Multi-objective optimisation in air-conditioning systems : comfort/discomfort definition by IF sets.

The problem of multi-objective optimisation of air-conditioning (AC) systems is treated in the paper in the framework of intuitionistic fvzzy (lF) set theory. The nature of the problem is multi-objective one with requirements for minimal costs (generally, life cycle costs; more specifically, energy costs) and maximal occupants' comfort (minimal discomforl). Moreover, its definition by conventional means is bounded to a number of restrictions and assumptions, which are often far from the real-life situations. Attempts have been made to formulate and solve this problem by means of the fuzzy optimisation [4]. The present paper makes further step by exploring the innovative concept of IF sets [6] into definition of the trickiest issue: comfort and discomforr definition. The new approach allows to formulate more precisely the problem which compromises energy saving and thermal comfort satisfaction under given constraints. The resulting IF optimisation problem could be solved numerically or, under some assumptions, analytically Il]-t21. An example illustrates the viability of the proposed approach. A solution which significantly (with 3S%) improves comfort is found which is more energetically expensive with only 0.6Yo. This illustrates the possibility to use the approach for trade-off analysis in multi-objective optimisation of AC systems

Development of Hybrids of Hypersoft Set with Complex Fuzzy Set, Complex Intuitionistic Fuzzy set and Complex Neutrosophic Set

The complex fuzzy soft set and its generalized hybrids are such effective structures which not only minimize the impediments of all complex fuzzy-like structures for dealing uncertainties but also fulfill all the parametric requirements of soft sets. This feature makes it a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set as it transforms the single attribute function into a multi-attribute function. This generalization demands an extension of complex fuzzy soft-like structures to hypersoft structure for more precise results. In this study, hybrids of hypersoft set with complex fuzzy set and its generalized structures i.e. complex intuitionistic fuzzy set and complex neutrosophic set, are developed along with illustrative examples to address the demand of literature. Moreover, some of their fundamentals i.e. subset, equal sets, null set, absolute set etc. and theoretic operations i.e. compliment, union, intersection etc. are discussed

Generalized closed sets in ditopological texture spaces with application in rough set theory

In this paper, the counterparts of generalized open (g-open) and generalized closed (g-closed) sets for ditopological texture spaces are introduced and some of their characterizations are obtained. Some characterizations are presented for generalized bicontinuous difunctions. Also, we introduce new notions of compactness and stability in ditopological texture spaces based on the notion of g-open and g-closed sets. Finally, as an application of g-open and g-closed sets, we generalize the subsystem based denition of rough set theory by using new subsystem, called generalized open sets to dene new types of lower and upper approximation operators, called g-lower and g-upper approximations. These decrease the upper approximation and increase the lower approximation and hence increase the accuracy. Properties of these approximations are studied. An example of multi-valued information systems are given

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (1/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (2/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022

NN-soft sets: OWA aggregation operators and multi-agent decisions --- Slides in 22nd IPMC 2022 (3/3)

[EN]The 22nd International Pure Mathematics Conference 2022 (22nd IPMC 2022) on Algebra, Analysis and Geometry, was held in Islamabad (Pakistan) from August 21–23, 2022