this paper examines the historical development of operations research (or) and represents different or methods (methodologies) developed during its lifetime. then, considering thomas kuhn’s paradigm model of scientific development as a basis for our work, the former and current status of or are analyzed and the future trend is discussed.

This paper is an inquiry into the nature and characteristics of the so-called soft approaches in Operational Research (OR). After a first outline of soft approaches, six wellknown and widely applied soft approaches are selected for further study and characterisation applying a multi-dimensional framework. In addition, some reflexions about the limitations of such a framework are discussed.

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

the concept of soft sets, introduced by molodtsov [20] is a mathematicaltool for dealing with uncertainties, that is free from the difficultiesthat have troubled the traditional theoretical approaches. in this paper, weapply the notion of the soft sets of molodtsov to the theory of hilbert algebras.the notion of soft hilbert (abysmal and deductive) algebras, soft subalgebras,soft abysms and sof...

We first describe how to “fuzzify” the estimated binary columns to create a [0,1]-valued column. Werefer to this [0,1] -valued column as the soft segmentation column of the noisy spectrogram column.Similarly to the collection of soft segmentation columns as the soft segmentation image, or simply asthe soft segmentation. The band-dependent posterior probability that the hard segmentation columnv...