligent & Fuzzy Systems, vol. 37, no. 4, pp. 5179-5186, 2019