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Search Results (13)
  • 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

    Introduction to U-Number Calculus

    R. A. Alieva,b

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 211-216, 2018, DOI:10.1080/10798587.2017.1330311

    Abstract Commonsense reasoning plays a pivotal role in the development of intelligent systems for decisionmaking, system analysis, control and other applications. As Prof. L. Zadeh mentions a kernel of the theory of commonsense is the concept of usuality. Zadeh suggested main principles of the theory of usuality, unfortunately up to present day; a fundamental and systemic approach to reasoning with usual knowledge is not developed.
    In this study, we develop a new approach to calculus of usual numbers (U-numbers). We consider a U-number as a Z-number, where the second component is “usually”. Validity of the suggested approach 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

    A Z-Number Valued Regression Model and Its Application

    Lala M. Zeinalovaa, O. H. Huseynovb, P. Sharghic

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 187-192, 2018, DOI:10.1080/10798587.2017.1327551

    Abstract Regression analysis is widely used for modeling of real-world processes in various fields. It should be noted that information relevant to real-world processes is characterized by imprecision and partial reliability. This involves combination of fuzzy and probabilistic uncertainties. Prof.. L. Zadeh introduced the concept of a Z-number as a formal construct for dealing with such information. The present stateof-the-art of regression analysis under Z-number valued information is very scarce. In this paper we consider a Z-number valued multiple regression analysis and its application to a real-world decisionmaking problem. The obtained results show applicability of the More >

  • Open Access

    ARTICLE

    Modeling of Consumer Buying Behaviour Using Z-Number Concept

    Gunay Sadikoglu

    Intelligent Automation & Soft Computing, Vol.24, No.1, pp. 173-178, 2018, DOI:10.1080/10798587.2017.1327159

    Abstract Consumer behaviour has always been of a great interest in marketing research. The consumer buying behaviour has become an integral part of strategic market planning and includes mental, emotional and physical activities. The consumer behaviour and decision-making process are usually subject to uncertainties related to influences of socio-cultural, psychological and personal factors. In this paper, the Z-number concept is applied for handling uncertainties in analysing the consumer buying behaviour. 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 >

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