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States on pseudo EQ-algebras

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Abstract

In this paper, we mainly introduce the concepts of states on pseudo EQ-algebras and investigate their properties and existence as well as their relationships. Firstly, we define some notions and investigate their properties, which will be used in the following sections. Then, we define the concepts of Bosbach states and state-morphisms on pseudo EQ-algebras and investigate their properties and relationships. We prove that each state-morphism is a Bosbach state. Also, we introduce the fantastic filters and pseudo MV-filters and investigate the existence of states by using the two filters. We prove that they coincide on good pseudo EQ-algebras and there exists a Bosbach state if and only if there exists a fantastic filter under special pseudo EQ-algebras. Moreover, we introduce the notion of Riečan state and investigate their properties and connections between the Bosbach states and Riečan states. Also, we prove that any Bosbach state is a Riečan state in the normal pseudo EQ-algebras, but the inverse is not true in general. Finally, we prove that the Bosbach states and Riečan states coincide for a kind of particular pseudo EQ-algebras.

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Funding

This research was partially supported by a grant of National Natural Science Foundation of China (11971384).

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Authors and Affiliations

  1. School of Mathematics, Northwest University, Xi’an, 710127, China

    Jie Qiong Shi & Xiao Long Xin

  2. School of Science, Xi’an Polytechnic University, Xi’an, 710048, China

    Xiao Long Xin

  3. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    Rajab Ali Borzooei

Authors
  1. Jie Qiong Shi
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  2. Xiao Long Xin
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  3. Rajab Ali Borzooei
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Contributions

JQS was involved in writing—original draft preparation. XLX was involved in conceptualization and methodology. RAB was involved in writing—reviewing and editing.

Corresponding author

Correspondence to Xiao Long Xin.

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Shi, J.Q., Xin, X.L. & Borzooei, R.A. States on pseudo EQ-algebras. Soft Comput 26, 13219–13231 (2022). https://doi.org/10.1007/s00500-022-07496-9

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