Yushan Yin¹, Witold Pedrycz^1,2, Zhiwu Li^1,*

CMC-Computers, Materials & Continua, Vol.79, No.1, pp. 623-650, 2024, DOI:10.32604/cmc.2024.048787

Abstract Utilizing granular computing to enhance artificial neural network architecture, a new type of network emerges—the granular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability to process both numerical and granular data, leading to improved interpretability. This paper proposes a novel design method for constructing GNNs, drawing inspiration from existing interval-valued neural networks built upon NNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzy numbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizes a uniform distribution of information granularity to granulate connections with… More >

Shahid Mahmood^1,*, Muhammad Amin², Mubashir Baig Mirza¹, Salem Abu-Ghumsan¹, Muhammad Akram³, Zahid Mahmood Janjua⁴, Arslan Shahid⁵, Usman Shahid⁶

CMC-Computers, Materials & Continua, Vol.74, No.2, pp. 4469-4481, 2023, DOI:10.32604/cmc.2023.030728

Abstract Cancer is a disease that is rapidly expanding in prevalence all over the world. Cancer cells can metastasize, or spread, across the body and impact several different cell types. Additionally, the incidence rates of several subtypes of cancer have been on the rise in India. The countermeasures for the cancer disease can be taken by determining the specific expansion rate of each type. To rank the various forms of cancer’s rate of progression, we used some of the available data. Numerous studies are available in the literature which show the growth rate of cancer by different techniques. The accuracy of… More >

Raman Kumar Goyal¹, Jaskirat Singh¹, Nidhi Kalra¹, Anshu Parashar^1,*, Gagan Singla², Sakshi Kaushal²

Computer Systems Science and Engineering, Vol.41, No.1, pp. 157-170, 2022, DOI:10.32604/csse.2022.018962

Abstract This paper proposes anoptimal fuzzy-based model for obtaining crisp priorities for Fuzzy-AHP comparison matrices. Crisp judgments cannot be given for real-life situations, as most of these include some level of fuzziness and complexity. In these situations, judgments are represented by the set of fuzzy numbers. Most of the fuzzy optimization models derive crisp priorities for judgments represented with Triangular Fuzzy Numbers (TFNs) only. They do not work for other types of Triangular Shaped Fuzzy Numbers (TSFNs) and Trapezoidal Fuzzy Numbers (TrFNs). To overcome this problem, a sum of squared error (SSE) based optimization model is proposed. Unlike some other methods,… More >

S. Rout¹, S. Chakraverty^1,*

CMES-Computer Modeling in Engineering & Sciences, Vol.121, No.3, pp. 947-980, 2019, DOI:10.32604/cmes.2019.08036

Abstract The dynamic analysis of damped structural system by using finite element method leads to nonlinear eigenvalue problem (NEP) (particularly, quadratic eigenvalue problem). In general, the parameters of NEP are considered as exact values. But in actual practice because of different errors and incomplete information, the parameters may have uncertain or vague values and such uncertain values may be considered in terms of fuzzy numbers. This article proposes an efficient fuzzy-affine approach to solve fully fuzzy nonlinear eigenvalue problems (FNEPs) where involved parameters are fuzzy numbers viz. triangular and trapezoidal. Based on the parametric form, fuzzy numbers have been transformed into… More >

Diptiranjan Behera^1,2, Hong-Zhong Huang¹, S. Chakraverty³

CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.2, pp. 67-87, 2015, DOI:10.3970/cmes.2015.108.067

Abstract Fuzzy systems of linear equations play a vital role in various applications of engineering, science and finance problems. This paper proposes a new method for solving Fully Fuzzy System of Linear Equations (FFSLE) using the linear programming problem approach. There is no restriction on the elements of coefficient matrix. The proposed method is able to solve the system, when the elements of the fuzzy unknown vector are both non-negative and non-positive. Triangular convex normalized fuzzy sets are considered for the present analysis. Known example problems are solved and compared with the results of existing methods to illustrate the efficacy and… More >

S. Chakraverty^1,2, Smita Tapaswini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.103, No.2, pp. 71-90, 2014, DOI:10.3970/cmes.2014.103.071

Abstract Fractional Fornberg-Whitham equation has a vast application in physics. There exist various investigations for the above problem by considering the variables and parameters as crisp/exact. In practice, we may not have these parameters exactly but those may be known in some uncertain form. In the present paper, these uncertainties are taken as interval/fuzzy and the authors proposed here a new method viz. that of the double parametric form of fuzzy numbers to handle the uncertain fractional Fornberg-Whitham equation. Using the single parametric form of fuzzy numbers, original fuzzy fractional Fornberg-Whitham equation is converted first to an interval based fuzzy differential… More >

Diptiranjan Behera¹, Snehashish Chakraverty²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.5, pp. 317-337, 2013, DOI:10.3970/cmes.2013.096.317

Abstract This paper targets to analyse the static response of structures with fuzzy parameters using fuzzy finite element method. Here the material, geometrical properties and external load applied to the structures are taken as uncertain. Uncertainties presents in the parameters are modelled through convex normalised fuzzy sets. Fuzzy finite element method converts the problem into fuzzy or fully fuzzy system of linear equations for static analysis. As such here, two new methods are proposed to solve the fuzzy and fully fuzzy system of linear equations. Numerical examples for structures with uncertain system parameters that are in term of triangular fuzzy number… More >

Nizami Gasilov¹, Şahin Emrah Amrahov², Afet Golayoğlu Fatullayev¹, Halil İbrahim Karakaş¹, Ömer Akın³

CMES-Computer Modeling in Engineering & Sciences, Vol.75, No.3&4, pp. 189-204, 2011, DOI:10.3970/cmes.2011.075.189

Abstract In this paper, linear systems with a crisp real coefficient matrix and with a vector of fuzzy triangular numbers on the right-hand side are studied. A new method, which is based on the geometric representations of linear transformations, is proposed to find solutions. The method uses the fact that a vector of fuzzy triangular numbers forms a rectangular prism in n-dimensional space and that the image of a parallelepiped is also a parallelepiped under a linear transformation. The suggested method clarifies why in general case different approaches do not generate solutions as fuzzy numbers. It is geometrically proved that if… More >