A multi-objective mathematical programming problem with fuzzy relation constraints

In this study we discuss the problem of multi-objective mathematical programming with constraints defined by ‘max-min’ composite fuzzy relation equations. Since the feasible region is normally non-convex, the properties of the efficient points of a non-convex feasible region under multi-objectives are investigated and illustrated by examples. The necessary and sufficient conditions are proposed and proved. To facilitate decisions, a procedure that transforms these efficient points of an interval-valued decision space into a constant-valued decision space is proposed when the level of confidence is given by a decision maker. Then the transformed problem becomes a multi-attribute decision problem that can be evaluated by Yager's method to find the optimal alternative.     

A new look at time and eternity

In his Systematic Theology, Vol. III, Wolfhart Pannenberg argues that God as eternal comprehends the different moments of time simultaneously and orders them to constitute a whole or totality. The author contends that this approach to time and eternity might solve the logical tension between the classical notion of divine sovereignty and the common sense belief in creaturely spontaneity/human freedom. For, if the existence of the events constituting a temporal sequence is primarily due to the spontaneous decisions of creatures, and if their being ordered into a totality or meaningful whole is primarily due to the superordinate activity of God, then both God and creatures play indispensable but nevertheless distinct roles in the cosmic process.     

Endless forms most beautiful 1

Beautiful form rather than efficient cause is the crucial category for understanding living processes, especially evolution. Drawing on the fields of non-equilibrium thermodynamics and citing Darwin's own observations, the author proposes a new understanding of form that corresponds to the dynamism present in living forms and overcomes the limitations of other metaphysical notions of form. Form as beautiful “dynamic form” promises an enriched empiricism, which not only can speak “correctly” about nature but also “well” of nature. In other words, an enriched empiricism of beautiful dynamic forms allows for a fruitful dialogue between science and theology. It avoids theological explanations that call for special divine intervention in the world of Nature which threaten the dignity and self-integrity of Creation. It opens up a view, however, of a divine “milieu,” a divine “Openness,” that providentially calls for beautiful dynamic forms to emerge and entangle through the evolutionary process of nature.     

Balancing Effort and Information Transmission During Language Acquisition: Evidence From Word Order and Case Marking

Across languages of the world, some grammatical patterns have been argued to be more common than expected by chance. These are sometimes referred to as (statistical) language universals. One such universal is the correlation between constituent order freedom and the presence of a case system in a language. Here, we explore whether this correlation can be explained by a bias to balance production effort and informativity of cues to grammatical function. Two groups of learners were presented with miniature artificial languages containing optional case marking and either flexible or fixed constituent order. Learners of the flexible order language used case marking significantly more often. This result parallels the typological correlation between constituent order flexibility and the presence of case marking in a language and provides a possible explanation for the historical development of Old English to Modern English, from flexible constituent order with case marking to relatively fixed order without case marking. In addition, learners of the flexible order language conditioned case marking on constituent order, using more case marking with the cross‐linguistically less frequent order, again mirroring typological data. These results suggest that some cross‐linguistic generalizations originate in functionally motivated biases operating during language learning.     

Historical Semantic Chaining and Efficient Communication: The Case of Container Names

Semantic categories in the world's languages often reflect a historical process of chaining: A name for one referent is extended to a conceptually related referent, and from there on to other referents, producing a chain of exemplars that all bear the same name. The beginning and end points of such a chain might in principle be rather dissimilar. There is also evidence supporting a contrasting picture: Languages tend to support efficient, informative communication, often through semantic categories in which all exemplars are similar. Here, we explore this tension through computational analyses of existing cross‐language naming and sorting data from the domain of household containers. We find (a) formal evidence for historical semantic chaining, and (b) evidence that systems of categories in this domain nonetheless support near‐optimally efficient communication. Our results demonstrate that semantic chaining is compatible with efficient communication, and they suggest that chaining may be constrained by the functional need for efficient communication.     

Stepwise contouring of efficient criterion vectors for large-scale MOLP

In this paper a new method of presenting the overall (focused) structure of the efficient criterion vectors (N) for large-scale MOLP is proposed. The proposed algorithm ASEOV (approximation of the set of efficient objective vectors) determines the representative subset of N and ensures full coverage of N , with corresponding coverage precision indicated. ASEOV works in objective space directly and eliminates unnecessary computational effort at the collapsing extreme points of X , which are transformed to non-extreme points in objective space. The Tchebycheff metric is employed to measure the coverage precision. ASEOV allows a decision maker (DM) to control the determination procedure by assessing the coverage allowance for each criterion. When the DM's preference is available, ASEOV can focus contouring on the subset of N which fits with the extracted preference. Combined with proper interactive methods, this focused contour over N can reduce the DM's burden, inconsistency or cognitive bias in assessing his preference from which to derive the final best-compromise solution. An illustrative example is presented.     

Closed systems,explanations, and the cosmological argument

Examples involving infinite suspended chains or infinite trains are sometimes used to defend perceived weaknesses in traditional cosmological arguments. In this article, we distinguish two versions of the cosmological argument, suggest that such examples can only be relevant if it is one specific type of cosmological argument that is being considered, and then criticize the use of such examples in this particular type of cosmological argument. Our criticism revolves around a discussion of what it means to call a system closed, and what it means to call an explanation complete. Our analysis makes no suppositions about the nature of the infinite, and is therefore independent of many of the issues around which contemporary discussions of the cosmological argument have tended to revolve.     

A critique of causality in Islamic philosophy

After the problems of epistemology, the most fundamental problem of Islamic philosophy is that of causality. Causality has been studied from various perspectives. This paper endeavors first to analyze the issues of causality in Islamic philosophy and then to critique them. A sketch is provided of the history of the development of theories of causality in Islamic philosophy, with particular attention to how religious considerations came to determine the shape of the philosophical theories that were accepted. It is suggested that outstanding philosophical and theological problems that have plagued the tradition of Islamic philosophy require a new approach to the issue of causality.

Efficient Communication in Written and Performed Music

Since its inception, Shannon's information theory has attracted interest for the study of language and music. Recently, a wide range of converging studies have shown how efficient communication pervades language, from phonetics to syntax. Efficient principles imply that more resources should be assigned to highly informative items. For instance, average information content was shown to be a better predictor of word length than frequency, revisiting the famous Zipf's law. However, in spite of the success of the efficient communication framework in the study of language and speech, very little work has investigated its relevance in the analysis of music. Here, we examine the organization of harmonic information in two large corpora of Western music, one made of MIDI files directly sequenced from scores, and the other made of MIDI recordings of live performances of highly skilled piano players. We show that there is a clear positive relationship between (contextual) information content of harmonic sequences and two essential musical properties, namely duration and loudness: the more unexpected a harmonic event is, the longer and the louder it is.