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We consider one variant of stable assignment problems in a bipartite graph endowed with nonnegative capacities on the edges and quotas on the vertices. It can be viewed as a generalization of the stable allocation problem introduced by Baïou and Balinsky, which arises when strong linear orders of preferences on the vertices in the latter are replaced by weak ones. At the same time, our stability problem can be stated in the framework of a theory by Alkan and Gale on stable schedule matchings generated by choice functions of a wide scope. In our case, the choice functions are of a special, so-called mixed , type. The main content of this paper is devoted to a study of rotations in our mixed model, functions on the edges determining "elementary" transformations between close stable assignments. These look more sophisticated compared with rotations in the stable allocation problem (which are generated by simple cycles). We efficiently construct a poset of rotations and show that the stable assignments are in bijection with the so-called closed functions for this poset; this gives rise to a "compact" affine representation for the lattice of stable assignments and leads to an efficient method to find a stable assignment of minimum cost. [ABSTRACT FROM AUTHOR]

The paper studies complementary choice functions, i.e. monotonic and consistent choice functions. Such choice functions were introduced and used in the work [13] for investigation of matchings with complementary contracts. We provide three (universal) ways of constructing such choice functions: through pre-topologies, as direct images of completely complementary (or pre-ordered) choice functions, and with the help of supermodular set-functions. [ABSTRACT FROM AUTHOR]

The idea of confining the idea of 'rationality' with that of the 'choice of best elements' unnecessarily limits the sense and scope of 'rationality'. The existing internal consistency conditions that are popularly used in the social choice theory to assess a choice function are insufficient to analyse several choice patterns. The paper tries to address that problem by accepting a broader definition of rationality and characterizes choice behaviours where an individual chooses a k-th best element from set of alternatives, where k is an integer. [ABSTRACT FROM AUTHOR]

In an earlier paper [Rational choice and AGM belief revision, Artificial Intelligence, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of filtered belief revision and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic partial belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information.

This paper proposes an optimized mobile robot navigation strategy using a functional firefly algorithm (FFA) and choice function. This approach has two key advantages: first, the linear objective function performs efficiently with the single degree and finite-order polynomial time operation, and second, the cartesian constraint performs compactly with the chosen degree of freedom on the finite interval. This functional approach optimizes the size of operational parameters in context with key size, operation time, and a finite range of verification. The choice function achieves parameter order (size) reduction. The attraction characteristic of fireflies is represented by the choice function for optimizing the choice between low and high intensities of fireflies. In 2D and 3D environments, the proposed robot navigation performs well in an uncertain environment with static and dynamic obstacles. This efficiency includes the robot’s speed as determined by the choice function’s minimum path lengths. The collision-free path is achieved by the non-void family of non-void sets. The obtained results are optimal in terms of path length and navigational time. The proposed controller is also compared with the other existing controllers, and it is observed that the FFA gives the shortest path in less time for the same environmental condition.

This paper proposes an optimized mobile robot navigation strategy using a functional firefly algorithm (FFA) and choice function. This approach has two key advantages: first, the linear objective function performs efficiently with the single degree and finite-order polynomial time operation, and second, the cartesian constraint performs compactly with the chosen degree of freedom on the finite interval. This functional approach optimizes the size of operational parameters in context with key size, operation time, and a finite range of verification. The choice function achieves parameter order (size) reduction. The attraction characteristic of fireflies is represented by the choice function for optimizing the choice between low and high intensities of fireflies. In 2D and 3D environments, the proposed robot navigation performs well in an uncertain environment with static and dynamic obstacles. This efficiency includes the robot's speed as determined by the choice function's minimum path lengths. The collision-free path is achieved by the non-void family of non-void sets. The obtained results are optimal in terms of path length and navigational time. The proposed controller is also compared with the other existing controllers, and it is observed that the FFA gives the shortest path in less time for the same environmental condition. [ABSTRACT FROM AUTHOR]

Dogan and Yildiz introduce and analyze the pro-con model that is inspired by Franklin's prudential algebra. Consider an agent who is endowed with two sets of orderings: pro- and con-orderings. For each choice set, if an alternative is the top-ranked by a pro-ordering (con-ordering), then this is a pro (con) for choosing that alternative. The alternative with more pros than cons is chosen from each choice set. Each ordering may have a weight reflecting its salience. In this case, the probability that an alternative is chosen equals the difference between the total weights of its pros and cons. Although, this is an additive model similar to the random utility model with structurally invariant primitives, authors show that every (random) choice function is (random) pro-con rational. Their technique requires a generalization of Ford-Fulkerson theorem. The connection between the random model and its deterministic counterpart demonstrates a fruitful use of classical integer programming techniques in choice theory. We consider an agent who is endowed with two sets of orderings: pro- and con-orderings. For each choice set, if an alternative is the top-ranked by a pro-ordering (con-ordering), then this is a pro (con) for choosing that alternative. The alternative with more pros than cons is chosen from each choice set. Each ordering may have a weight reflecting its salience. In this case, the probability that an alternative is chosen equals the difference between the total weights of its pros and cons. We show that every nuance of the rich human choice behavior can be captured via this structured model. Our technique requires a generalization of the Ford-Fulkerson theorem, which may be of independent interest. As an application of our results, we show that every choice rule is plurality-rationalizable. Funding: K. Yildiz is grateful for the hospitality of New York University, Department of Economics during his visit in the 2017–2018 academic year, and the support from the Scientific and Research Council of Turkey (TUBITAK) [Grant 1059B191601712]. [ABSTRACT FROM AUTHOR]

A review of works devoted to the theory of stable matchings or, more generally, of stable networks of contracts is given. A set (network) of contracts is called stable if no coalition has an available contract that gives all coalition members strictly more than the proposed set. In a special case, this concept was introduced in 1962 by Gale and Shapley and has since gone a long way in its development both theoretically (theorems, structures, and algorithms) and in the field of applications in economics, physics, biology, and mathematics. [ABSTRACT FROM AUTHOR]

Automated synthesis of computer-aided assembly planning (CAAP) processes is a crucial task for engineering practice and design theory. It is of especial relevance for modern robotic industries, which need in technological assembly instructions to be described in-depth and in-detail as much as possible. The assembly sequence is a key design decision on which many operational properties of the product and economic characteristics of production depend.Choosing a rational assembly sequence planning (ASP) is a challenge. It requires significant computing resources and taking into consideration a large number of technical parameters and economic characteristics that affect the quality of design alternatives. Insights into the quality of alternatives are given as the expert’s preferences rather than as the numerical criteria.The abovementioned features do not allow us to apply the classical optimization methods or mathematical programming for making ASP decision. For this, most modern publications offer various search engine optimization methods based on biological and behavioral analogies. In this paradigm, it is believed that a set of acceptable alternatives that form the original choice space is a priori known. In most design situations this presumption is unrealistic.In engineering practice, considerable technological knowledge about the assembly of products for different function purposes is gained. These are mostly ad hoc data that exist in the form of rules, recommendations, recipes, heuristics, expert preferences, descriptions of successful precedents, etc. The paper suggests a new method for a choice of the rational assembly sequence based on the use of the decision theory apparatus. The proposal contains formalization of important design and technological heuristics, namely consistency with the dimensional chain system, geometric “freedom” during assembly, monotony in size, weight, accuracy, etc.A set of choice functions is open and can be completed by additional choice functions that describe engineering heuristics and decision rules that are relevant in the given design situation. The proposed approach allows the assessment and choice of alternatives according to several aspects or criteria. To do this, it is possible to use various methods of generating a common choice function from the totality of particular functions.

Two scenarios illustrate uses of von Neumann–Morgenstern stable sets in the construction of choice functions. A comparison is made to the construction of choice functions by the selection of maximal elements. A characterization is given of choice functions that are von Neumann–Morgenstern stable set rationalizable by acyclic, asymmetric binary relations. Two examples illustrate the use of the characterization. [ABSTRACT FROM AUTHOR]

We study choice functions which arise in the context of matching with contracts. A choice function is rationalizable if it coincides with a choice function induced by a preference relation over sets of contracts. We show that a choice function is rationalizable if and only if it satisfies the Strong Axiom of Revealed Preference (SARP), and give an algorithm for verifying the rationalizability of a given choice function. Consequently, we prove that every path independent choice function is rationalizable. This implies that under the substitutability assumption, the rationalizability condition and the irrelevance of rejected contracts (IRC) condition are equivalent. [ABSTRACT FROM AUTHOR]