An extension of TOPSIS based on linguistic terms in triangular intuitionistic fuzzy structure

Chen [24] introduced the extension of TOPSIS in the fuzzy structure, while this article stretches the modern approach of TOPSIS to the intuitionistic fuzzy framework. Linguistic terms are used in this study to evaluate the weight of each criterion and the rating of alternatives in the context of a triangular intuitionistic fuzzy number. A new intuitionistic fuzzy positive ideal solution (IFPIS) and intuitionistic fuzzy negative ideal solution (IFNIS) are proposed in this model of extended TOPSIS. Euclidean distance is introduced between two triangular intuitionistic fuzzy numbers to calculate separation between each alternative to both (IFPIS) and (IFNIS). The proposed model’s mechanism is presented with the help of an algorithm, and then it is applied to the personal selection problem. Finally, a comparative study is given between this model and other TOPSIS techniques.

An Extension of TODIM with VIKOR approach based on Gini Simpson Index of Diversity under Picture fuzzy framework to Evaluate Opinion Polls

Cuong and Kreinovich was the first who gives the idea of Picture fuzzy set (PFS), which is an extension of intuitionistic fuzzy set (IFS) by cosidering positive, negative and neutral membership of element. In this paper, we have been worked on new entropy measure of PFS from the probabilistic view point and it’s properties are examined from mathematical point of view. A hybrid aproach is presented with the assistance of TODIM (Portuguese abbreviation for Interactive Multi-Criteria Decision Making) and VIKOR (Vlsekriterijumska Optimizacija I Kompromisno Resenje) methods. Further, we applied it to MCDM (multi criterion decision making) problems with picture fuzzy numbers (PFNs), where the information about criteria synthetic weights is partially known and completely unknown and show its existence with the help of some practical cases. After getting the output, we are able to infer that the proposed hybrid approach is comparatively better so as to handle the uncertainty and vulnerabilities for the decision making problems. Based upon these two approaches we can determine the opinion poll of voting outcomes and then, we compare its result with other MCDM approaches that exists in the literature.

On fuzzy Volterra-Fredholm integrodifferential equation associated with Hilfer-generalized proportional fractional derivative

<abstract><p>This investigation communicates with an initial value problem (IVP) of Hilfer-generalized proportional fractional ($ \mathcal{GPF} $) differential equations in the fuzzy framework is deliberated. By means of the Hilfer-$ \mathcal{GPF} $ operator, we employ the methodology of successive approximation under the generalized Lipschitz condition. Based on the proposed derivative, the fractional Volterra-Fredholm integrodifferential equations $ (\mathcal{FVFIE}s) $ via generalized fuzzy Hilfer-$ \mathcal{GPF} $ Hukuhara differentiability ($ \mathcal{HD} $) having fuzzy initial conditions are investigated. Moreover, the existence of the solution is proposed by employing the fixed-point formulation. The uniqueness of the solution is verified. Furthermore, we derived the equivalent form of fuzzy $ \mathcal{FVFIE}s $ which is supposed to demonstrate the convergence of this group of equations. Two appropriate examples are presented for illustrative purposes.</p></abstract>