August 2024

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4 Reads

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1 Citation

International Journal of General Systems

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August 2024

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4 Reads

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1 Citation

International Journal of General Systems

August 2024

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15 Reads

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1 Citation

Information Sciences

August 2023

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9 Reads

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2 Citations

Fuzzy Sets and Systems

May 2023

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2 Reads

Fuzzy Sets and Systems

February 2023

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32 Reads

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9 Citations

Information Sciences

December 2022

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78 Reads

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10 Citations

Information Sciences

In this article, we study calculus for gH-subdifferential of convex interval-valued functions (IVFs) and apply it in a nonconvex composite model of an interval optimization problem (IOP). Towards this, we define convexity, convex hull, closedness, and boundedness of a set of interval vectors. In identifying the closedness of the convex hull of a set of interval vectors and the union of closed sets, we analyze the convergence of the sequence of interval vectors. We prove a relation on the gH-directional derivative of the maximum of finitely many comparable IVFs. With the help of existing calculus on the gH-subdifferential of an IVF, we derive a Fritz-John-type and a KKT-type efficiency condition for weak efficient solutions of IOPs. In the sequel, we analyze the supremum and infimum of a set of intervals. Further, we report a characterization of the weak efficient solutions of nonconvex composite IOPs by applying the proposed concepts. The whole analysis is supported by illustrative examples.

September 2022

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19 Reads

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5 Citations

Fuzzy Sets and Systems

It is well known that the usual point-wise ordering over the set T of t-norms makes it a poset but not a lattice, i.e., the point-wise maximum or minimum of two t-norms need not always be a t-norm again. In this work, we propose, two binary operations on the set TCA of continuous Archimedean t-norms and obtain, via these binary operations, a partial order relation ⊑, different from the usual point-wise order ≤, on the set TCA. As an interesting outcome of this structure, some stronger versions of some existing results dealing with the upper and lower bounds of two continuous Archimedean t-norms with respect to the point-wise order ≤ are also obtained. Finally, with the help of the operations on the set TCA, two binary operations ⊕,⊗ on the set TC of continuous t-norms are proposed and showed that (TC,⊕,⊗) is a lattice. Thus we have both a way of generating continuous t-norms from continuous t-norms and also obtain an order on them.

August 2022

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55 Reads

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28 Citations

Journal of Ambient Intelligence and Humanized Computing

A useful expansion of the intuitionistic fuzzy set (IFS) for dealing with ambiguities in information is the Pythagorean fuzzy set (PFS), which is one of the most frequently used fuzzy sets in data science. Due to these circumstances, the Aczel-Alsina operations are used in this study to formulate several Pythagorean fuzzy (PF) Aczel-Alsina aggregation operators, which include the PF Aczel-Alsina weighted average (PFAAWA) operator, PF Aczel-Alsina order weighted average (PFAAOWA) operator, and PF Aczel-Alsina hybrid average (PFAAHA) operator. The distinguishing characteristics of these potential operators are studied in detail. The primary advantage of using an advanced operator is that it provides decision-makers with a more comprehensive understanding of the situation. If we compare the results of this study to those of prior strategies, we can see that the approach proposed in this study is more thorough, more precise, and more concrete. As a result, this technique makes a significant contribution to the solution of real-world problems. Eventually, the suggested operator is put into practise in order to overcome the issues related to multi-attribute decision-making under the PF data environment. A numerical example has been used to show that the suggested method is valid, useful, and effective.

June 2022

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36 Reads

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13 Citations

Sadhana

In this article, the concepts of gH-subgradient and gH-subdifferential of interval-valued functions are illustrated. Several important characteristics of the gH-subdifferential of a convex interval-valued function, e.g., closeness, boundedness, chain rule, etc. are studied. Alongside, we prove that gH-subdifferential of a gH-differentiable convex interval-valued function contains only the gH-gradient. It is observed that the directional gH-derivative of a convex interval-valued function is the maximum of all the products between gH-subgradients and the direction. Importantly, we prove that a convex interval-valued function is gH-Lipschitz continuous if it has gH-subgradients at each point in its domain. Furthermore, relations between efficient solutions of an optimization problem with interval-valued function and its gH-subgradients are derived.

June 2022

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19 Reads

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3 Citations

Fuzzy Sets and Systems

In a recent paper by the authors, Jensen's inequality for Choquet integral was given, and a wrong assertion—“Jensen's inequality does not hold for asymmetric Choquet integral” was made. This paper can be viewed as a continuation of the previous one, Jensen's inequality for asymmetric Choquet integral is proved, the error is corrected. As its generalization, Jensen's inequality for generalized asymmetric Choquet integral is obtained.

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... Due to the many applications of the Choquet integral for modeling non-deterministic problems, a generalization of the Choquet integral is recently presented in [21]. Study [22] generalizes the generalized Choquet-type integral in terms of a double set-function Choquet integral for a real-valued function based on a set-function and fuzzy measure. ...

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August 2024

Information Sciences

... The class of all measurable closed-valued functions on Ω is denoted by ℜ[Ω]. For more details dealing with set-valued functions, see [1,8] (see also [3][4][5]7,22]). Let ∈ ℜ[Ω]. ...

- Citing Article
February 2023

Information Sciences

... Motivated by [29], the theory of gH-subdifferential and gH-subgradient of IVFs were discussed in [30]. With this, numerous researchers [28,31,32,33,34,35] have contributed to the gH-subdifferentiability of IVFs. ...

- Citing Article
December 2022

Information Sciences

... where T is a t-norm on L. Since then, the partial order induced by fuzzy logic connective has led to an extensive research by many scholars (see Liu and Wang 2022;Liu 2023;Karaçal and Mesiar 2014;Kesicioglu 2020;Lu et al. 2018;Vemuri et al. 2023). Also it is worth noting that nullnorms and uninorms are a generalization of t-norms and t-conorms, correspondingly, the partial orders induced by nullnorms and uninorms, respectively, have been introduced in Aşıcı (2017); Ertugrul et al. (2016). ...

- Citing Article
September 2022

Fuzzy Sets and Systems

... Zarasiz [34] utilized bipolar fuzzy numbers to propose new AOs using the concept of AA operations. Senapati et al. [35] also broadened the concepts of t-Nm and t-CNm to propose PF-AA AOs. In [36], Farid et al. thoroughly studied the optimizing filtration technology by expanding the AA operations q-rung Ortho pair FS. ...

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August 2022

Journal of Ambient Intelligence and Humanized Computing

... The ̅ − for real functions introduced in [3], and investigated in [7], mark a new development in the field of Pseudo-Analysis. Based on the fundamental properties of these ̅ − , [2], [9], [10], [19], [20], [21], for the first time in this paper, we have studied and verified other properties for pseudo-linearity/nonlinearity of ̅ − and generalization of the table of ̅ − , [3] of transformed functions, [2]. The eight exceptional ̅ − cases are considered for some ̅ − functions' pseudolinear and pseudo-nonlinear combinations with some conditions. ...

- Citing Article
June 2022

Fuzzy Sets and Systems

... According to Moore's algorithm, for a nonzero interval A, it is impossible to find any interval B such that A + B = 0. Due to the limitations of Moore's algorithm, Hukuhara [3] proposed 'Hukuhara difference' of intervals. Although this method satisfies A ⊖ H A = 0, but for the calculation of A ⊖ H B, the Hukuhara difference can only be derived if the length of A is greater than B (for more details refer to reference [2] and [27]). Markov [4] introduced a new interval subtraction method in order to solve this problem, i.e., 'nonstandard subtraction', which was subsequently named by Stefanini [5] as 'generalized Hukuhara difference (gH-difference)'. ...

- Citing Article
June 2022

Sadhana

- Citing Article
September 2021

Fuzzy Sets and Systems

... For example, reference [29] summarises the principles and ideas of XAI, whereas [30] proposes a framework for developing transparent and intelligible models. A full examination of several XAI approaches and algorithms is provided in [31], and the use of fault-tolerant solutions in XAI systems is covered in [32]. Furthermore, we found that the need for XAI framework development is growing. ...

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- Full-text available
March 2021

Knowledge-Based Systems

... On the other hands, in many problems, it is not possible to provide the Laplace transformation. Due to the many applications of the Choquet integral for modeling non-deterministic problems, a generalization of the Choquet integral is recently presented in [21]. Study [22] generalizes the generalized Choquet-type integral in terms of a double set-function Choquet integral for a real-valued function based on a set-function and fuzzy measure. ...

- Citing Article
December 2020

Fuzzy Sets and Systems