Interval-Valued Pythagorean Fuzzy Set (IVPFS), originally proposed by Peng and Yang, is a novel tool to deal with vagueness and incertitude. As a generalized Set, IVPFS has close relationship with Interval-Valued intuitionistic Fuzzy Set (IVIFS). IVPFS can be reduced to IVIFS satisfying the condition $\mu^++\nu^+ \leq 1$. However, the related operations of IVPFS do not take different conditions into consideration. In this paper, we initiate some new Interval-Valued Pythagorean Fuzzy operators ($\diamondsuit, \Box, \spadesuit, \clubsuit, \maltese, \rightarrow, \$ $) and discuss their properties in relation with some existing operators $(\cup, \cap, \oplus, \otimes)$ in detail. It will promote the development of Interval-Valued Pythagorean Fuzzy operators. Later, we propose an algorithm to deal with multi-attribute decision making (MADM) problem based on proposed $\spadesuit$ operator. Finally, the effectiveness and feasibility of approach is demonstrated by mine emergency decision making example.

Intervals are related to the representation of uncertainty. In this sense, we introduce an integral of Gould type for an Interval-Valued multifunction relative to an Interval-Valued Set multifunction, with respect to Guo and Zhang order relation. Classical and specific properties of this new type of integral are established and several examples and applications from multicriteria decision making problems are provided.

In this note the notion of Interval-Valued Fuzzy B-algebras (briefly, i-v Fuzzy B-algebras), the level and strong level B-subalgebra is introduced. Then we state and proV8 some theorems which detennin8 the relationship between these notions and B-subalgebras. The images and inverse images of i-v Fuzzy B-subalgebras are defined, and how the homomorphic images and inverse images of i-v Fuzzy B-subalgebra becomes i-v Fuzzy B-algebras are studied.

In this study, we attempted to demonstrate the Interval-Valued Fuzzy code by extending the concept of an Interval-Valued Fuzzy Set. Further, we discussed the operations of the Interval-Valued Fuzzy code. The Interval-Valued Fuzzy soft code is introduced, and various related properties are investigated in this paper. Finally, we show that the operations of Interval-Valued Fuzzy soft code are discussed. Through this paper, we use the Set of integers modulo 2, that is = {0, 1}.

In this paper, we define the new notion of Interval-Valued Pythagorean Fuzzy ideals in semigroups and established the properties of its with suitable examples. Also, we introduce the concept of Interval Valued Pythagorean Fuzzy sub-semigroup, Interval Valued Pythagorean Fuzzy left (resp. right) ideal, Interval Valued Pythagorean Fuzzy bi-ideal, Interval Valued Pythagorean Fuzzy interior ideal and homomorphism of an Interval Valued Pythagorean Fuzzy ideal in semigroups with suitable illustration. We show that every Interval Valued Pythagorean Fuzzy left (resp. right) ideal is an Interval Valued Pythagorean Fuzzy bi-ideal.

In this work, we examine several widely-used Interval-Valued Fuzzy logical connectives with respect to admissible orders. We are concerned with Interval-Valued Fuzzy negations, automorphisms, Fuzzy implications and aggregation functions with respect to $K_{\alpha,\beta}$ orders and arbitrary Intervals on $L([0, 1])$. We also make a discussion of width-preserving Interval-Valued Fuzzy equivalence functions and Fuzzy dissimilarity functions with respect to arbitrary admissible orders and the Intervals with the same width on $L([0, 1])$. Then we bring some approaches to constructing the proposed Interval-Valued Fuzzy logical connectives with respect to admissible orders.

In this paper we introduce the concept of the spherical Interval-Valued Fuzzy bi-ideal of gamma near-ring R and its some results. The union and intersection of the spherical Interval-Valued Fuzzy bi-ideal of gamma near-ring R is also a spherical Interval-Valued Fuzzy bi-ideal of gamma near-ring R. Further we discuss about the relationship between bi-ideal and spherical Interval-Valued Fuzzy bi-ideal of gamma near-ring R.

Multiple twin support vector machine (MTSVM) which evaluates all the training data into a ``one-versus-rest'' structure is a multi-class classification algorithm. It has extensive applications in the multi-class classification problems. Like twin support vector machine (TSVM), MTSVM treats all sample points equally because it lacks the ability to judge the importance of different sample points. In order to improve the classification performance of MTSVM, a new method of adding Interval-Valued Fuzzy membership degree to sample points is proposed. In this way, a novel Interval-Valued Fuzzy multiple twin support vector machine (IVF-MTSVM) is established in this paper. Previous methods of adding Fuzzy membership degree to sample points are totally based on their importance to the class, while the method in this paper emphasizes the importance of sample points to the classification model, and takes into account the importance to the class to some extent. This is a new perspective to establish Fuzzy membership degree to sample points in support vector machines since it is different from the previous methods in thinking. Then the solution to IVF-MTSVM is derived. Experiments on UCI dataSets show that this new method has certain advantages over other multi-class twin support vector machine methods in ``one-versus-rest'' structure and other Fuzzy multiple twin support vector machine established by some previous methods. Finally, Friedman test and Benferroni-Dunn test are used to verify the statistical significance of this new method.