Original Research Article

Article volume = 2024 and issue = 1

Pages: 60–67

Article publication Date: December 09, 2023

# A Suggestion for Exploring an Interval-Valued Fermatean Fuzzy Shortest Path Problem

#### Said Broumi(a) and S.Krishna Prabha(b)

(a) Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco Regional Center for the Professions of Education and Training (C.R.M.E.F), Casablanca-Settat, Morocco.

(b) Department of Mathematics PSNA College of Engineering and Technology-Dindigul.

##### Abstract:

Fermatean fuzzy set theory, a state-of-the-art mathematical method, has been developed to address the uncertainty of various real-world scenarios. The Fermatean fuzzy set was created to allow analytical management of uncertain data from common real-world decision-making situations. Due to the inadequate data available, decision-makers find it challenging to define the degree of membership (MG) and non-membership (NG) with sharp values. In these situations, intervals BG and NG are good choices. In this article, we use an interval set of values in the Fermatean fuzzy context to formulate the shortest path problem(SPP). Next, a defuzzification method using score function is proposed. To further illustrate the viability and efficacy of the suggested framework, a mathematical formulation is also presented.

##### Keywords:

Fermatean fuzzy set, Shortest path problem, Interval value Fermatean fuzzy number, Score function, Intuitionistic fuzzy set, Pythagorean fuzzy set.

##### References:
• [1] V. Anusuya and R. Sathyaa, Type-2 fuzzy shortest path on similarity measure, Bull. Math. Stat. Res,2, (2014) 418–422. 1
• [2] K.T. Atanassov, Intuitionistic fuzzy sets Fuzzy Sets Syst , 20,(1986) 87–96, 1
• [3] A. Dey, A. Pal, and T. Pal Interval Type 2 Fuzzy Set in Fuzzy Shortest Path Problem. In Mathematics ,MDPIAG, Vol.4, (2016), 62 1
• [4] A. Ebrahimnejad, S. Tabatabaei, and F.J.Santos-Arteaga, A novel lexicographic optimization method for solving shortest path problems with interval-valued triangular fuzzy arc weights, In Journal of Intelligent and Fuzzy Systems ,39(1), (2020), 1277–1287.
• [5] V.Geetha Sivaraman, Lakshmana Gomathi Nayagam, and S. Muralikrishnan, Multi-criteria decision-making method based on interval-valued intuitionistic fuzzy sets, Expert Systems with Applications,38(3), (2011),1464-1467 1
• [6] N. Jan, M Aslam, K. Ullah, T. Mahmood and J. Wang, An approach towards decision making and shortest path problems using the concepts of interval‐valued Pythagorean fuzzy information, In International Journal of Intelligent Systems ,34(10), (2019). 1
• [7] G. Kumar, R.K.Bajaj and N. Gandotra, Algorithm for Shortest Path Problem in a Network with Interval-valued Intuitionistic Trapezoidal Fuzzy Number, In Procedia Computer Science ,38(3) ,(2015),123–129. 1
• [8] R.Parvathi , M.Karunambigai , Intuitionistic fuzzy graphs. In: Reusch B, ed. Computational Intelligence, Theory and Applications. Berlin, Heidelberg:(2006) Springer,139‐150. 1
• [9] L.Sahoo ,Some score functions on fermatean fuzzy sets and its application to bride selection based on TOPSIS method,Int J Fuzzy Syst Appl , 10(3),(2021),18–29. 1
• [10] T. Senapati and R. Yager , Fermatean Fuzzy Sets, Journal of Ambient Intelligence and Humanized Computing , 11,( 2020), 663-674. 1
• [11] T. Senapati, and R.R.Yager, Some New Operations Over Fermatean Fuzzy Numbers and Application of Fermatean Fuzzy WPM in Multiple Criteria Decision Making, In Informatica , 11(3), ( 2019), 391–412. 1
• [12] A. Shannon and K. Atanassov , A first step to a theory of the intuitionistic fuzzy graphs”, Proc. of the First Workshop on Fuzzy Based Expert Systems (D. Lakov, Ed.),11(3), Sofia,(1994), 59-61. 1
• [13] V.P .Singh,K. Sharma, and U.Jain, Solving Fuzzy Shortest Path Problem with Decision Maker’s Perspective”, In: Laishram, B., Tawalare, A. (eds) Recent Advancements in Civil Engineering. Lecture Notes in Civil Engineering, Springer, Singapore,175, 2022. 1
• [14] G. Thamizhendhi ,C. Kiruthica and S. Suresh , Fermatean fuzzy hypergraph ,Journal of Hunan University Natural Sciences, 48(12) (2011), 2333-2340. 1
• [15] K. Vidhya and A. Saraswathi, An improved A search algorithm for the shortest path under interval-valued Pythagorean fuzzy environment,. Granul. Comput. (2022). 1