A Steepest Descent Method for Set Optimization Problems with Set-Valued Mappings of Finite Cardinality

In this paper, we study a first-order solution method for a particular class of set optimization problems where the solution concept is given by the set approach. We consider the case in which the set-valued objective mapping is identified by a finite number of continuously differentiable selections. The corresponding set optimization problem is then equivalent to find optimistic solutions to vector optimization problems under uncertainty with a finite uncertainty set. We develop optimality conditions for these types of problems and introduce two concepts of critical points. Furthermore, we propose a descent method and provide a convergence result to points satisfying the optimality conditions previously derived. Some numerical examples illustrating the performance of the method are also discussed. This paper is a modified and polished version of Chapter 5 in the dissertation by Quintana (On set optimization with set relations: a scalarization approach to optimality conditions and algorithms, Martin-Luther-Universität Halle-Wittenberg, 2020).

Qualitative Comparative Analysis

This chapter examines qualitative comparative analysis (QCA), which strives to bridge the methodological rift between case study-based research and quantitative studies. QCA belongs to the broader family of configurational comparative methods (CCMs). From an analytical perspective, QCA can be distinguished from quantitative approaches. The emphasis shifts from covariance to the analysis of set relations. Being strongly tied to a profound theoretical and conceptual reasoning which is typical for comparison in general, the analysis of set relations is based on three steps: first, a score is attributed to a social phenomenon (representing either a dichotomous or a graded set membership), usually in relation to other phenomena. Second, necessary conditions are defined. Third, through the help of a truth table analysis, (combinations of) sufficient conditions are analysed.

Set Relations via Families of Scalar Functions and Approximate Solutions in Set Optimization

Via a family of monotone scalar functions, a preorder on a set is extended to its power set and then used to construct a hull operator and a corresponding complete lattice of sets. Functions mapping into the preordered set are extended to complete lattice-valued ones, and concepts for exact and approximate solutions for corresponding set optimization problems are introduced and existence results are given. Well-posedness for complete lattice-valued problems is introduced and characterized. The new approach is compared with existing ones in vector and set optimization. Its relevance is shown by means of many examples from multicriteria decision making, statistics, and mathematical economics and finance.

Revisiting Internal Marketing for the Determinants of Job (Dis)Satisfaction by Using Asymmetric Approach

Research in the fields of organizational behavior, human resources, or sustainable development management has paid much attention to employee job satisfaction and suggests it is critical to a firm obtaining a dominant position and gaining competitive advantage in a competitive environment. From the internal marketing perspective, how to satisfy employee job satisfaction to retain the valuable human resources needed to achieve sustainable development of the organization is a major concern of scholars and practitioners. However, most studies focus on above-average job satisfaction and relatively neglect below-average job satisfaction. Accordingly, this study categorized relevant antecedents into causal configurations for identifying the sufficient conditions of job (dis)satisfaction. Specifically, this study investigated how employees can achieve job satisfaction or dissatisfaction based on a fuzzy set qualitative comparative analysis (fsQCA). Most problems and theories of social science are formulated in terms of sets and set relations, while study employs asymmetric thinking in data analysis of previous linear relationships. The fsQCA found three and two causal configurations to be sufficient for high employee job satisfaction and dissatisfaction, respectively. For instance, the results indicate one configuration, namely task-related, innovation-related, coworker-related, and personal-related characteristics present but supervisor-related characteristics absent, can achieve high employee job satisfaction when the values of task-related, innovation-related, coworker-related, and personal-related characteristics are high with lower values of supervisor-related characteristics.

Using Soft Set Relations and Mappings of Kernels and Closures

In this paper, the views of anti-reflexive kernel, symmetric kernel, reflexive closure, and symmetric closure of a SS relation are initially presented, respectively. Then, their correct calculation formulae and a few laws are received. Finally, SS relation function and inverse SS relation functions are introduced, and some related conditions are discussed.

The Choice between Crisp and Fuzzy Sets in Qualitative Comparative Analysis and the Ambiguous Consequences for Finding Consistent Set Relations

Empirical researchers using qualitative comparative analysis (QCA) can work with crisp, multivalue, and fuzzy sets. The relative advantages of crisp and multivalue sets have been discussed in the QCA literature. There has been little reflection on the more frequent decision between crisp and fuzzy sets for which there often is no theoretical guidance. A review shows that researchers often prefer fuzzy over crisp sets, sometimes because they contain more information. This meets with the argument that fuzzy sets produce more conservative consistency measures and constitute tougher tests. In my article, I demonstrate analytically and with data from published QCA studies that the relationship between crisp sets, fuzzy sets, and the consistency score is ambiguous. It depends on the distribution of cases whether the consistency value is more or less conservative for fuzzy sets than for crisp sets. I outline the implications of the ambiguous relationship for empirical research.