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  • Open Access

    ARTICLE

    Fully Completed Spherical Fuzzy Approach-Based Z Numbers (PHI Model) for Enhanced Group Expert Consensus

    Phi-Hung Nguyen*

    CMC-Computers, Materials & Continua, Vol.80, No.1, pp. 1655-1675, 2024, DOI:10.32604/cmc.2024.050713

    Abstract This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets (SFSs) and Z-Numbers (SFZs). A novel group expert consensus technique, the PHI model, is developed to address the inherent limitations of both SFSs and the traditional Delphi technique, particularly in uncertain, complex scenarios. In such contexts, the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations. This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers, encompassing weighted geometric and arithmetic operators alongside fully developed operators… More >

  • Open Access

    ARTICLE

    Pythagorean Fuzzy Einstein Aggregation Operators with Z-Numbers: Application in Complex Decision Aid Systems

    Shahzad Noor Abbasi1, Shahzaib Ashraf1,*, M. Shazib Hameed1, Sayed M. Eldin2,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2795-2844, 2023, DOI:10.32604/cmes.2023.028963

    Abstract The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making. The PFS is known to address the levels of participation and non-participation. To begin, we introduce the novel concept of a PFZN, which is a hybrid structure of Pythagorean fuzzy sets and the ZN. The PFZN is graded in terms of membership and non-membership, as well as reliability, which provides a strong advice in real-world decision support concerns. The PFZN is a… More >

  • Open Access

    ARTICLE

    Failure Mode and Effects Analysis Based on Z-Numbers and the Graded Mean Integration Representation

    Hanhan Zhang1, Zhihui Xu2, Hong Qian1, Xiaoyan Su1,*

    CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.2, pp. 1005-1019, 2023, DOI:10.32604/cmes.2022.021898

    Abstract Failure mode and effects analysis (FMEA) is a widely used safety assessment method in many fields. Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration. However, the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations. In this paper, an improved method is proposed based on Z-numbers and the graded mean integration representation (GMIR) to deal with the uncertain information in FMEA. First, Z-numbers are constructed based on the evaluations of risk factors O, S, D for each More >

  • Open Access

    ARTICLE

    Application of Intuitionistic Z-Numbers in Supplier Selection

    Nik Muhammad Farhan Hakim Nik Badrul Alam1,2, Ku Muhammad Naim Ku Khalif1,*, Nor Izzati Jaini1

    Intelligent Automation & Soft Computing, Vol.35, No.1, pp. 47-61, 2023, DOI:10.32604/iasc.2023.024660

    Abstract Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees. In contrast, Z-numbers consist of restriction components, with the existence of a reliability component describing the degree of certainty for the restriction. The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers, namely intuitionistic Z-numbers (IZN). The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are characterized by the membership and non-membership functions, exhibiting the degree of the hesitancy of decision-makers. This paper presents the application of such numbers… More >

  • Open Access

    ARTICLE

    New Multi-layer Method for Z-number Ranking Using Hyperbolic Tangent Function and Convex Combination

    Somayeh Ezadia, Tofigh Allahviranloob

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 217-221, 2018, DOI:10.1080/10798587.2017.1367146

    Abstract Many practical applications, under the definitive evolutionary state of the nature, the consequences of the decisions, mental states of a decision maker are required. Thus, the need is for a new concept in the analysis of decision-making. Zadeh has introduced this concept as the Z-number. Because the concept is relatively new, Z-number in fuzzy sets, hence, its basic theoretical aspects are yet undetermined. This paper presents a method for ranking Z-numbers. Hence, we propose a new method for ranking fuzzy numbers based on that of hyperbolic tangent function and convex combination. Then, using the same More >

  • Open Access

    ARTICLE

    Z-Numbers and Type-2 Fuzzy Sets: A Representation Result

    R. A. Alieva,b, Vladik Kreinovichc

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 205-210, 2018, DOI:10.1080/10798587.2017.1330310

    Abstract Traditional [0; 1] based fuzzy sets were originally invented to describe expert knowledge expressed in terms of imprecise “fuzzy” words from the natural language. To make this description more adequate, several generalizations of the traditional [0; 1] based fuzzy sets have been proposed, among them type- 2 fuzzy sets and Z-numbers. The main objective of this paper is to study the relation between these two generalizations. As a result of this study, we show that if we apply data processing to Z-numbers, then we get type-2 sets of special type —that we call monotonic. We More >

  • Open Access

    ARTICLE

    Numerical Solution of Linear Regression Based on Z-Numbers by Improved Neural Network

    Somayeh Ezadia, Tofigh Allahviranloob

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 193-204, 2018, DOI:10.1080/10798587.2017.1328812

    Abstract In this article, the researcher at first focuses on introducing a linear regression based on the Z-number. In this regression, observations are real, but the coefficients and results of observations are unknown and in the form of Z-rating. Therefore, to estimate this type of regression, we have three distinct ways depending on different conditions dominating the problem. The three methods are a combination of artificial neural networks and fuzzy generalized improvements of the technique. Moreover the method of calculating the weights of the Z-number neural network has been mentioned and the stability of neural network More >

  • Open Access

    ARTICLE

    Failure Mode and Effects Analysis Based on Z-numbers

    Wen Jiang, Chunhe Xie, Boya Wei, Yongchuan Tang

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 165-172, 2018, DOI:10.1080/10798587.2017.1327158

    Abstract The main objective of this paper is to propose a new method for failure mode and effects analysis (FMEA) based on Z-numbers. In the proposed method, firstly, Z-numbers are used to perform the valuations (Z-valuation) of the risk factors like occurrence (O), severity (S) and detection (D). Secondly, the Z-valuations of the risk factors are integrated by fuzzy weighted mean method. A new risk priority number named as ZRPN is calculated to prioritize failure modes based on a modified method of ranking fuzzy numbers. Finally, a case study for the rotor blades of an aircraft More >

  • Open Access

    ARTICLE

    Numerical Solution of Fuzzy Equations with Z-numbers Using Neural Networks

    Raheleh Jafaria, Wen Yua, Xiaoou Lib

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 151-158, 2018, DOI:10.1080/10798587.2017.1327154

    Abstract In this paper, the uncertainty property is represented by the Z-number as the coefficients of the fuzzy equation. This modification for the fuzzy equation is suitable for nonlinear system modeling with uncertain parameters. We also extend the fuzzy equation into dual type, which is natural for linearin-parameter nonlinear systems. The solutions of these fuzzy equations are the controllers when the desired references are regarded as the outputs. The existence conditions of the solutions (controllability) are proposed. Two types of neural networks are implemented to approximate solutions of the fuzzy equations with Z-number coefficients. More >

  • Open Access

    ARTICLE

    On an Optimization Method Based on Z-Numbers and the Multi-Objective Evolutionary Algorithm

    Dong Qiu, Rongwen Dong, Shuqiao Chen, Andi Li

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 147-150, 2018, DOI:10.1080/10798587.2017.1327153

    Abstract In this paper, we research the optimization problems with multiple Z-number valued objectives. First, we convert Z-numbers to classical fuzzy numbers to simplify the calculation. A new dominance relationship of two fuzzy numbers based on the lower limit of the possibility degree is proposed. Then according to this dominance relationship, we present a multi-objective evolutionary algorithm to solve the optimization problems. Finally, a simple example is used to demonstrate the validity of the suggested algorithm. More >

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