COUNTERFACTUAL TEMPORAL MODEL OF CAUSAL RELATIONSHIPS FOR CONSTRUCTING EXPLANATIONS IN INTELLIGENT SYSTEMS

The subject of the research is the processes of constructing explanations based on causal relationships between states or actions of an intellectualsystem. An explanation is knowledge about the sequence of causes and effects that determine the process and result of an intelligent informationsystem. The aim of the work is to develop a counterfactual temporal model of cause-and-effect relationships as part of an explanation of the process offunctioning of an intelligent system in order to ensure the identification of causal dependencies based on the analysis of the logs of the behavior ofsuch a system. To achieve the stated goals, the following tasks are solved: determination of the temporal properties of the counterfactual description ofcause-and-effect relationships between actions or states of an intelligent information system; development of a temporal model of causal connections,taking into account both the facts of occurrence of events in the intellectual system, and the possibility of occurrence of events that do not affect theformation of the current decision. Conclusions. The structuring of the temporal properties of causal links for pairs of events that occur sequentially intime or have intermediate events is performed. Such relationships are represented by alternative causal relationships using the temporal operators"Next" and "Future", which allows realizing a counterfactual approach to the representation of causality. A counterfactual temporal model of causalrelationships is proposed, which determines deterministic causal relationships for pairs of consecutive events and pairs of events between which thereare other events, which determines the transitivity property of such dependencies and, accordingly, creates conditions for describing the sequence ofcauses and effects as part of the explanation in intelligent system with a given degree of detail The model provides the ability to determine cause-andeffect relationships, between which there are intermediate events that do not affect the final result of the intelligent information system.

Combinative distance based assessment (CODAS) framework using logarithmic normalization for multi-criteria decision making

The purpose of this paper is to present an extended Combinative Distance based Assessment (CODAS) framework using logarithmic normalization (LN) scheme. LN is useful in the situations where criteria values differ significantly. This framework is used to carry out a comparative performance based ranking of the popular smartphones in India. The result obtained from this extended version of CODAS method (CODAS-LN) shows consistency with that generated by using some other established multi-criteria decision making (MCDM) approaches. The sensitivity analysis shows considerable stability in the result. Further, it is observed that CODAS-LN is free from rank reversal phenomenon and follows the transitivity property. Findings of the case study suggest that the smartphones with higher computational capability and features rank in top brackets.

A Comparison of Complete Parts on m-Idempotent Hyperrings

On a particular class of m-idempotent hyperrings, the relation ξ m * is the smallest strongly regular equivalence such that the related quotient ring is commutative. Thus, on such hyperrings, ξ m * is a new representation for the α * -relation. In this paper, the ξ m -parts on hyperrings are defined and compared with complete parts, α -parts, and m-complete parts, as generalizations of complete parts in hyperrings. It is also shown how the ξ m -parts help us to study the transitivity property of the ξ m -relation. Finally, ξ m -complete hyperrings are introduced and studied, stressing on the fact that they can be characterized by ξ m -parts. The symmetry plays a fundamental role in this study, since the protagonist is an equivalence relation, defined using also the symmetrical group of permutations of order n.

Rational Choice with Intransitive Preferences

Traditional rational choice theory assumes that the weak preference relation of an agent is an ordering that is it satisfies reflexivity, completeness and transitivity. It is also well known that the ordering property is essential to build the traditional ordinal utility analysis of consumer behaviour. However, there can be many situations when the weak preference relation of an agent may violate transitivity property, and hence, is not an ordering. In such situations traditional ordinal utility analysis breaks down. This paper develops a framework and discusses all the important results of rational choice theory when preferences are intransitive. It looks at weaker rationality properties such as quasi-transitivity and acyclicity and based on that it introduces weaker concepts of rationality such as quasi-transitive rationality and acyclic rationality and characterizes them. It also brings in the congruence axioms and property of path independence, and establishes the link with rationality. Finally, it analyzes how the results will change if we bring in restricted domain assumption of the choice function. JEL Classification: D01, D10, D11

Transitive action on finite points of a full shift and a finitary Ryan’s theorem

We show that on the four-symbol full shift, there is a finitely generated subgroup of the automorphism group whose action is (set-theoretically) transitive of all orders on the points of finite support, up to the necessary caveats due to shift-commutation. As a corollary, we obtain that there is a finite set of automorphisms whose centralizer is $\mathbb{Z}$ (the shift group), giving a finitary version of Ryan’s theorem (on the four-symbol full shift), suggesting an automorphism group invariant for mixing subshifts of finite type (SFTs). We show that any such set of automorphisms must generate an infinite group, and also show that there is also a group with this transitivity property that is a subgroup of the commutator subgroup and whose elements can be written as compositions of involutions. We ask many related questions and prove some easy transitivity results for the group of reversible Turing machines, topological full groups and Thompson’s $V$ .

On Comparability Relations in the Class of Interval-Valued Fuzzy Relations

In this paper, a new relation for the set of interval-valued fuzzy relations is introduced. This relation is an interval order for the family of intervals and for the family of interval-valued fuzzy relations in a given set, it has the reflexivity property. Consequences of considering such a relation are studied in the context of operations on interval-valued fuzzy relations. A new transitivity property, namely possible T-transitivity is studied (pos-T-transitivity for short). This transitivity property is connected with the new relation proposed in this paper. Preservation of this type of transitivity by some operations is also discussed.