scholarly journals An Improved A* Algorithm Based on Hesitant Fuzzy Set Theory for Multi-Criteria Arctic Route Planning

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 765 ◽  
Author(s):  
Yangjun Wang ◽  
Ren Zhang ◽  
Longxia Qian
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Climate Models ◽  
Route Planning ◽  
Planning System ◽  
Hesitant Fuzzy Set ◽  
The Arctic ◽  
Planning Problem ◽  
A Algorithm

This paper presents a new route planning system for the purpose of evaluating the strategic prospects for future Arctic routes. The route planning problem can be regarded as a multi criteria decision making problem with large uncertainties originating from multi-climate models and experts’ knowledge and can be solved by a modified A* algorithm where the hesitant fuzzy set theory is incorporated. Compared to the traditional A* algorithm, the navigability of the Arctic route is firstly analyzed as a measure to determine the obstacle nodes and three key factors to the vessel navigation including sailing time, economic cost and risk are overall considered in the HFS-A* algorithm. A numerical experiment is presented to test the performance of the proposed algorithm.

scholarly journals HESITANT FUZZY SET THEORY APPLIED TO FILTERS IN MTL-ALGEBRAS

2014 ◽  
Vol 36 (4) ◽  
pp. 813-830 ◽  
Author(s):  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hesitant Fuzzy Set

Reliability Analysis for Environment Systems Using Dual Hesitant Fuzzy Set

2019 ◽  
pp. 162-173 ◽  
Author(s):  
Akshay Kumar ◽  
Mangey Ram
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Reliability Function ◽  
Hesitant Fuzzy Set ◽  
Electronic Systems ◽  
Hesitant Fuzzy Sets ◽  
Fuzzy Reliability ◽  
Dual Hesitant Fuzzy Set

In this chapter, we deal with dual hesitant fuzzy set theory and compute the fuzzy reliability with lifetime components of different electronic systems, such as series and parallel systems from a Markov chain technique. In dual hesitant fuzzy sets, we have membership and non-membership degree function whereas hesitant fuzzy sets only have membership function. In this chapter we also discuss the Weibull distribution and reliability function of the proposed systems. A numerical example is also given in the end of proposed algorithm.

On Connections of Soft Set Theory with Existing Mathematics of Uncertainties: A Short Discussion for Non-Mathematicians with Respect to Soft Set Theory

2018 ◽  
Vol 14 (01) ◽  
pp. 1-9 ◽  
Author(s):  
Santanu Acharjee
Keyword(s):  
Set Theory ◽  
Rough Set ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Rough Set Theory ◽  
Mathematical Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Hesitant Fuzzy Set ◽  
Short Discussion

This paper focuses on two very important questions: “what is the future of a hybrid mathematical structure of soft set in science and social science?” and “why should we take care to use hybrid structures of soft set?”. At present, these are the most fundamental questions; which encircle a few prominent areas of mathematics of uncertainties viz. fuzzy set theory, rough set theory, vague set theory, hesitant fuzzy set theory, IVFS theory, IT2FS theory, etc. In this paper, we review connections of soft set theory and hybrid structures in a non-technical manner; so that it may be helpful for a non-mathematician to think carefully to apply hybrid structures in his research areas. Moreover, we must express that we do not have any intention to nullify contributions of fuzzy set theory or rough set theory, etc. to mankind; but our main intention is to show that we must be careful to develop any new hybrid structure with soft set. Here, we have a short discussion on needs of artificial psychology and artificial philosophy to enrich artificial intelligence.

scholarly journals Inf-Hesitant Fuzzy Ideals in BCK/BCI-Algebras

2020 ◽  
Vol 49 (1) ◽  
Author(s):  
Young Bae Jun ◽  
Seok-Zun Song
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Ideal

Based on the hesitant fuzzy set theory which is introduced by Torra in the paper [12], the notions of Inf-hesitant fuzzy subalgebras, Inf-hesitant fuzzy ideals and Inf-hesitant fuzzy p-ideals in BCK/BCI-algebras are introduced, and their relations and properties are investigated. Characterizations of an Inf-hesitant fuzzy subalgebras, an Inf-hesitant fuzzy ideals and an Inf-hesitant fuzzy p-ideal are considered. Using the notion of BCK-parts, an Inf-hesitant fuzzy ideal is constructed. Conditions for an Inf-hesitant fuzzy ideal to be an Inf-hesitant fuzzy p-ideal are discussed. Using the notion of Inf-hesitant fuzzy (p-) ideals, a characterization of a p-semisimple BCI-algebra is provided. Extension properties for an Inf-hesitant fuzzy p-ideal is established.

scholarly journals Subalgebras and Ideals in BCK/BCI-algebras Based on Uni-hesitant Fuzzy Set Theory

2018 ◽  
Vol 11 (2) ◽  
pp. 417-430 ◽  
Author(s):  
G. Muhiuddin ◽  
Shuaa Aldhafeeri
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Closed Ideal ◽  
Hesitant Fuzzy Set ◽  
Fuzzy Algebra ◽  
Fuzzy Ideal

In the present paper, the notions of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals in BCK-algebras and BCI-algebras are introduced, and several related properties are investigated. Characterizations of uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are considered, and a new uni-hesitant fuzzy algebra (resp. uni-hesitant fuzzy (closed) ideal) from old one is established. Relations between uni-hesitant fuzzy algebras and uni-hesitant fuzzy (closed) ideals are discussed, and conditions for a uni-hesitant fuzzy ideal to be hesitant closed are provided.

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