Common Fixed Points of Intuitionistic Fuzzy Maps for Meir-Keeler Type Contractions by Shazia Kanwal, Akbar Azam

“…The main purpose of this paper is to establish and prove some new common fixed point theorems for intuitionistic fuzzy maps in the context of (α,β)-cut sets of intuitionistic fuzzy sets on a complete metric space in association with the Hausdorff metric. …”
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Martelli Chaotic Properties of a Generalized Form of Zadeh’s Extension Principle by Yaoyao Lan, Chunlai Mu

“…Let X denote a compact metric space and let f : X→X be a continuous map. It is known that a discrete dynamical system (X,f) naturally induces its fuzzified counterpart, that is, a discrete dynamical system on the space of fuzzy compact subsets of X. …”
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A porosity result in convex minimization by P. G. Howlett, A. J. Zaslavski

“…We study the minimization problem f(x)→min, x∈C, where f belongs to a complete metric space ℳ of convex functions and the set C is a countable intersection of a decreasing sequence of closed convex sets Ci in a reflexive Banach space. …”
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A Geometric Fuzzy-Based Approach for Airport Clustering by Maria Nadia Postorino, Mario Versaci

“…By representing each airport as a point in the given reference metric space, the geometric distance among airports—which corresponds to a measure of similarity—has in fact an intrinsic fuzzy nature due to the airport specific characteristics. …”
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Restrictive metric regularity and generalized differential calculus in Banach spaces by Boris S. Mordukhovich, Bingwu Wang

“…We consider nonlinear mappings f:X→Y between Banach spaces and study the notion of restrictive metric regularity of f around some point x¯, that is, metric regularity of f from X into the metric space E=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case when f is strictly differentiable at x¯ but its strict derivative ∇f(x¯) is not surjective. …”
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Existence and Uniqueness of Mild Solution for Fractional-Order Controlled Fuzzy Evolution Equation by Naveed Iqbal, Azmat Ullah Khan Niazi, Ramsha Shafqat, Shamsullah Zaland

“…In this article, we investigated the existence and uniqueness of mild solutions for fractional-order controlled fuzzy evolution equations with Caputo derivatives of the controlled fuzzy nonlinear evolution equation of the form  0cDIγxI=αxI+PI,xI+AIWI,I∈0,T,xI0=x0, in which γ∈0,1, E1 is the fuzzy metric space and I=0,T is a real line interval. With the help of few conditions on functions P:I×E1×E1⟶E1, WI is control and it belongs to E1, A∈FI,LE1, and α stands for the highly continuous fuzzy differential equation generator. …”
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Recognition method based on hesitant fuzzy set for unequal length sequences and its application by Shuangming LI, Xin GUAN, Guidong SUN

“…Aiming at the problem that unequal length sequences were difficult to recognize, a recognition method based on hesitant fuzzy distance measure was proposed.Firstly, the problem was described from the perspective of fuzzy value, and the hesitant fuzzy information recognition model of unequal length sequence was established by lattice closeness degree.Secondly, the mean value, variance, relative range and hesitancy degree of hesitant fuzzy values were defined.Combined with membership difference of the shorter part, the generalized integrated feature distance measure and the generalized weighted integrated feature distance measure were defined to meet relevant properties of metric space, and the strict mathematical proof process was given.Finally, entropy measure and support measure were proposed to determine the weight, and the VIKOR recognition method based on hesitant distance measure was given.The simulation results verify the effectiveness and feasibility of proposed method from numerical examples, energy strategy selection and target recognition respectively.…”
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MDTR: a knowledge-guided interpretable representation for quantifying liver toxicity at transcriptomic level by Inyoung Sung, Sangseon Lee, Dongmin Bang, Dongmin Bang, Jungseob Yi, Sunho Lee, Sun Kim, Sun Kim, Sun Kim, Sun Kim

“…In addition, MDTR shows interpretability at the level of DILI mechanisms in terms of the distance, i.e., in a metric space. Furthermore, we provided a user-friendly and freely accessible website (http://biohealth.snu.ac.kr/software/MDTR), enabling users to easily measure DILI in drug-induced transcriptome data.…”
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A 3D Clinical Face Phenotype Space of Genetic Syndromes Using a Triplet-Based Singular Geometric Autoencoder by Soha S. Mahdi, Eduarda Caldeira, Harold Matthews, Michiel Vanneste, Nele Nauwelaers, Meng Yuan, Giorgos Bouritsas, Gareth S. Baynam, Peter Hammond, Richard Spritz, Ophir D. Klein, Michael Bronstein, Benedikt Hallgrimsson, Hilde Peeters, Peter Claes

“…This study introduces a novel approach to enhance clinical diagnosis through the development and exploration of a low-dimensional metric space referred to as the clinical face phenotypic space (CFPS). …”
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