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A New Generalization of Hesitant and Interval-Valued Fuzzy Ideals of Ternary Semigroups
Pongpun Julatha,Aiyared Iampan 한국지능시스템학회 2021 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.21 No.2
The main aim of this article is to introduce the concept of a sup-hesitant fuzzy ideal, which is a generalization of a hesitant fuzzy ideal and an interval-valued fuzzy ideal, in a ternary semigroup. Some characterizations of a sup-hesitant fuzzy ideal are examined in terms of a fuzzy set, a hesitant fuzzy set, and an interval valued fuzzy set. Further, we discuss the relation between an ideal and a generalization of a characteristic hesitant fuzzy set and a characteristic interval-valued fuzzy set.
(inf,sup)-HESITANT FUZZY BI-IDEALS OF SEMIGROUPS
PONGPUN JULATHA,AIYARED IAMPAN The Korean Society for Computational and Applied M 2023 Journal of applied mathematics & informatics Vol.41 No.2
In this paper, we introduce the concepts of (inf, sup)-hesitant fuzzy subsemigroups and (inf, sup)-hesitant fuzzy (generalized) bi-ideals of semigroups, and investigate their properties. The concepts are established in terms of sets, fuzzy sets, negative fuzzy sets, interval-valued fuzzy sets, Pythagorean fuzzy sets, hesitant fuzzy sets, and bipolar fuzzy sets. Moreover, some characterizations of bi-ideals, fuzzy bi-ideals, anti-fuzzy bi-ideals, negative fuzzy bi-ideals, Pythagorean fuzzy bi-ideals, and bipolar fuzzy bi-ideals of semigroups are given in terms of the (inf, sup)-type of hesitant fuzzy sets. Also, we characterize a semigroup which is completely regular, a group and a semilattice of groups by (inf, sup)-hesitant fuzzy bi-ideals.
Pythagorean fuzzy soft sets over UP-algebras
Akarachai Satirad,Rukchart Prasertpong,Pongpun Julatha,Ronnason Chinram,Aiyared Iampan 한국전산응용수학회 2023 Journal of applied mathematics & informatics Vol.41 No.3
This paper aims to apply the concept of Pythagorean fuzzy soft sets (PFSSs) to UP-algebras. Then we introduce five types of PFSSs over UP-algebras, study their generalization, and provide illustrative examples. In addition, we study the results of four operations of two PFSSs over UP-algebras, namely, the union, the restricted union, the intersection, and the extended intersection. Finally, we will also discuss $t$-level subsets of PFSSs over UP-algebras to study the relationships between PFSSs and special subsets of UP-algebras.
Bipolar Fuzzy Shift UP-Filters
Thiti Gaketem,Pannawit Khamrot,Pongpun Julatha,Rukchart Prasertpong,Aiyared Iampan 한국지능시스템학회 2023 INTERNATIONAL JOURNAL of FUZZY LOGIC and INTELLIGE Vol.23 No.3
In this paper, we present the concept of bipolar fuzzy shift UP-filters of UP-algebras by applying the concept of shift UP-filters to bipolar fuzzy sets and investigating their essential properties. In UP-algebras, we found that every bipolar fuzzy strong UP-ideal is a bipolar fuzzy shift UP-filter, and every bipolar fuzzy shift UP-filter is a bipolar fuzzy UP-filter. An important relationship between bipolar fuzzy shift UP-filters and their bipolar fuzzy characteristic functions is presented. The relations between bipolar fuzzy shift UP-filters and other shift UP-filters (fuzzy and neutrosophic shift UP-filters) are given. Finally, characterizations of bipolar fuzzy shift UP-filters are investigated in terms of level, fuzzy, and neutrosophic sets.