Hukuhara difference of Z-numbers

Aliev, R. A.; Pedrycz, Witold; Huseynov, Oleg H.

doi:10.1016/j.ins.2018.07.033

Cited by 41 publications

(4 citation statements)

References 37 publications

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“…One of the limitations of the original OPA is its inability to handle linguistic information, and the fuzzy set theory provides a promising avenue to overwhelm this limitation . In real-world problems, values of interest are often not measured but are estimated based on the perception and knowledge of a human being thus, natural language-based estimations can be used, which can be formally described by fuzzy numbers (Aliev et al 2018 ). In light of this background, it is stated that the OPA-F attempts to transform linguistic information into triangular fuzzy numbers and then uses the OPA's unique approach of linear programming based multi-attribute decision making in the two-fold setting.…”

Section: Opa For Fuzzy Linguistic Information (Opa-f)mentioning

confidence: 99%

Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era

2021

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Because of the COVID-19 outbreak, the supply of both essential and non-essential goods and services has been unprecedentedly disrupted. In the absence of any playbook, the need for innovative technologies to aid recovery from the Supply Chain (SC) disruptions quickly and effectively becomes persistent. The study aims to develop an innovative decision-making technology to handle the supplier selection problems arising from the frequent impreciseness and incompleteness in the nowadays' SC reports within the framework of the gresilient supply chain management. Through the integration of green and resilience aspects of the SCs, the supply chain 'gresilience' has been conceptualized. In light of this construct and based on the data collected from a manufacturing firm, the study deploys a two-fold decomposition of the core algorithm of the Ordinal Priority Approach (OPA), one for attributes and other for alternatives. It extends the OPA to the Fuzzy OPA (OPA-F) for solving the supplier selection problems. The study illustrates how green and resilience aspects of the SC can be integrated to better understand the gresilient suppliers in the wake of the SC disruptions. A novel construct of SC Gresilience is also furnished along with a novel definition of SC Gresilience. It also provides an innovative SC decision-making technology to help procurement managers to evaluate their suppliers. The resultant framework can help them better prepare for the COVID-19 like disruptions in the future.

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Section: Opa For Fuzzy Linguistic Information (Opa-f)mentioning

confidence: 99%

Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era

2021

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“…Subsequently, the operations of continuous Z-numbers were further provided by Aliev et al [24] through discretization. Aiming to reduce computational complexity and improve computational efficiency, Aliev et al [25] presented a basic approach for developing the concept of Z-Numbers and provided examples to demonstrate the validity of their method using the Hukuhara distance. Qiu et al [26] presented the process of computing the generalized difference for discrete and continuous Z-numbers.…”

Section: Introductionmentioning

confidence: 99%

The Operational Laws of Symmetric Triangular Z-Numbers

Li,

Liao,

et al. 2024

Mathematics

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To model fuzzy numbers with the confidence degree and better account for information uncertainty, Zadeh came up with the notion of Z-numbers, which can effectively combine the objective information of things with subjective human interpretation of perceptive information, thereby improving the human comprehension of natural language. Although many numbers are in fact Z-numbers, their higher computational complexity often prevents their recognition as such. In order to reduce computational complexity, this paper reviews the development and research direction of Z-numbers and deduces the operational rules for symmetric triangular Z-numbers. We first transform them into classical fuzzy numbers. Using linear programming, the extension principle of Zadeh, the convolution formula, and fuzzy number algorithms, we determine the operational rules for the basic operations of symmetric triangular Z-numbers, which are number-multiplication, addition, subtraction, multiplication, power, and division. Our operational rules reduce the complexity of calculation, improve computational efficiency, and effectively reduce the information difference while being applicable to other complex operations. This paper innovatively combines Z-numbers with classical fuzzy numbers in Z-number operations, and as such represents a continuation and innovation of the research on the operational laws of Z-numbers.

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“…It looks more adaptable and significant from an intuitive perspective for formalizing the functionality of a decision-making procedure. Many scholars work with fuzzy Z̆ - numbers such as ranking Z̆ -numbers [ 4 ], numerical solution of fuzzy equation [ 5 ], modeling for uncertain nonlinear systems [ 6 ], Hukuhara difference [ 7 ], decision-making using Z̆ -numbers [ 8 , 9 ],etc.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of economic development policies using a spherical fuzzy extended TODIM model with Z̆-numbers

et al. 2023

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Zadeh’s Z̆-numbers are able to more effectively characterize uncertain information. Combined with “constraint” and “reliability”. It is more powerful at expressing human knowledge. While the reliability of data can have a direct impact on the precision of decisions. The key challenge in solving a Z̆-number issue is reasoning about both fuzzy and probabilistic uncertainty. Existing research on the Z̆-number measure is only some, and most studies cannot adequately convey the benefits of Z̆-information and the properties of Z̆-number. Considering this study void, this work concurrently investigated the randomness and fuzziness of Z̆-number with Spherical fuzzy sets. We first introduced the spherical fuzzy Z-numbers (SFZNs), whose elements are pairwise comparisons of the decision-maker’s options. It can be used effectively to make true ambiguous judgments, reflecting the fuzzy nature, flexibility, and applicability of decision making data. We developed the operational laws and aggregation operators such as the weighted averaging operator, the ordered weighted averaging operator, the hybrid averaging operator, the weighted geometric operator, the ordered weighted geometric operator, and the hybrid geometric operator for SFZ̆Ns. Furthermore, two algorithm are developed to tackle the uncertain information in the form of spherical fuzzy Z̆-numbers based to the proposed aggregation operators and TODIM methodology. Finally, we developed the relative comparison and discussion analysis to show the practicability and efficacy of the suggested operators and approach.

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Hukuhara difference of Z-numbers

Cited by 41 publications

References 37 publications

Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era

Gresilient supplier selection through Fuzzy Ordinal Priority Approach: decision-making in post-COVID era

The Operational Laws of Symmetric Triangular Z-Numbers

Evaluation of economic development policies using a spherical fuzzy extended TODIM model with Z̆-numbers

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