Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set

Abstract

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Intuitionistic fuzzy solid assignment problems: a software-based approach

“…In this article, the novelty of the analysis is given into a coherent, concise, and meaningful manner of analysis (Note: The optimal solution of the proposed problem is same as the solution obtained by both the PSK method [Kumar (2020c) Developing a New Approach to Solve Solid Assignment Problems Under Intuitionistic Fuzzy Environment. International Journal of Fuzzy System Applications (IJFSA), Volume 9, Issue 1, Article 1] and TORA software [Kumar (2019b) Algorithms for solving the optimization problems using fuzzy and intuitionistic fuzzy set. International Journal of System Assurance Engineering and Management]).…”

An Interval-Valued Intuitionistic Hesitant Fuzzy Methodology and Application

“…Angelov [ 1 ] has investigated an optimization technique that was based on the intersection property of intuitionistic fuzzy sets, called an intuitionistic fuzzy optimization technique, and it finds a better optimal solution of an optimization problem after fuzzy optimization technique. Recently, Mahajan [ 23 , 24 ] and Senthil et al [ 16 – 19 ] have studied IFS and applied it in several real-life optimization problems. An interval-valued intuitionistic fuzzy set (IVIFS) is a further extension of IFS and is investigated by Atanassov and Gargov [ 4 ] in which the membership and nonmembership degrees of an element are, respectively, represented by intervals in [0, 1] rather than fixed real numbers between 0 and 1.…”

Diagnosing and routing electronic service quality improvement of academic libraries with the FMEA approach in an intuitionistic fuzzy environment

“…In 1986, IFSs were proposed by Atanassov (1986, 1989, 2000), extending the notion of an FS by adding a non-membership function (He et al , 2020; Krawczak and Szkatuła, 2020; Kumar, 2020; Ngan et al , 2020; Alcantud et al , 2020). The concept of IFS is a more effective approach to dealing with vagueness than the concept of fuzzy set because it is characterized both by a membership degree and a nonmember ship degree (He et al , 2020; Krawczak and Szkatuła, 2020; Kumar, 2020; Ngan et al , 2020; Alcantud et al , 2020; Zhang et al , 2020; Verma and Sharma, 2015).…”

“…Overcoming the restrictions of fuzzy sets in handling conflicting information concerning membership of objects, this concept is used in modeling imprecision, pattern recognition, computational intelligence and decision-making (Deschrijver and Kerre, 2007; Valchos and Sergiadis, 2007; De Cock et al , 2005; Rahman, 2016; Szmidt and Kacprzyk, 2004; Ali et al , 2018; Davvaz and Hassani Sadrabadi, 2016; Ngan et al , 2020; Krawczak and Szkatuła, 2020; He et al , 2020; Alcantud et al , 2020). As a significant content in fuzzy mathematics, it has attracted many researchers (He et al , 2020; Krawczak and Szkatuła, 2020; Kumar, 2020; Ngan et al , 2020; Alcantud et al , 2020) and IFSs have been used across different fields of science (Zhang et al , 2020; Qin et al , 2020; Ngan et al , 2020; Kumar, 2020; Krawczak and Szkatuła, 2020; He et al , 2020; Alcantud et al , 2020; Ali et al , 2018). Rather than deriving the non-membership degree of an element directly from its membership degree, it is sometimes more reasonable to specify the nonmember ship degree independently of µ c = 1 − µ (Zhang et al , 2020; Ngan et al , 2020; Kumar, 2020; He et al , 2020; Garg and Rani, 2020).…”

“…As a significant content in fuzzy mathematics, it has attracted many researchers (He et al , 2020; Krawczak and Szkatuła, 2020; Kumar, 2020; Ngan et al , 2020; Alcantud et al , 2020) and IFSs have been used across different fields of science (Zhang et al , 2020; Qin et al , 2020; Ngan et al , 2020; Kumar, 2020; Krawczak and Szkatuła, 2020; He et al , 2020; Alcantud et al , 2020; Ali et al , 2018). Rather than deriving the non-membership degree of an element directly from its membership degree, it is sometimes more reasonable to specify the nonmember ship degree independently of µ c = 1 − µ (Zhang et al , 2020; Ngan et al , 2020; Kumar, 2020; He et al , 2020; Garg and Rani, 2020). Compared to traditional fuzzy sets, Atanassov’s IFS offer membership degree µ and non-membership degree ν for each element of a set (Zhang et al , 2020; Ngan et al , 2020; Kumar, 2020; He et al , 2020; Garg and Rani, 2020; Alcantud et al , 2020).…”