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Keywords = ordered semihypergroup

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11 pages, 286 KB  
Article
Multipolar Fuzzy Hyperideals in Ordered Semihypergroups
by Osman Kazancı, Sarka Hoskova-Mayerova and Bijan Davvaz
Mathematics 2022, 10(19), 3424; https://doi.org/10.3390/math10193424 - 21 Sep 2022
Cited by 4 | Viewed by 1273
Abstract
An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The multi-polar fuzzy sets was created as a useful mechanism to portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of multi-polar [...] Read more.
An multi-polar fuzzy set is a robust mathematical model to examine multipolar, multiattribute, and multi-index data. The multi-polar fuzzy sets was created as a useful mechanism to portray uncertainty in multiattribute decision making. In this article, we consider the theoretical applications of multi-polar fuzzy sets. We present the notion of multi-polar fuzzy sets in ordered semihypergroups and define multi-polar fuzzy hyperideals (bi-hyperideals, quasi hyperideals) in an ordered semihypergroup. Relations between multi-polar fuzzy hyperideals, multi-polar fuzzy bi-hyperideals and multi-polar fuzzy quasi hyperideals are discussed. Full article
30 pages, 4869 KB  
Article
On Cyclic Associative Semihypergroups and Neutrosophic Extended Triplet Cyclic Associative Semihypergroups
by Minghao Hu and Xiaohong Zhang
Mathematics 2022, 10(4), 535; https://doi.org/10.3390/math10040535 - 9 Feb 2022
Cited by 9 | Viewed by 1917
Abstract
This paper introduces a new concept called cyclic associative semihypergroup (CA-semihypergroup). The relationships among CA-semihypergroups, Semihypergroups and LA-semihypergroups are studied through some interesting examples. The relationships among various NET-CA-semihypergroups are also studied. The main properties of strong pure neutrosophic extended triplet CA-semihypergroups (SP-NET-CA-semihypergroups) [...] Read more.
This paper introduces a new concept called cyclic associative semihypergroup (CA-semihypergroup). The relationships among CA-semihypergroups, Semihypergroups and LA-semihypergroups are studied through some interesting examples. The relationships among various NET-CA-semihypergroups are also studied. The main properties of strong pure neutrosophic extended triplet CA-semihypergroups (SP-NET-CA-semihypergroups) are obtained. In particular, the algorithm of a generated CA-semihypergroup of order tm+n by two known CA-semihypergroups of order m and n is proven, and a CA-semihypergroup of order 19 is obtained by using a Python program. Moreover, it is proven that five different definitions, which can all be used as the definition of SP-NET-CA-Semihypergroup, are equivalent. Full article
(This article belongs to the Special Issue Algebra and Discrete Mathematics 2021)
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10 pages, 251 KB  
Article
An Investigation on Weak Concepts in Ordered Hyperstructures
by Yongsheng Rao, Jietong Zhao, Aysha Khan, Maryam Akhoundi and Saber Omidi
Symmetry 2021, 13(12), 2300; https://doi.org/10.3390/sym13122300 - 2 Dec 2021
Cited by 1 | Viewed by 1548
Abstract
The class of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures is a generalization of pseudoorders and interior hyperideals. In this work, we study the concept of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures and explore some results [...] Read more.
The class of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures is a generalization of pseudoorders and interior hyperideals. In this work, we study the concept of weak pseudoorders and left weak interior hyperideals in ordered hyperstructures and explore some results concerning the new defined concepts for ordered hyperrings and ordered Γ-semihypergroups. In this regards, we intend to concentrate our efforts on the relationship between the left weak interior hyperideal and interior hyperideal of an ordered hyperstructure. A characterization of a regular ordered hyperstructure via a left weak interior hyperideal is given. Finally, we characterize the notion of left weak interior simple ordered hyperstructures in terms of left weak interior hyperideals. Full article
21 pages, 314 KB  
Article
Regularities in Ordered n-Ary Semihypergroups
by Jukkrit Daengsaen and Sorasak Leeratanavalee
Mathematics 2021, 9(16), 1857; https://doi.org/10.3390/math9161857 - 5 Aug 2021
Cited by 6 | Viewed by 2051
Abstract
This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1jn and n3. We first introduce the notion of (softly) left [...] Read more.
This paper deals with a class of hyperstructures called ordered n-ary semihypergroups which are studied by means of j-hyperideals for all positive integers 1jn and n3. We first introduce the notion of (softly) left regularity, (softly) right regularity, (softly) intra-regularity, complete regularity, generalized regularity of ordered n-ary semihypergroups and investigate their related properties. Several characterizations of them in terms of j-hyperideals are provided. Finally, the relationships between various classes of regularities in ordered n-ary semihypergroups are also established. Full article
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