Convex and Concave Hypersoft Sets with Some Properties

Abstract. Convexity plays an imperative role in optimization, pattern classification and recognition, image processing and many other relating topics in different fields of mathematical sciences like operation research, numerical analysis etc. The concept of soft sets was first formulated by Molodtsov as a completely new mathematical tool for solving problems dealing with uncertainties. Smarandache conceptualized hypersoft set as a generalization of soft set (hS, E) as it transforms the function hS into a multi-attribute function hHS. Deli introduced the concept of convexity cum concavity on soft sets to cover above topics under uncertain scenario. In this study, a theoretic and analytical approach is employed to develop a conceptual framework of convexity cum concavity on hypersoft set which is generalized and more effective concept to deal with optimization relating problems. Moreover, some generalized properties like δ-inclusion, intersection and union, are established. The novelty of this work is maintained with the help of illustrative examples and pictorial version first time in literature

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

Development of Some New Hybrid Structures of Hypersoft Set with Possibility-degree Settings

The concept of a hypersoft membership function is introduced in the extension of a soft set known as a hypersoft set, permitting it to handle complicated and uncertain information in a more powerful and flexible manner. Many academics have already become fascinated with this new area of study, leading to the development of a number of hybrid structures. This chapter develops some new hybrid hypersoft set structures by taking into account multiple fuzzy set-like settings and possibility degree-based settings collectively. Additionally, numerical examples are included to clarify the concept of these structures. Researchers can utilize this work to better understand and apply a variety of mathematical ideas

Weighted Ostrowski type inequalities via Montgomery identity involving double integrals on time scales

In this paper, the Montgomery identity is generalized for double integrals on time scales by employing a novel analytical approach to develop the generalized Ostrowski type integral inequalities involving double integrals. Some inimitable cases are discussed for different parameters and parametric functions. Moreover, applications to some particular time scales are also presented

An innovative decision-making framework for supplier selection based on a hybrid interval-valued neutrosophic soft expert set

The best way to achieve sustainable construction is to choose materials with a smaller environmental impact. In this regard, specialists and architects are advised to take these factors into account from the very beginning of the design process. This study offers a framework for selecting the optimal sustainable building material. The core goal of this article is to depict a novel structure of a neutrosophic soft expert set hybrid called an interval-valued neutrosophic soft expert set for utilization in construction supply chain management to select a suitable supplier for a construction project. This study applies two different techniques. One is an algorithmic technique, and the other is set-theoretic. The first one is applied for the structural characterization of an interval-valued neutrosophic expert set with its necessary operators like union and OR operations. The second one is applied for the construction of a decision-making system with the help of pre-described operators. The main purpose of the algorithm is to be used in supply chain management to select a suitable supplier for construction. This paper proposes a new model based on interval-valued, soft expert and neutrosophic settings. In addition to considering these settings jointly, this model is more flexible and reliable than existing ones because it overcomes the obstacles of existing studies on neutrosophic soft set-like models by considering interval-valued conditions, soft expert settings and neutrosophic settings. In addition, an example is presented to demonstrate how the decision support system would be implemented in practice. In the end, analysis, along with benefits, comparisons among existing studies and flexibility, show the efficacy of the proposed structure

Theory of Bijective Hypersoft Set with Application in Decision Making

Hypersoft set (an extension of soft set) is a new mathematicaltool to tackle the inadequacy of soft set for attribute-valued sets. Inthis study, concept of bijective hypersoft set is proposed and some of itsset theoretic operations like restricted-AND and relaxed-AND, are characterized.Moreover, new operations of bijective hypersoft set such as dependency,decision system, significance of decision system, reduced decisionsystem and decision rules in decision system, are discussed withillustrated examples. A decision making algorithm and application arediscussed with the support of these proposed operations

A Rudimentary Approach to Develop Context for Convexity cum Concavity on Soft Expert Set with Some Generalized Results

Soft set theory is considered as the preeminent tool to tacklethe problems involving vagueness by controlling all complexities of optimizationtheory, fuzzy set theory and interval theory. Some models havebeen developed to solve problems in decision making and medical diagnosiswith one expert by using this theory. This causes a problem withthose who use questionnaires in their research. Soft expert set overcomesthis problem and facilitates the user to know the opinion of all expertsin one model. The concept of convexity plays a key role to deal optimization,pattern recognition-classification and many other related topicsin operation research, numerical analysis and other disciplines of mathematicalsciences. In this study, a mathematical cum abstract techniqueis employed to develop basic concept of convex and concave soft expertsets to deal with their important applications. Some classical results onconvexity cum concavity are modified under uncertain multi-decisive environmentwith the support of explicatory proofs.AMS (MOS) Subject Classification Codes: 26A51, 26B25, 32F17, 35E10, 46N10.KeyWords: Soft set, Soft expert set, Convex soft expert set, Concave soft expert se

An Inclusive Study on Fundamentals of Hypersoft Expert Set with Application

Soft set deals with single set of attributes whereas its extensionhypersoft set deals with multi attribute-valued disjoint sets correspondingto distinct attributes. Many researchers have created some models basedon soft set to solve problems in decision-making, but most of these modelsdeal with only one expert. This causes a problem with the users, especiallywith those who use questionnaires in their work. Therefore we present anovel model hypersoft expert set which not only addresses this limitationof soft-like models with the emphasis on the opinion of all experts butalso resolves the inadequacy of soft set for attribute-valued disjoint setscorresponding to distinct attributes. In this study, the existing conceptof hypersoft expert set is modified and some fundamental properties i.e.subset, not set and equal set, whole set, absolute set, relative null set,relative absolute set; results i.e. commutative, associative, distributive andDe’ Morgan’s Laws and set-theoretic operations i.e. complement, unionintersection, restricted union, extended intersection, AND, and OR aredeveloped. An algorithm is proposed to solve decision-making problemand applied to recruitment process for hiring ”right person for the rightjob”.AMS (MOS) Subject Classification Codes: 91B06; 93E25Key Words: Soft Set, Soft Expert Set, Hypersoft Set, Hypersoft Expert Set, RecruitmentProcess.

Multi-Attribute Decision Support Model Based on Bijective Hypersoft Expert Set

Soft set tackles a single set of attributes whereas its extensionhypersoft set is projected for dealing attribute-valued disjoint sets corresponding to distinct attributes with entitlement of multi-argument approximate function. In order to furnish soft set-like models with multi-decisive opinions of multi-experts, a new model i.e. soft expert set has been developed but this is inadequate for handling the scenario where partitioningof attributes into their respective attribute-valued sets is necessary. Hencehypersoft expert set has made its place to be developed. This article intendsto develop a new type of hypersoft set called bijective hypersoftexpert set which is more flexible and effective. After characterization ofits essential properties and set-theoretic operations like union, relaxed andrestricted AND, a decision-support system is designed which is characterizedby new operations such as decision system, reduced decision system,etc. with illustrated examples. The proposed decision-support system isapplied in multi-attribute decision-making process to manage a real-lifeapplication.AMS (MOS) Subject Classification Codes: 91B06; 93E25Key Words: Soft set, Soft expert set, Bijective soft set, Hypersoft set, Hypersoft expertset, Bijective hypersoft set, Bijective hypersoft expert set

(m; n)-Convexity-cum-Concavity on Fuzzy Soft Set with Applications in First and Second Sense

Soft set theory is considered as one of the best effective toolwhich provides parameterization approach to tackle the inadequacy offuzzy set. So far, it has been applied to different mathematical conceptssuch as set operations, algebraic structure (e.g., group and ring theory)and topological spaces. Many researchers have studied classical conceptof convex and concave set under fuzzy-like, soft-like and fuzzy soft-likeenvironments. In this paper, new notions of (m; n)-convex and (m; n)-concave fuzzy soft sets are developed first and then their versions for firstand second senses are established. Further some known classical resultsand properties are generalized under fuzzy soft set environment. Moreover,special cases of (m; n)-convexity on fuzzy soft sets are established